%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL748-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 10:30:08 AM UTC 2026
% Result : Unsatisfiable 159.88s 27.20s
% Output : CNFRefutation 26.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 371
% Syntax : Number of formulae : 2967 (1859 unt; 0 typ; 0 def)
% Number of atoms : 15244 (6267 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 39217 (3469 ~;4515 |; 0 &;31233 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 58 usr; 5 con; 0-3 aty)
% Number of variables : 8649 ( 0 ^;8649 !; 0 ?;8649 :)
% Comments :
%------------------------------------------------------------------------------
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_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(tp_c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tp_c_InductTermi_OIT,type,
c_InductTermi_OIT: $i > $o ).
thf(tp_c_Lambda_Obeta,type,
c_Lambda_Obeta: $i > $i > $o ).
thf(tp_c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(tp_c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: $i > $i > $i ).
thf(tp_c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(tp_c_Lambda_Olift,type,
c_Lambda_Olift: $i > $i > $i ).
thf(tp_c_Lambda_Oliftn,type,
c_Lambda_Oliftn: $i > $i > $i > $i ).
thf(tp_c_Lambda_Osko__Lambda__Xbeta__cases__2__1,type,
c_Lambda_Osko__Lambda__Xbeta__cases__2__1: $i > $i > $i ).
thf(tp_c_Lambda_Osubst,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(tp_c_Lambda_Osubstn,type,
c_Lambda_Osubstn: $i > $i > $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_Suc,type,
c_Suc: $i > $i ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocomm__monoid__mult,type,
class_OrderedGroup_Ocomm__monoid__mult: $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__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_Ring__and__Field_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_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__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(tp_class_Ring__and__Field_Opordered__ring,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(tp_class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_ia,type,
v_ia: $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(1,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(2,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(3,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(4,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(5,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(6,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(7,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(8,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(9,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(10,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(11,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(12,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(13,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(14,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(15,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(16,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(17,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(18,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(19,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(20,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(21,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(22,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(23,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(24,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(25,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(26,axiom,
! [V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) @ ( c_Lambda_OdB_OAbs @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
thf(27,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) @ ( c_Lambda_Olift @ V_s @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(28,axiom,
! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(29,axiom,
! [V_r: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) )
| ~ ( c_InductTermi_OIT @ V_r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(30,axiom,
! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ V_s @ V_t ) @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(31,axiom,
! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(32,axiom,
! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(33,axiom,
! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(34,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(35,axiom,
! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(36,axiom,
! [V_s: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ V_s @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(38,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) @ V_s @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(39,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(40,axiom,
! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(41,axiom,
! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(42,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_0) ).
thf(43,axiom,
! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__gt_0) ).
thf(44,axiom,
! [V_r: $i,V_s: $i] :
( ( c_Lambda_Obeta @ V_r @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I2_J_1) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(46,axiom,
! [V_i: $i,V_t: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) @ V_t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(47,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(48,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(49,axiom,
! [V_n: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
thf(50,axiom,
! [V_s: $i,V_t: $i] : ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_t ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
thf(51,axiom,
! [T_a: $i,V_m: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
thf(52,axiom,
! [T_a: $i,V_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ V_m @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
thf(53,axiom,
! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(54,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_m @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(59,axiom,
! [V_t: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_s @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I3_J_0) ).
thf(60,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
thf(61,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
= ( c_HOL_Oplus__class_Oplus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
thf(62,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(63,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(66,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/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(76,axiom,
! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
thf(77,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(78,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(79,axiom,
! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ V_t @ V_s @ V_j ) @ V_i )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_i ) @ ( c_Lambda_Olift @ V_s @ V_i ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(87,axiom,
! [V_t: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_s @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Olift @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
thf(88,axiom,
! [V_t: $i,V_v: $i,V_i: $i,V_j: $i,V_u: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Olift @ V_v @ V_i ) @ ( c_Suc @ V_j ) ) @ ( c_Lambda_Osubst @ V_u @ V_v @ V_j ) @ V_i )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_v @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__subst_0) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(90,axiom,
! [V_u: $i,V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ V_u @ V_s ) @ ( c_Lambda_OdB_OApp @ V_u @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
thf(91,axiom,
! [V_s: $i,V_u: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ V_s @ V_u ) @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
thf(92,axiom,
! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(93,axiom,
! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ V_t @ V_s @ V_j ) @ V_i )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst_0) ).
thf(94,axiom,
! [V_t: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ V_t @ V_i ) @ ( c_Suc @ V_k ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__lift_0) ).
thf(95,axiom,
! [V_s: $i,V_r: $i] :
( ( V_s
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I2_J_0) ).
thf(96,axiom,
! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(104,axiom,
! [T_a: $i,V_m: $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_HOL_Otimes__class_Otimes @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_m @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(106,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/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(108,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) @ V_s @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
thf(109,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(118,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/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(121,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_m @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(123,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(124,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(125,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(126,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(127,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(128,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(129,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(130,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(131,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(132,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(133,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(134,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(135,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(137,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/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(139,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
thf(140,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(141,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(142,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(143,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(144,axiom,
! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OApp @ V_s @ V_t ) @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
thf(145,axiom,
! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
thf(146,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_0) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(148,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(149,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(150,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
thf(151,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/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(155,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(161,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(162,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(172,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(178,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(179,axiom,
! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(180,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/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(181,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(184,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(187,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(188,axiom,
! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(191,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(192,axiom,
! [T_a: $i,V_x: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(194,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(195,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(196,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(199,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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(200,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(201,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(202,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(203,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(204,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(205,axiom,
! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ry @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(206,axiom,
! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ry @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(207,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_rx @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(208,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(209,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(212,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/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(218,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(219,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(220,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(221,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(222,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(225,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
thf(226,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
thf(227,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(228,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/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(230,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/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(231,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/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(233,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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(234,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/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(235,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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(236,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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(237,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/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(238,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(239,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
thf(241,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ 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/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
thf(242,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(243,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(244,axiom,
! [T_a: $i,V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(245,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/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(246,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/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(247,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/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(248,axiom,
! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
thf(249,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(250,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(251,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(252,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/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(253,axiom,
! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).
thf(254,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/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(255,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(257,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(258,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(259,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/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(260,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(261,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(262,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(266,axiom,
! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(267,axiom,
! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(268,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/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(269,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/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(270,axiom,
! [V_n: $i] :
( ( V_n
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).
thf(271,axiom,
! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ 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/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(273,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/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(274,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(275,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(276,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/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(277,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/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(278,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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(279,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(280,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/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(281,axiom,
! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_n @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
thf(282,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/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(283,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(284,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/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(285,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(286,axiom,
! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(287,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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(288,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/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(289,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_n @ tc_nat ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).
thf(290,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(291,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(292,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(293,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(294,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(295,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(296,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(297,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(298,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(299,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(300,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(301,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/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(302,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/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(303,axiom,
! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(304,axiom,
! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(305,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(306,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( V_c
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(307,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a )
= V_d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(308,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/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(309,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/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(310,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/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(311,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/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(312,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/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(313,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/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(314,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/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(315,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/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(316,axiom,
! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_n ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).
thf(317,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/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(318,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/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(319,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(320,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/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(321,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/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(322,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/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(323,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/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(324,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/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(325,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/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(326,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/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(327,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/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(328,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/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(329,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/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(330,axiom,
! [V_n: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ V_n ) @ V_t @ V_k )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) @ V_k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
thf(331,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/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(332,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/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(333,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/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(334,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(335,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/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(336,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
thf(337,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(338,axiom,
! [T_a: $i,V_c: $i,V_b: $i,V_a: $i,V_e: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(339,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(340,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_e: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(341,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(342,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(343,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(344,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/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(345,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/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(346,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/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(347,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/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(348,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/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(349,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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(350,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/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(351,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(352,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(353,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(354,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(355,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
thf(356,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/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(357,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(358,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(359,axiom,
! [T_a: $i,V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) )
| ( V_y = V_z )
| ( V_w = V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(360,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(361,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/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(362,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/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(363,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/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(364,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/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(365,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_ry @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(366,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(367,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_ry @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(368,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(369,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[368]) ).
thf(370,negated_conjecture,
~ ( c_InductTermi_OIT @ ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ v_r ) @ v_ia ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(371,negated_conjecture,
! [V_i: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Olift @ v_r @ V_i ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(372,negated_conjecture,
c_InductTermi_OIT @ v_r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(373,plain,
$false = $false,
inference(unfold_def,[status(thm)],[369]) ).
thf(374,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(375,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(376,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(377,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(378,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(379,plain,
( ( class_Ring__and__Field_Osemiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(380,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(381,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(382,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(383,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(384,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(385,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(386,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(387,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(388,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(389,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(390,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(391,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(392,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(393,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(394,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(395,plain,
( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(396,plain,
( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(397,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(398,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(399,plain,
( ( ! [V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) @ ( c_Lambda_OdB_OAbs @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(400,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) @ ( c_Lambda_Olift @ V_s @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(401,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(402,plain,
( ( ! [V_r: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(403,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ V_s @ V_t ) @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(404,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(405,plain,
( ( ! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(406,plain,
( ( ! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(407,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(408,plain,
( ( ! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(409,plain,
( ( ! [V_s: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ V_s @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(410,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)],[37]) ).
thf(411,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) @ V_s @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(412,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(413,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(414,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(415,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(416,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(417,plain,
( ( ! [V_r: $i,V_s: $i] :
( ( c_Lambda_Obeta @ V_r @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(418,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)],[45]) ).
thf(419,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) @ V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(420,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(421,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(422,plain,
( ( ! [V_n: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(423,plain,
( ( ! [V_s: $i,V_t: $i] : ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_t ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(424,plain,
( ( ! [T_a: $i,V_m: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(425,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ V_m @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(426,plain,
( ( ! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(427,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_m @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(428,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)],[55]) ).
thf(429,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)],[56]) ).
thf(430,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)],[57]) ).
thf(431,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)],[58]) ).
thf(432,plain,
( ( ! [V_t: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_s @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(433,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(434,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
= ( c_HOL_Oplus__class_Oplus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(435,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(436,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(437,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)],[64]) ).
thf(438,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)],[65]) ).
thf(439,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)],[66]) ).
thf(440,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)],[67]) ).
thf(441,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)],[68]) ).
thf(442,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)],[69]) ).
thf(443,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)],[70]) ).
thf(444,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)],[71]) ).
thf(445,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)],[72]) ).
thf(446,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)],[73]) ).
thf(447,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)],[74]) ).
thf(448,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)],[75]) ).
thf(449,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(450,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(451,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(452,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ V_t @ V_s @ V_j ) @ V_i )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_i ) @ ( c_Lambda_Olift @ V_s @ V_i ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(453,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)],[80]) ).
thf(454,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)],[81]) ).
thf(455,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)],[82]) ).
thf(456,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)],[83]) ).
thf(457,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)],[84]) ).
thf(458,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)],[85]) ).
thf(459,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)],[86]) ).
thf(460,plain,
( ( ! [V_t: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_s @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Olift @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(461,plain,
( ( ! [V_t: $i,V_v: $i,V_i: $i,V_j: $i,V_u: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Olift @ V_v @ V_i ) @ ( c_Suc @ V_j ) ) @ ( c_Lambda_Osubst @ V_u @ V_v @ V_j ) @ V_i )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_v @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(462,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)],[89]) ).
thf(463,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ V_u @ V_s ) @ ( c_Lambda_OdB_OApp @ V_u @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(464,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ V_s @ V_u ) @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(465,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(466,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ V_t @ V_s @ V_j ) @ V_i )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(467,plain,
( ( ! [V_t: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ V_t @ V_i ) @ ( c_Suc @ V_k ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(468,plain,
( ( ! [V_s: $i,V_r: $i] :
( ( V_s
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(469,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(470,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)],[97]) ).
thf(471,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)],[98]) ).
thf(472,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)],[99]) ).
thf(473,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)],[100]) ).
thf(474,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)],[101]) ).
thf(475,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)],[102]) ).
thf(476,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)],[103]) ).
thf(477,plain,
( ( ! [T_a: $i,V_m: $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_HOL_Otimes__class_Otimes @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_m @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(478,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)],[105]) ).
thf(479,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)],[106]) ).
thf(480,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)],[107]) ).
thf(481,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) @ V_s @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(482,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(483,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)],[110]) ).
thf(484,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)],[111]) ).
thf(485,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)],[112]) ).
thf(486,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)],[113]) ).
thf(487,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)],[114]) ).
thf(488,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)],[115]) ).
thf(489,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)],[116]) ).
thf(490,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)],[117]) ).
thf(491,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)],[118]) ).
thf(492,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)],[119]) ).
thf(493,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)],[120]) ).
thf(494,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(495,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)],[122]) ).
thf(496,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(497,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(498,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(499,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(500,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(501,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(502,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(503,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(504,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(505,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(506,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(507,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(508,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(509,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)],[136]) ).
thf(510,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)],[137]) ).
thf(511,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)],[138]) ).
thf(512,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(513,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(514,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(515,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(516,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(517,plain,
( ( ! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OApp @ V_s @ V_t ) @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(518,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(519,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(520,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)],[147]) ).
thf(521,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(522,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(523,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(524,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)],[151]) ).
thf(525,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)],[152]) ).
thf(526,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)],[153]) ).
thf(527,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)],[154]) ).
thf(528,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(529,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)],[156]) ).
thf(530,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)],[157]) ).
thf(531,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)],[158]) ).
thf(532,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)],[159]) ).
thf(533,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)],[160]) ).
thf(534,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)],[161]) ).
thf(535,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(536,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)],[163]) ).
thf(537,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)],[164]) ).
thf(538,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)],[165]) ).
thf(539,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)],[166]) ).
thf(540,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)],[167]) ).
thf(541,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)],[168]) ).
thf(542,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)],[169]) ).
thf(543,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)],[170]) ).
thf(544,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)],[171]) ).
thf(545,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)],[172]) ).
thf(546,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)],[173]) ).
thf(547,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)],[174]) ).
thf(548,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)],[175]) ).
thf(549,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)],[176]) ).
thf(550,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)],[177]) ).
thf(551,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)],[178]) ).
thf(552,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)],[179]) ).
thf(553,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)],[180]) ).
thf(554,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)],[181]) ).
thf(555,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)],[182]) ).
thf(556,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)],[183]) ).
thf(557,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(558,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)],[185]) ).
thf(559,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)],[186]) ).
thf(560,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(561,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(562,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)],[189]) ).
thf(563,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)],[190]) ).
thf(564,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(565,plain,
( ( ! [T_a: $i,V_x: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(566,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)],[193]) ).
thf(567,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(568,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(569,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(570,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)],[197]) ).
thf(571,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)],[198]) ).
thf(572,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)],[199]) ).
thf(573,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)],[200]) ).
thf(574,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(575,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(576,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(577,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(578,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(579,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ry @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(580,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_rx @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(581,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(582,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(583,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)],[210]) ).
thf(584,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)],[211]) ).
thf(585,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)],[212]) ).
thf(586,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)],[213]) ).
thf(587,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)],[214]) ).
thf(588,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)],[215]) ).
thf(589,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)],[216]) ).
thf(590,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)],[217]) ).
thf(591,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(592,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(593,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(594,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(595,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(596,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)],[223]) ).
thf(597,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)],[224]) ).
thf(598,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)],[225]) ).
thf(599,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)],[226]) ).
thf(600,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(601,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)],[228]) ).
thf(602,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)],[229]) ).
thf(603,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)],[230]) ).
thf(604,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)],[231]) ).
thf(605,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)],[232]) ).
thf(606,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)],[233]) ).
thf(607,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)],[234]) ).
thf(608,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)],[235]) ).
thf(609,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)],[236]) ).
thf(610,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)],[237]) ).
thf(611,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(612,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(613,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)],[240]) ).
thf(614,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)],[241]) ).
thf(615,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(616,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(617,plain,
( ( ! [T_a: $i,V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(618,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)],[245]) ).
thf(619,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)],[246]) ).
thf(620,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)],[247]) ).
thf(621,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(622,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(623,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(624,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(625,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)],[252]) ).
thf(626,plain,
( ( ! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(627,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)],[254]) ).
thf(628,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)],[255]) ).
thf(629,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)],[256]) ).
thf(630,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(631,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)],[258]) ).
thf(632,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)],[259]) ).
thf(633,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(634,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(635,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)],[262]) ).
thf(636,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)],[263]) ).
thf(637,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)],[264]) ).
thf(638,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)],[265]) ).
thf(639,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(640,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(641,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)],[268]) ).
thf(642,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)],[269]) ).
thf(643,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ 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)],[270]) ).
thf(644,plain,
( ( ! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ 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)],[271]) ).
thf(645,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)],[272]) ).
thf(646,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)],[273]) ).
thf(647,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)],[274]) ).
thf(648,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)],[275]) ).
thf(649,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)],[276]) ).
thf(650,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)],[277]) ).
thf(651,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)],[278]) ).
thf(652,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)],[279]) ).
thf(653,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)],[280]) ).
thf(654,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_n @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(655,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)],[282]) ).
thf(656,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)],[283]) ).
thf(657,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)],[284]) ).
thf(658,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(659,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(660,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)],[287]) ).
thf(661,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)],[288]) ).
thf(662,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_n @ tc_nat ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(663,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(664,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(665,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(666,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(667,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(668,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(669,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(670,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(671,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(672,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(673,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(674,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)],[301]) ).
thf(675,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)],[302]) ).
thf(676,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(677,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(678,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(679,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( V_c
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(680,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a )
= V_d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(681,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)],[308]) ).
thf(682,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)],[309]) ).
thf(683,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)],[310]) ).
thf(684,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)],[311]) ).
thf(685,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)],[312]) ).
thf(686,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)],[313]) ).
thf(687,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)],[314]) ).
thf(688,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)],[315]) ).
thf(689,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_n ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(690,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)],[317]) ).
thf(691,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)],[318]) ).
thf(692,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)],[319]) ).
thf(693,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)],[320]) ).
thf(694,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)],[321]) ).
thf(695,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)],[322]) ).
thf(696,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)],[323]) ).
thf(697,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)],[324]) ).
thf(698,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)],[325]) ).
thf(699,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)],[326]) ).
thf(700,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)],[327]) ).
thf(701,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)],[328]) ).
thf(702,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)],[329]) ).
thf(703,plain,
( ( ! [V_n: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ V_n ) @ V_t @ V_k )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) @ V_k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(704,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)],[331]) ).
thf(705,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)],[332]) ).
thf(706,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)],[333]) ).
thf(707,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)],[334]) ).
thf(708,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)],[335]) ).
thf(709,plain,
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(710,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(711,plain,
( ( ! [T_a: $i,V_c: $i,V_b: $i,V_a: $i,V_e: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(712,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(713,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_e: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(714,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(715,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(716,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(717,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)],[344]) ).
thf(718,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)],[345]) ).
thf(719,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)],[346]) ).
thf(720,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)],[347]) ).
thf(721,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)],[348]) ).
thf(722,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)],[349]) ).
thf(723,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)],[350]) ).
thf(724,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(725,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(726,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(727,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(728,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(729,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)],[356]) ).
thf(730,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)],[357]) ).
thf(731,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(732,plain,
( ( ! [T_a: $i,V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(733,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(734,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)],[361]) ).
thf(735,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)],[362]) ).
thf(736,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)],[363]) ).
thf(737,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)],[364]) ).
thf(738,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(739,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(740,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(741,plain,
( ( ~ ( c_InductTermi_OIT @ ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ v_r ) @ v_ia ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(742,plain,
( ( ! [V_i: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Olift @ v_r @ V_i ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(743,plain,
( ( c_InductTermi_OIT @ v_r )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(744,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[373]) ).
thf(745,plain,
( ( c_InductTermi_OIT @ v_r )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(746,plain,
( ( ! [V_i: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Olift @ v_r @ V_i ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(747,plain,
( ( ~ ( c_InductTermi_OIT @ ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ v_r ) @ v_ia ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(748,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(749,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(750,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(751,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)],[737]) ).
thf(752,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)],[736]) ).
thf(753,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)],[735]) ).
thf(754,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)],[734]) ).
thf(755,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(756,plain,
( ( ! [T_a: $i,V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(757,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(758,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)],[730]) ).
thf(759,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)],[729]) ).
thf(760,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(761,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(762,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(763,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(764,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(765,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)],[723]) ).
thf(766,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)],[722]) ).
thf(767,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)],[721]) ).
thf(768,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)],[720]) ).
thf(769,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)],[719]) ).
thf(770,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)],[718]) ).
thf(771,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)],[717]) ).
thf(772,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(773,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(774,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(775,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_e: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(776,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(777,plain,
( ( ! [T_a: $i,V_c: $i,V_b: $i,V_a: $i,V_e: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(778,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(779,plain,
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(780,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)],[708]) ).
thf(781,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(782,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)],[706]) ).
thf(783,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)],[705]) ).
thf(784,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)],[704]) ).
thf(785,plain,
( ( ! [V_n: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ V_n ) @ V_t @ V_k )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) @ V_k ) ) )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(786,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)],[702]) ).
thf(787,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)],[701]) ).
thf(788,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)],[700]) ).
thf(789,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)],[699]) ).
thf(790,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)],[698]) ).
thf(791,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)],[697]) ).
thf(792,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)],[696]) ).
thf(793,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)],[695]) ).
thf(794,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)],[694]) ).
thf(795,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)],[693]) ).
thf(796,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)],[692]) ).
thf(797,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)],[691]) ).
thf(798,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)],[690]) ).
thf(799,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_n ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(800,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)],[688]) ).
thf(801,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)],[687]) ).
thf(802,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)],[686]) ).
thf(803,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)],[685]) ).
thf(804,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)],[684]) ).
thf(805,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)],[683]) ).
thf(806,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)],[682]) ).
thf(807,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)],[681]) ).
thf(808,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a )
= V_d ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(809,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( V_c
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(810,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(811,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(812,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(813,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)],[675]) ).
thf(814,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)],[674]) ).
thf(815,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(816,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(817,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[671]) ).
thf(818,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[670]) ).
thf(819,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[669]) ).
thf(820,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[668]) ).
thf(821,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[667]) ).
thf(822,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[666]) ).
thf(823,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[665]) ).
thf(824,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(825,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(826,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_n @ tc_nat ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[662]) ).
thf(827,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)],[661]) ).
thf(828,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)],[660]) ).
thf(829,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(830,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(831,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)],[657]) ).
thf(832,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)],[656]) ).
thf(833,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)],[655]) ).
thf(834,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_n @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(835,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)],[653]) ).
thf(836,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)],[652]) ).
thf(837,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)],[651]) ).
thf(838,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)],[650]) ).
thf(839,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)],[649]) ).
thf(840,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[648]) ).
thf(841,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)],[647]) ).
thf(842,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(843,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(844,plain,
( ( ! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ 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)],[644]) ).
thf(845,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oone__class_Oone @ 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)],[643]) ).
thf(846,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)],[642]) ).
thf(847,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)],[641]) ).
thf(848,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(849,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(850,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)],[638]) ).
thf(851,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)],[637]) ).
thf(852,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)],[636]) ).
thf(853,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)],[635]) ).
thf(854,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(855,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(856,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)],[632]) ).
thf(857,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)],[631]) ).
thf(858,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(859,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)],[629]) ).
thf(860,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)],[628]) ).
thf(861,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)],[627]) ).
thf(862,plain,
( ( ! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ) )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(863,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)],[625]) ).
thf(864,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(865,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(866,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(867,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[621]) ).
thf(868,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)],[620]) ).
thf(869,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)],[619]) ).
thf(870,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)],[618]) ).
thf(871,plain,
( ( ! [T_a: $i,V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[617]) ).
thf(872,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(873,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[615]) ).
thf(874,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)],[614]) ).
thf(875,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)],[613]) ).
thf(876,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(877,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(878,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)],[610]) ).
thf(879,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)],[609]) ).
thf(880,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)],[608]) ).
thf(881,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)],[607]) ).
thf(882,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)],[606]) ).
thf(883,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)],[605]) ).
thf(884,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)],[604]) ).
thf(885,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)],[603]) ).
thf(886,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)],[602]) ).
thf(887,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)],[601]) ).
thf(888,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(889,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)],[599]) ).
thf(890,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)],[598]) ).
thf(891,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)],[597]) ).
thf(892,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)],[596]) ).
thf(893,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(894,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[594]) ).
thf(895,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(896,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(897,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(898,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)],[590]) ).
thf(899,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)],[589]) ).
thf(900,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)],[588]) ).
thf(901,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)],[587]) ).
thf(902,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)],[586]) ).
thf(903,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)],[585]) ).
thf(904,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)],[584]) ).
thf(905,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)],[583]) ).
thf(906,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[582]) ).
thf(907,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(908,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_rx @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(909,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ry @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(910,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(911,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(912,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(913,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(914,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(915,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)],[573]) ).
thf(916,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)],[572]) ).
thf(917,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)],[571]) ).
thf(918,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)],[570]) ).
thf(919,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(920,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(921,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(922,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)],[566]) ).
thf(923,plain,
( ( ! [T_a: $i,V_x: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(924,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(925,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)],[563]) ).
thf(926,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)],[562]) ).
thf(927,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(928,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(929,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)],[559]) ).
thf(930,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)],[558]) ).
thf(931,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(932,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)],[556]) ).
thf(933,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)],[555]) ).
thf(934,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)],[554]) ).
thf(935,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)],[553]) ).
thf(936,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)],[552]) ).
thf(937,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)],[551]) ).
thf(938,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)],[550]) ).
thf(939,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)],[549]) ).
thf(940,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)],[548]) ).
thf(941,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)],[547]) ).
thf(942,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)],[546]) ).
thf(943,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)],[545]) ).
thf(944,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)],[544]) ).
thf(945,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)],[543]) ).
thf(946,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)],[542]) ).
thf(947,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)],[541]) ).
thf(948,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)],[540]) ).
thf(949,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)],[539]) ).
thf(950,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)],[538]) ).
thf(951,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)],[537]) ).
thf(952,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)],[536]) ).
thf(953,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(954,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)],[534]) ).
thf(955,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)],[533]) ).
thf(956,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)],[532]) ).
thf(957,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)],[531]) ).
thf(958,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)],[530]) ).
thf(959,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)],[529]) ).
thf(960,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(961,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)],[527]) ).
thf(962,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)],[526]) ).
thf(963,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)],[525]) ).
thf(964,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)],[524]) ).
thf(965,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(966,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(967,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(968,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)],[520]) ).
thf(969,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(970,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(971,plain,
( ( ! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OApp @ V_s @ V_t ) @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[517]) ).
thf(972,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(973,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(974,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(975,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(976,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(977,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)],[511]) ).
thf(978,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)],[510]) ).
thf(979,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)],[509]) ).
thf(980,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(981,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(982,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(983,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(984,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(985,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(986,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(987,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(988,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(989,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(990,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(991,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(992,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(993,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)],[495]) ).
thf(994,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(995,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)],[493]) ).
thf(996,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)],[492]) ).
thf(997,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)],[491]) ).
thf(998,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)],[490]) ).
thf(999,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)],[489]) ).
thf(1000,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)],[488]) ).
thf(1001,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)],[487]) ).
thf(1002,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)],[486]) ).
thf(1003,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)],[485]) ).
thf(1004,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)],[484]) ).
thf(1005,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)],[483]) ).
thf(1006,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(1007,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) @ V_s @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(1008,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)],[480]) ).
thf(1009,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)],[479]) ).
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(copy,[status(thm)],[478]) ).
thf(1011,plain,
( ( ! [T_a: $i,V_m: $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_HOL_Otimes__class_Otimes @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_m @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(1012,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)],[476]) ).
thf(1013,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)],[475]) ).
thf(1014,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)],[474]) ).
thf(1015,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)],[473]) ).
thf(1016,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)],[472]) ).
thf(1017,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)],[471]) ).
thf(1018,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)],[470]) ).
thf(1019,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(1020,plain,
( ( ! [V_s: $i,V_r: $i] :
( ( V_s
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(1021,plain,
( ( ! [V_t: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ V_t @ V_i ) @ ( c_Suc @ V_k ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(1022,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ V_t @ V_s @ V_j ) @ V_i )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(1023,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(1024,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ V_s @ V_u ) @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(1025,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ V_u @ V_s ) @ ( c_Lambda_OdB_OApp @ V_u @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(1026,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)],[462]) ).
thf(1027,plain,
( ( ! [V_t: $i,V_v: $i,V_i: $i,V_j: $i,V_u: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Olift @ V_v @ V_i ) @ ( c_Suc @ V_j ) ) @ ( c_Lambda_Osubst @ V_u @ V_v @ V_j ) @ V_i )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_v @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(1028,plain,
( ( ! [V_t: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_s @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ V_t @ ( c_Lambda_Olift @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(1029,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)],[459]) ).
thf(1030,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)],[458]) ).
thf(1031,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)],[457]) ).
thf(1032,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)],[456]) ).
thf(1033,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)],[455]) ).
thf(1034,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)],[454]) ).
thf(1035,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)],[453]) ).
thf(1036,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ V_t @ V_s @ V_j ) @ V_i )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_i ) @ ( c_Lambda_Olift @ V_s @ V_i ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(1037,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(1038,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(1039,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(1040,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)],[448]) ).
thf(1041,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)],[447]) ).
thf(1042,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)],[446]) ).
thf(1043,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)],[445]) ).
thf(1044,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)],[444]) ).
thf(1045,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)],[443]) ).
thf(1046,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)],[442]) ).
thf(1047,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)],[441]) ).
thf(1048,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)],[440]) ).
thf(1049,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)],[439]) ).
thf(1050,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)],[438]) ).
thf(1051,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)],[437]) ).
thf(1052,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(1053,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(1054,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
= ( c_HOL_Oplus__class_Oplus @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(1055,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(1056,plain,
( ( ! [V_t: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_s @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(1057,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)],[431]) ).
thf(1058,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)],[430]) ).
thf(1059,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)],[429]) ).
thf(1060,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)],[428]) ).
thf(1061,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_m @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(1062,plain,
( ( ! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(1063,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ V_m @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(1064,plain,
( ( ! [T_a: $i,V_m: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(1065,plain,
( ( ! [V_s: $i,V_t: $i] : ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_t ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(1066,plain,
( ( ! [V_n: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(1067,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(1068,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(1069,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) @ V_t ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(1070,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)],[418]) ).
thf(1071,plain,
( ( ! [V_r: $i,V_s: $i] :
( ( c_Lambda_Obeta @ V_r @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(1072,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_j @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(1073,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(1074,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(1075,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(1076,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(1077,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) @ V_s @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(1078,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)],[410]) ).
thf(1079,plain,
( ( ! [V_s: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ V_s @ ( c_HOL_Oplus__class_Oplus @ V_k @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(1080,plain,
( ( ! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(1081,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(1082,plain,
( ( ! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(1083,plain,
( ( ! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(1084,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(1085,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ V_s @ V_t ) @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(1086,plain,
( ( ! [V_r: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(1087,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(1088,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) @ ( c_Lambda_Olift @ V_s @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(1089,plain,
( ( ! [V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) @ ( c_Lambda_OdB_OAbs @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(1090,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(1091,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(1092,plain,
( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(1093,plain,
( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_nat )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(1094,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(1095,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(1096,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(1097,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(1098,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(1099,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(1100,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(1101,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(1102,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(1103,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(1104,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(1105,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(1106,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(1107,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(1108,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(1109,plain,
( ( class_Ring__and__Field_Osemiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(1110,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(1111,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(1112,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(1113,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(1114,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(1115,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[744]) ).
thf(1116,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)],[957]) ).
thf(1117,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)],[1040]) ).
thf(1118,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[848]) ).
thf(1119,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)],[796]) ).
thf(1120,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)],[1033]) ).
thf(1121,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[876]) ).
thf(1122,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)],[1031]) ).
thf(1123,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1080]) ).
thf(1124,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[811]) ).
thf(1125,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)],[782]) ).
thf(1126,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Lambda_OdB_OApp @ SX0 @ SX1 )
!= ( c_Lambda_OdB_OVar @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1019]) ).
thf(1127,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)],[941]) ).
thf(1128,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)],[798]) ).
thf(1129,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)],[1029]) ).
thf(1130,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)],[783]) ).
thf(1131,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[812]) ).
thf(1132,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX3 @ SX0 ) @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX1 @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX4 @ SX0 ) @ SX0 ) )
| ( SX3 = SX4 )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[871]) ).
thf(1133,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Ring__and__Field_Oring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) @ SX3 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX4 @ SX2 @ SX0 ) @ SX5 @ SX0 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SX1 @ SX4 @ SX0 ) @ SX2 @ SX0 ) @ SX3 @ SX0 )
= SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[808]) ).
thf(1134,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)],[963]) ).
thf(1135,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Ring__and__Field_Oring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) @ SX3 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX4 @ SX2 @ SX0 ) @ SX5 @ SX0 ) )
| ( SX3
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SX4 @ SX1 @ SX0 ) @ SX2 @ SX0 ) @ SX5 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[809]) ).
thf(1136,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[773]) ).
thf(1137,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)],[1034]) ).
thf(1138,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Lambda_OdB_OApp @ SX0 @ SX1 )
!= ( c_Lambda_OdB_OAbs @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1081]) ).
thf(1139,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)],[956]) ).
thf(1140,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[849]) ).
thf(1141,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[772]) ).
thf(1142,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)],[1035]) ).
thf(1143,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SX0 )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[774]) ).
thf(1144,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)],[945]) ).
thf(1145,plain,
( ( ! [SX0: $i] :
( SX0
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[877]) ).
thf(1146,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OApp @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1082]) ).
thf(1147,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)],[943]) ).
thf(1148,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX4 @ SX0 ) @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX4 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX2 @ SX0 ) @ SX0 ) )
| ( SX2 = SX4 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[756]) ).
thf(1149,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)],[901]) ).
thf(1150,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Lambda_OdB_OApp @ SX0 @ SX1 )
!= ( c_Lambda_OdB_OApp @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1067]) ).
thf(1151,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX1 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX2 @ SX0 ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[872]) ).
thf(1152,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1083]) ).
thf(1153,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)],[904]) ).
thf(1154,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1084]) ).
thf(1155,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)],[1032]) ).
thf(1156,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)],[942]) ).
thf(1157,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)],[905]) ).
thf(1158,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)],[795]) ).
thf(1159,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)],[1030]) ).
thf(1160,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)],[962]) ).
thf(1161,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)],[944]) ).
thf(1162,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OApp @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1062]) ).
thf(1163,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX1 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX2 @ SX0 ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[873]) ).
thf(1164,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)],[794]) ).
thf(1165,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)],[839]) ).
thf(1166,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)],[793]) ).
thf(1167,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)],[900]) ).
thf(1168,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Lambda_OdB_OApp @ SX0 @ SX1 )
!= ( c_Lambda_OdB_OApp @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1068]) ).
thf(1169,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)],[784]) ).
thf(1170,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)],[766]) ).
thf(1171,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)],[765]) ).
thf(1172,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1076]) ).
thf(1173,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)],[958]) ).
thf(1174,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX4 @ SX0 ) @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX4 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX2 @ SX0 ) @ SX0 ) )
| ( SX2 = SX4 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[755]) ).
thf(1175,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)],[758]) ).
thf(1176,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[781]) ).
thf(1177,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[780]) ).
thf(1178,plain,
! [SV1: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ v_r @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(1179,plain,
( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ v_r ) @ v_ia ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(1180,plain,
! [SV2: $i] :
( ( ! [SY925: $i,SY926: $i,SY927: $i,SY928: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY925 @ SY926 @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SY927 @ SY928 @ SV2 ) @ SV2 )
= ( c_HOL_Otimes__class_Otimes @ SY927 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY925 @ SY926 @ SV2 ) @ SY928 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(1181,plain,
! [SV3: $i] :
( ( ! [SY929: $i,SY930: $i,SY931: $i,SY932: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV3 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY929 @ SY930 @ SV3 ) @ ( c_HOL_Otimes__class_Otimes @ SY931 @ SY932 @ SV3 ) @ SV3 )
= ( c_HOL_Otimes__class_Otimes @ SY929 @ ( c_HOL_Otimes__class_Otimes @ SY930 @ ( c_HOL_Otimes__class_Otimes @ SY931 @ SY932 @ SV3 ) @ SV3 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(1182,plain,
! [SV4: $i] :
( ( ! [SY933: $i,SY934: $i,SY935: $i,SY936: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY933 @ SY934 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SY935 @ SY936 @ SV4 ) @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY933 @ SY935 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SY934 @ SY936 @ SV4 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(1183,plain,
! [SV5: $i] :
( ( ! [SY937: $i] :
( ( SV5 = SY937 )
| ~ ( c_HOL_Oord__class_Oless @ SV5 @ ( c_Suc @ SY937 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV5 @ SY937 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(1184,plain,
! [SV6: $i] :
( ( ! [SY938: $i] :
( ( SV6 = SY938 )
| ~ ( c_HOL_Oord__class_Oless @ SY938 @ ( c_Suc @ SV6 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY938 @ SV6 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(1185,plain,
! [SV7: $i] :
( ( ! [SY939: $i] :
( ( SV7 = SY939 )
| ( c_HOL_Oord__class_Oless @ SV7 @ SY939 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV7 @ ( c_Suc @ SY939 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(1186,plain,
! [SV8: $i] :
( ( ! [SY940: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV8 ) @ ( c_Suc @ SY940 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV8 @ SY940 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(1187,plain,
! [SV9: $i] :
( ( ! [SY941: $i,SY942: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY941 @ SY941 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SY942 @ SY942 @ SV9 ) @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(1188,plain,
! [SV10: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV10 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_HOL_Ozero__class_Ozero @ SV10 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(1189,plain,
! [SV11: $i] :
( ( ! [SY943: $i,SY944: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV11 ) @ SY943 @ SY944 )
= ( c_Lambda_OdB_OVar @ SV11 ) )
| ( SV11 = SY944 )
| ( c_HOL_Oord__class_Oless @ SY944 @ SV11 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(1190,plain,
! [SV12: $i] :
( ( ! [SY945: $i,SY946: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV12 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SY945 @ SY946 @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SY946 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SY945 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(1191,plain,
! [SV13: $i] :
( ( ! [SY947: $i,SY948: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV13 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SY947 @ SY948 @ SV13 ) @ SV13 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SY948 @ SV13 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SY947 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(1192,plain,
! [SV14: $i] :
( ( ! [SY949: $i,SY950: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV14 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SY949 @ SV14 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SY950 @ SV14 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ ( c_HOL_Otimes__class_Otimes @ SY950 @ SY949 @ SV14 ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(1193,plain,
! [SV15: $i] :
( ( ! [SY951: $i,SY952: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV15 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SY951 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SY952 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ ( c_HOL_Otimes__class_Otimes @ SY951 @ SY952 @ SV15 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(1194,plain,
! [SV16: $i] :
( ( ! [SY953: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV16 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY953 @ SY953 @ SV16 ) @ ( c_HOL_Ozero__class_Ozero @ SV16 ) @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SY953 @ ( c_HOL_Ozero__class_Ozero @ SV16 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(1195,plain,
! [SV17: $i] :
( ( ! [SY954: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV17 )
| ( c_HOL_Oord__class_Oless @ SY954 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY954 @ SY954 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(1196,plain,
! [SV18: $i] :
( ( ! [SY955: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV18 )
| ( c_HOL_Oord__class_Oless @ SY955 @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY955 @ SY955 @ SV18 ) @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(1197,plain,
! [SV19: $i] :
( ( ! [SY956: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV19 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY956 @ SY956 @ SV19 ) @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
| ~ ( c_HOL_Oord__class_Oless @ SY956 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1198,plain,
! [SV20: $i] :
( ( ! [SY957: $i,SY958: $i,SY959: $i,SY960: $i,SY961: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV20 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY957 @ SY958 @ SV20 ) @ SY959 @ SV20 ) @ SY960 @ SV20 ) @ SY961 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY957 @ SY959 @ SV20 ) @ SY960 @ SV20 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY958 @ SY959 @ SV20 ) @ SY961 @ SV20 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1199,plain,
! [SV21: $i] :
( ( ! [SY962: $i,SY963: $i,SY964: $i,SY965: $i,SY966: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV21 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY962 @ SY963 @ SV21 ) @ SY964 @ SV21 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY965 @ SY963 @ SV21 ) @ SY966 @ SV21 ) @ SV21 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY962 @ SY965 @ SV21 ) @ SY963 @ SV21 ) @ SY964 @ SV21 ) @ SY966 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(1200,plain,
! [SV22: $i] :
( ( ! [SY967: $i,SY968: $i,SY969: $i,SY970: $i,SY971: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV22 )
| ( c_HOL_Oord__class_Oless @ SY967 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY968 @ SY969 @ SV22 ) @ SY970 @ SV22 ) @ SY971 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY969 @ SY970 @ SV22 ) @ SY967 @ SV22 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY968 @ SY970 @ SV22 ) @ SY971 @ SV22 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(1201,plain,
! [SV23: $i] :
( ( ! [SY972: $i,SY973: $i,SY974: $i,SY975: $i,SY976: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV23 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY972 @ SY973 @ SV23 ) @ SY974 @ SV23 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY975 @ SY973 @ SV23 ) @ SY976 @ SV23 ) @ SV23 )
| ~ ( c_HOL_Oord__class_Oless @ SY974 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY975 @ SY972 @ SV23 ) @ SY973 @ SV23 ) @ SY976 @ SV23 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(1202,plain,
! [SV24: $i] :
( ( ! [SY977: $i,SY978: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ SV24 ) @ SY977 @ SY978 )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ SV24 @ SY977 @ SY978 ) @ SY978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(1203,plain,
! [SV25: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV25 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1204,plain,
! [SV26: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV26 @ SV26 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1205,plain,
! [SV27: $i] :
( ( ! [SY979: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV27 )
| ~ ( class_Int_Onumber__ring @ SV27 )
| ( ( c_HOL_Ominus__class_Ominus @ SY979 @ SY979 @ SV27 )
= ( c_HOL_Ozero__class_Ozero @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1206,plain,
! [SV28: $i] :
( ( ! [SY980: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV28 )
| ( ( c_HOL_Ominus__class_Ominus @ SY980 @ SY980 @ SV28 )
= ( c_HOL_Ozero__class_Ozero @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1207,plain,
! [SV29: $i] :
( ( ! [SY981: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV29 )
| ( ( c_HOL_Ominus__class_Ominus @ SY981 @ ( c_HOL_Ozero__class_Ozero @ SV29 ) @ SV29 )
= SY981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1208,plain,
! [SV30: $i] :
( ( ! [SY982: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV30 )
| ( ( c_HOL_Ominus__class_Ominus @ SY982 @ SY982 @ SV30 )
= ( c_HOL_Ozero__class_Ozero @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1209,plain,
! [SV31: $i] :
( ( ! [SY983: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV31 )
| ( ( c_HOL_Ominus__class_Ominus @ SY983 @ SY983 @ SV31 )
= ( c_HOL_Ozero__class_Ozero @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1210,plain,
! [SV32: $i] :
( ( ! [SY984: $i,SY985: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SY984 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SY985 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY985 @ SV32 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY985 @ SY984 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1211,plain,
! [SV33: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV33 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= SV33 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1212,plain,
! [SV34: $i] :
( ( ! [SY986: $i,SY987: $i] :
( ( c_HOL_Oord__class_Oless @ SV34 @ ( c_HOL_Oplus__class_Oplus @ SY986 @ SY987 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV34 @ SY987 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1213,plain,
! [SV35: $i] :
( ( ! [SY988: $i,SY989: $i] :
( ( c_HOL_Oord__class_Oless @ SV35 @ ( c_HOL_Oplus__class_Oplus @ SY988 @ SY989 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV35 @ SY988 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1214,plain,
! [SV36: $i] :
( ( ! [SY990: $i,SY991: $i] :
( ( c_HOL_Oord__class_Oless @ SV36 @ SY990 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV36 @ SY991 @ tc_nat ) @ SY990 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1215,plain,
! [SV37: $i] :
( ( ! [SY992: $i,SY993: $i] :
( ( c_HOL_Oord__class_Oless @ SV37 @ ( c_HOL_Oplus__class_Oplus @ SY992 @ SY993 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV37 @ SY993 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1216,plain,
! [SV38: $i] :
( ( ! [SY994: $i,SY995: $i] :
( ( c_HOL_Oord__class_Oless @ SV38 @ ( c_HOL_Oplus__class_Oplus @ SY994 @ SY995 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV38 @ SY994 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1217,plain,
! [SV39: $i] :
( ( ! [SY996: $i] : ( c_HOL_Oord__class_Oless @ SV39 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV39 @ SY996 @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1218,plain,
! [SV40: $i] :
( ( ! [SY997: $i] : ( c_HOL_Oord__class_Oless @ SV40 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SY997 @ SV40 @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1219,plain,
! [SV41: $i] :
( ( ! [SY998: $i] : ( c_HOL_Oord__class_Oless @ SV41 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV41 @ SY998 @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1220,plain,
! [SV42: $i] :
( ( ! [SY999: $i,SY1000: $i,SY1001: $i,SY1002: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV42 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY999 @ SY1000 @ SV42 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1001 @ SY999 @ SV42 ) @ SY1000 @ SV42 ) @ SY1002 @ SV42 ) @ SV42 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1001 @ SY1000 @ SV42 ) @ SY1002 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1221,plain,
! [SV43: $i] :
( ( ! [SY1003: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ SV43 ) @ SY1003 @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV43 @ SY1003 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1222,plain,
! [SV44: $i] :
( ( ! [SY1004: $i] :
( ( c_HOL_Oplus__class_Oplus @ SV44 @ ( c_Suc @ SY1004 ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV44 @ SY1004 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1223,plain,
! [SV45: $i] :
( ( ! [SY1005: $i,SY1006: $i,SY1007: $i,SY1008: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV45 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1005 @ SY1006 @ SV45 ) @ SY1007 @ SV45 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1008 @ SY1006 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1005 @ SY1008 @ SV45 ) @ SY1006 @ SV45 ) @ SY1007 @ SV45 ) @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1224,plain,
! [SV46: $i] :
( ( ! [SY1009: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV46 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV46 ) @ SY1009 @ SV46 )
= SY1009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1225,plain,
! [SV47: $i] :
( ( ! [SY1010: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV47 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SY1010 @ SV47 )
= SY1010 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1226,plain,
! [SV48: $i] :
( ( ! [SY1011: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV48 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV48 ) @ SY1011 @ SV48 )
= SY1011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1227,plain,
! [SV49: $i] :
( ( ! [SY1012: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SY1012 @ SV49 )
= ( c_HOL_Ozero__class_Ozero @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1228,plain,
! [SV50: $i] :
( ( ! [SY1013: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1013 @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV50 )
= ( c_HOL_Ozero__class_Ozero @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1229,plain,
! [SV51: $i] :
( ( ! [SY1014: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV51 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1014 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 )
= ( c_HOL_Ozero__class_Ozero @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1230,plain,
! [SV52: $i] :
( ( ! [SY1015: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV52 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SY1015 @ SV52 )
= ( c_HOL_Ozero__class_Ozero @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1231,plain,
! [SV53: $i] :
( ( ! [SY1016: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ SV53 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1016 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
= ( c_HOL_Ozero__class_Ozero @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1232,plain,
! [SV54: $i] :
( ( ! [SY1017: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ SV54 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SY1017 @ SV54 )
= ( c_HOL_Ozero__class_Ozero @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1233,plain,
! [SV55: $i] :
( ( ! [SY1018: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SY1018 @ SV55 )
= ( c_HOL_Ozero__class_Ozero @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1234,plain,
! [SV56: $i] :
( ( ! [SY1019: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV56 @ SY1019 @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV56 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SY1019 @ tc_nat ) ) )
| ( SV56
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1235,plain,
! [SV57: $i] :
( ( ! [SY1020: $i,SY1021: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV57 @ SY1020 @ tc_nat ) @ SY1021 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV57 @ SY1021 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1236,plain,
! [SV58: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV58 @ SV58 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1237,plain,
! [SV59: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV59 @ SV59 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1238,plain,
! [SV60: $i] :
( ( ! [SY1022: $i] :
( ~ ( class_Orderings_Oorder @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SY1022 @ SY1022 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1239,plain,
! [SV61: $i] :
( ( ! [SY1023: $i] :
( ~ ( class_Orderings_Olinorder @ SV61 )
| ~ ( c_HOL_Oord__class_Oless @ SY1023 @ SY1023 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1240,plain,
! [SV62: $i] :
( ( ! [SY1024: $i] :
( ~ ( class_Orderings_Opreorder @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ SY1024 @ SY1024 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1241,plain,
! [SV63: $i] :
( ( ! [SY1025: $i,SY1026: $i] :
( ( ( c_Lambda_Oliftn @ SV63 @ ( c_Lambda_OdB_OVar @ SY1025 ) @ SY1026 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ SY1025 @ SV63 @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ SY1025 @ SY1026 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1242,plain,
! [SV64: $i] :
( ( ! [SY1027: $i,SY1028: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV64 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ ( c_HOL_Oplus__class_Oplus @ SY1027 @ SY1028 @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SY1028 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SY1027 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1243,plain,
! [SV65: $i] :
( ( ! [SY1029: $i,SY1030: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV65 )
| ( c_HOL_Oord__class_Oless @ SY1029 @ SY1030 @ SV65 )
| ( c_HOL_Oord__class_Oless @ SY1030 @ SY1029 @ SV65 )
| ( SY1030 = SY1029 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1244,plain,
! [SV66: $i] :
( ( ! [SY1031: $i,SY1032: $i] :
( ~ ( class_Orderings_Olinorder @ SV66 )
| ( SY1031 = SY1032 )
| ( c_HOL_Oord__class_Oless @ SY1032 @ SY1031 @ SV66 )
| ( c_HOL_Oord__class_Oless @ SY1031 @ SY1032 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1245,plain,
! [SV67: $i] :
( ( ! [SY1033: $i] :
( ( c_HOL_Oord__class_Oless @ SV67 @ SY1033 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1033 @ SV67 @ tc_nat )
| ( SY1033 = SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1246,plain,
! [SV68: $i] :
( ( ! [SY1034: $i] :
( ( c_HOL_Oord__class_Oless @ SV68 @ SY1034 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1034 @ SV68 @ tc_nat )
| ( SY1034 = SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1247,plain,
! [SV69: $i] :
( ( ! [SY1035: $i,SY1036: $i] :
( ~ ( class_Orderings_Olinorder @ SV69 )
| ( c_HOL_Oord__class_Oless @ SY1035 @ SY1036 @ SV69 )
| ( c_HOL_Oord__class_Oless @ SY1036 @ SY1035 @ SV69 )
| ( SY1036 = SY1035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1248,plain,
! [SV70: $i] :
( ( ! [SY1037: $i,SY1038: $i] :
( ~ ( class_Orderings_Olinorder @ SV70 )
| ( c_HOL_Oord__class_Oless @ SY1037 @ SY1038 @ SV70 )
| ( SY1038 = SY1037 )
| ( c_HOL_Oord__class_Oless @ SY1038 @ SY1037 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1249,plain,
! [SV71: $i] :
( ( ! [SY1039: $i,SY1040: $i] :
( ~ ( class_Orderings_Olinorder @ SV71 )
| ( SY1039 = SY1040 )
| ( c_HOL_Oord__class_Oless @ SY1039 @ SY1040 @ SV71 )
| ( c_HOL_Oord__class_Oless @ SY1040 @ SY1039 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1250,plain,
! [SV72: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV72 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= SV72 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV72 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1251,plain,
! [SV73: $i] :
( ( ( SV73
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV73 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV73 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1252,plain,
! [SV74: $i] :
( ( ! [SY1041: $i,SY1042: $i,SY1043: $i,SY1044: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV74 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1041 @ SY1042 @ SV74 ) @ ( c_HOL_Oplus__class_Oplus @ SY1043 @ SY1044 @ SV74 ) @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SY1042 @ SY1044 @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SY1041 @ SY1043 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1253,plain,
! [SV75: $i] :
( ( ! [SY1045: $i,SY1046: $i,SY1047: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV75 @ SY1045 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY1046 @ SY1047 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1045 @ SY1047 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV75 @ SY1046 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1254,plain,
! [SV76: $i] :
( ( ! [SY1048: $i,SY1049: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV76 )
| ( c_HOL_Oord__class_Oless @ SY1048 @ SY1049 @ SV76 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY1048 @ SY1049 @ SV76 ) @ ( c_HOL_Ozero__class_Ozero @ SV76 ) @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1255,plain,
! [SV77: $i] :
( ( ! [SY1050: $i,SY1051: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV77 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY1050 @ SY1051 @ SV77 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SY1050 @ SY1051 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1256,plain,
! [SV78: $i] :
( ( ! [SY1052: $i,SY1053: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV78 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1052 @ SV78 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1053 @ SV78 ) @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SY1052 @ SY1053 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1257,plain,
! [SV79: $i] :
( ( ! [SY1054: $i,SY1055: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 )
| ( c_HOL_Oord__class_Oless @ SY1054 @ SY1055 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1054 @ SV79 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1055 @ SV79 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1258,plain,
! [SV80: $i] :
( ( c_HOL_Oord__class_Oless @ SV80 @ ( c_Suc @ SV80 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1259,plain,
! [SV81: $i] :
( ( c_HOL_Oord__class_Oless @ SV81 @ ( c_Suc @ SV81 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1260,plain,
! [SV82: $i] :
( ( ! [SY1056: $i,SY1057: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV82 ) @ SY1056 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1057 @ SY1056 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV82 @ SY1057 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1261,plain,
! [SV83: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV83 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ ( c_HOL_Oone__class_Oone @ SV83 ) @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1262,plain,
! [SV84: $i] :
( ( ! [SY1058: $i,SY1059: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV84 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1058 @ ( c_HOL_Otimes__class_Otimes @ SY1058 @ SY1059 @ SV84 ) @ SV84 )
= ( c_HOL_Otimes__class_Otimes @ SY1058 @ SY1059 @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1263,plain,
! [SV85: $i] :
( ( ! [SY1060: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV85 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1060 @ SV85 ) @ SV85 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1060 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1264,plain,
! [SV86: $i] :
( ( ! [SY1061: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV86 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1061 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1061 @ SV86 ) @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1265,plain,
! [SV87: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV87 @ tc_nat )
| ( SV87
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1266,plain,
! [SV88: $i] :
( ( ! [SY1062: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV88 @ SY1062 )
= SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1267,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)],[863]) ).
thf(1268,plain,
! [SV89: $i] :
( ( ! [SY1063: $i,SY1064: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV89 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1063 @ SY1064 @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SY1063 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SY1064 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1269,plain,
! [SV90: $i] :
( ( ! [SY1065: $i,SY1066: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV90 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1065 @ SY1066 @ SV90 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SY1066 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SY1065 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1270,plain,
! [SV91: $i] :
( ( ! [SY1067: $i,SY1068: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV91 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1067 @ SY1068 @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SY1068 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY1067 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1271,plain,
! [SV92: $i] :
( ( ! [SY1069: $i] :
( ( c_Lambda_Osubstn @ SV92 @ SY1069 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ SV92 @ SY1069 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1272,plain,
! [SV93: $i] :
( ( ! [SY1070: $i,SY1071: $i,SY1072: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV93 )
| ( c_HOL_Oord__class_Oless @ SY1070 @ ( c_HOL_Oplus__class_Oplus @ SY1071 @ SY1072 @ SV93 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SY1070 @ SY1072 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SY1071 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1273,plain,
! [SV94: $i] :
( ( ! [SY1073: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV94 @ SY1073 @ tc_nat ) @ SV94 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1274,plain,
! [SV95: $i] :
( ( ! [SY1074: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV95 @ SY1074 @ tc_nat ) @ SY1074 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1275,plain,
! [SV96: $i] :
( ( ! [SY1075: $i,SY1076: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV96 @ SY1075 @ tc_nat ) @ SY1076 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV96 @ ( c_HOL_Ominus__class_Ominus @ SY1076 @ SY1075 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1276,plain,
! [SV97: $i] :
( ( ! [SY1077: $i,SY1078: $i] :
( ( c_HOL_Oord__class_Oless @ SV97 @ ( c_HOL_Ominus__class_Ominus @ SY1077 @ SY1078 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV97 @ SY1078 @ tc_nat ) @ SY1077 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1277,plain,
! [SV98: $i] :
( ( ! [SY1079: $i,SY1080: $i,SY1081: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV98 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1079 @ SY1080 @ SV98 ) @ ( c_HOL_Oplus__class_Oplus @ SY1081 @ SY1080 @ SV98 ) @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SY1079 @ SY1081 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1278,plain,
! [SV99: $i] :
( ( ! [SY1082: $i,SY1083: $i,SY1084: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV99 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1082 @ SY1083 @ SV99 ) @ ( c_HOL_Oplus__class_Oplus @ SY1084 @ SY1083 @ SV99 ) @ SV99 )
| ~ ( c_HOL_Oord__class_Oless @ SY1082 @ SY1084 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1279,plain,
! [SV100: $i] :
( ( ! [SY1085: $i,SY1086: $i,SY1087: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV100 )
| ( c_HOL_Oord__class_Oless @ SY1085 @ SY1086 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1085 @ SY1087 @ SV100 ) @ ( c_HOL_Oplus__class_Oplus @ SY1086 @ SY1087 @ SV100 ) @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1280,plain,
! [SV101: $i] :
( ( ! [SY1088: $i,SY1089: $i,SY1090: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV101 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1088 @ SY1089 @ SV101 ) @ ( c_HOL_Oplus__class_Oplus @ SY1088 @ SY1090 @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SY1089 @ SY1090 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1281,plain,
! [SV102: $i] :
( ( ! [SY1091: $i,SY1092: $i,SY1093: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV102 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1091 @ SY1092 @ SV102 ) @ ( c_HOL_Oplus__class_Oplus @ SY1091 @ SY1093 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SY1092 @ SY1093 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1282,plain,
! [SV103: $i] :
( ( ! [SY1094: $i,SY1095: $i,SY1096: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV103 )
| ( c_HOL_Oord__class_Oless @ SY1094 @ SY1095 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1096 @ SY1094 @ SV103 ) @ ( c_HOL_Oplus__class_Oplus @ SY1096 @ SY1095 @ SV103 ) @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1283,plain,
! [SV104: $i] :
( ( ! [SY1097: $i,SY1098: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV104 @ SY1097 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY1098 @ SY1097 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV104 @ SY1098 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1284,plain,
! [SV105: $i] :
( ( ! [SY1099: $i,SY1100: $i] :
( ( c_HOL_Oord__class_Oless @ SV105 @ SY1099 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1100 @ SV105 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY1100 @ SY1099 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1285,plain,
! [SV106: $i] :
( ( ! [SY1101: $i,SY1102: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV106 @ SY1101 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV106 @ SY1102 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1101 @ SY1102 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1286,plain,
! [SV107: $i] :
( ( ! [SY1103: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV107 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1103 @ SY1103 @ SV107 )
= SY1103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1287,plain,
! [SV108: $i] :
( ( ! [SY1104: $i] :
( ( c_HOL_Oord__class_Oless @ SV108 @ SY1104 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY1104 @ SV108 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1288,plain,
! [SV109: $i] :
( ( ! [SY1105: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV109 @ SY1105 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1105 @ SV109 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1289,plain,
! [SV110: $i] :
( ( ! [SY1106: $i] :
( ( c_HOL_Oord__class_Oless @ SV110 @ SY1106 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV110 ) @ SY1106 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1290,plain,
! [SV111: $i] :
( ( ! [SY1107: $i] :
( ( c_HOL_Oord__class_Oless @ SV111 @ ( c_Suc @ SY1107 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV111 @ SY1107 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1291,plain,
! [SV112: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV112 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ SV112 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ SV112 ) @ SV112 )
= ( c_HOL_Ozero__class_Ozero @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1292,plain,
! [SV113: $i] :
( ( ! [SY1108: $i,SY1109: $i,SY1110: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV113 )
| ( c_HOL_Oord__class_Oless @ SY1108 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
| ( c_HOL_Oord__class_Oless @ SY1109 @ SY1110 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1109 @ SY1108 @ SV113 ) @ ( c_HOL_Otimes__class_Otimes @ SY1110 @ SY1108 @ SV113 ) @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1293,plain,
! [SV114: $i] :
( ( ! [SY1111: $i,SY1112: $i,SY1113: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV114 )
| ( c_HOL_Oord__class_Oless @ SY1111 @ SY1112 @ SV114 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SY1113 @ SV114 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1112 @ SY1113 @ SV114 ) @ ( c_HOL_Otimes__class_Otimes @ SY1111 @ SY1113 @ SV114 ) @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1294,plain,
! [SV115: $i] :
( ( ! [SY1114: $i,SY1115: $i,SY1116: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV115 )
| ( c_HOL_Oord__class_Oless @ SY1114 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
| ( c_HOL_Oord__class_Oless @ SY1115 @ SY1116 @ SV115 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1114 @ SY1115 @ SV115 ) @ ( c_HOL_Otimes__class_Otimes @ SY1114 @ SY1116 @ SV115 ) @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1295,plain,
! [SV116: $i] :
( ( ! [SY1117: $i,SY1118: $i,SY1119: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV116 )
| ( c_HOL_Oord__class_Oless @ SY1117 @ SY1118 @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SY1119 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1119 @ SY1118 @ SV116 ) @ ( c_HOL_Otimes__class_Otimes @ SY1119 @ SY1117 @ SV116 ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1296,plain,
! [SV117: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV117 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV117 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1297,plain,
! [SV118: $i] :
( ( ! [SY1120: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV118 @ SY1120 @ tc_nat ) @ SV118 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV118 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1120 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1298,plain,
! [SV119: $i] :
( ( ! [SY1121: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV119 @ ( c_HOL_Ominus__class_Ominus @ SY1121 @ SV119 @ tc_nat ) @ tc_nat )
= SY1121 )
| ( c_HOL_Oord__class_Oless @ SY1121 @ SV119 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1299,plain,
! [SV120: $i] :
( ( ! [SY1122: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV120 @ ( c_Suc @ SY1122 ) @ tc_nat ) @ SV120 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV120 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1300,plain,
! [SV121: $i] :
( ( ! [SY1123: $i,SY1124: $i,SY1125: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV121 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1123 @ SY1124 @ SV121 ) @ SY1125 @ SV121 )
= ( c_HOL_Otimes__class_Otimes @ SY1123 @ ( c_HOL_Otimes__class_Otimes @ SY1124 @ SY1125 @ SV121 ) @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1301,plain,
! [SV122: $i] :
( ( ! [SY1126: $i,SY1127: $i,SY1128: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV122 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1126 @ SY1127 @ SV122 ) @ SY1128 @ SV122 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1126 @ SY1128 @ SV122 ) @ SY1127 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1302,plain,
! [SV123: $i] :
( ( ! [SY1129: $i,SY1130: $i,SY1131: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV123 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1129 @ SY1130 @ SV123 ) @ SY1131 @ SV123 )
= ( c_HOL_Otimes__class_Otimes @ SY1129 @ ( c_HOL_Otimes__class_Otimes @ SY1130 @ SY1131 @ SV123 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1303,plain,
! [SV124: $i] :
( ( ! [SY1132: $i,SY1133: $i,SY1134: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV124 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1132 @ ( c_HOL_Otimes__class_Otimes @ SY1133 @ SY1134 @ SV124 ) @ SV124 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1132 @ SY1133 @ SV124 ) @ SY1134 @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1304,plain,
! [SV125: $i] :
( ( ! [SY1135: $i,SY1136: $i,SY1137: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1135 @ ( c_HOL_Otimes__class_Otimes @ SY1136 @ SY1137 @ SV125 ) @ SV125 )
= ( c_HOL_Otimes__class_Otimes @ SY1136 @ ( c_HOL_Otimes__class_Otimes @ SY1135 @ SY1137 @ SV125 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1305,plain,
! [SV126: $i] :
( ( ! [SY1138: $i,SY1139: $i,SY1140: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV126 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1138 @ ( c_HOL_Otimes__class_Otimes @ SY1139 @ SY1140 @ SV126 ) @ SV126 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1138 @ SY1139 @ SV126 ) @ SY1140 @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1306,plain,
! [SV127: $i] :
( ( ! [SY1141: $i,SY1142: $i,SY1143: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1141 @ SY1142 @ SV127 ) @ SY1143 @ SV127 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1141 @ SY1143 @ SV127 ) @ ( c_HOL_Otimes__class_Otimes @ SY1142 @ SY1143 @ SV127 ) @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1307,plain,
! [SV128: $i] :
( ( ! [SY1144: $i,SY1145: $i,SY1146: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV128 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1144 @ SY1145 @ SV128 ) @ SY1146 @ SV128 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1144 @ SY1146 @ SV128 ) @ ( c_HOL_Otimes__class_Otimes @ SY1145 @ SY1146 @ SV128 ) @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1308,plain,
! [SV129: $i] :
( ( ! [SY1147: $i,SY1148: $i,SY1149: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV129 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1147 @ ( c_HOL_Oplus__class_Oplus @ SY1148 @ SY1149 @ SV129 ) @ SV129 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1147 @ SY1148 @ SV129 ) @ ( c_HOL_Otimes__class_Otimes @ SY1147 @ SY1149 @ SV129 ) @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1309,plain,
! [SV130: $i] :
( ( ! [SY1150: $i,SY1151: $i] :
( ~ ( class_Orderings_Oorder @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SY1150 @ SY1151 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SY1151 @ SY1150 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1310,plain,
! [SV131: $i] :
( ( ! [SY1152: $i,SY1153: $i] :
( ~ ( class_Orderings_Olinorder @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ SY1152 @ SY1153 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ SY1153 @ SY1152 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1311,plain,
! [SV132: $i] :
( ( ! [SY1154: $i,SY1155: $i] :
( ~ ( class_Orderings_Opreorder @ SV132 )
| ~ ( c_HOL_Oord__class_Oless @ SY1154 @ SY1155 @ SV132 )
| ~ ( c_HOL_Oord__class_Oless @ SY1155 @ SY1154 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1312,plain,
! [SV133: $i] :
( ( ! [SY1156: $i,SY1157: $i] :
( ~ ( class_Orderings_Opreorder @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SY1156 @ SY1157 @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SY1157 @ SY1156 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1313,plain,
! [SV134: $i] :
( ( ! [SY1158: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV134 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1158 @ ( c_HOL_Oone__class_Oone @ SV134 ) @ SV134 )
= SY1158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1314,plain,
! [SV135: $i] :
( ( ! [SY1159: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV135 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1159 @ ( c_HOL_Oone__class_Oone @ SV135 ) @ SV135 )
= SY1159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1315,plain,
! [SV136: $i] :
( ( ! [SY1160: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV136 ) @ SY1160 @ SV136 )
= SY1160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1316,plain,
! [SV137: $i] :
( ( ! [SY1161: $i,SY1162: $i,SY1163: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV137 )
| ~ ( class_Int_Onumber__ring @ SV137 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1161 @ SY1162 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SY1161 @ SY1163 @ SV137 ) @ SV137 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1161 @ SY1163 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SY1161 @ SY1162 @ SV137 ) @ SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1317,plain,
! [SV138: $i] :
( ( ! [SY1164: $i,SY1165: $i,SY1166: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV138 )
| ~ ( class_Int_Onumber__ring @ SV138 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1164 @ SY1165 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SY1164 @ SY1166 @ SV138 ) @ SV138 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1164 @ SY1166 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SY1164 @ SY1165 @ SV138 ) @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1318,plain,
! [SV139: $i] :
( ( ( SV139
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV139 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1319,plain,
! [SV140: $i] :
( ( ! [SY1167: $i,SY1168: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV140 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY1167 @ SY1168 @ SV140 ) @ SY1168 @ SV140 )
= SY1167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1320,plain,
! [SV141: $i] :
( ( ! [SY1169: $i,SY1170: $i] :
( ( c_Lambda_Osubstn @ SV141 @ SY1169 @ SY1170 )
= ( c_Lambda_Osubst @ SV141 @ ( c_Lambda_Oliftn @ SY1170 @ SY1169 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1321,plain,
! [SV142: $i] :
( ( ! [SY1171: $i,SY1172: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV142 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1171 @ SY1172 @ SV142 )
= ( c_HOL_Otimes__class_Otimes @ SY1172 @ SY1171 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1322,plain,
! [SV143: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV143 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV143 ) @ ( c_HOL_Ozero__class_Ozero @ SV143 ) @ SV143 )
= ( c_HOL_Ozero__class_Ozero @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1323,plain,
! [SV144: $i] :
( ( ! [SY1173: $i,SY1174: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1173 @ SY1174 @ SV144 )
= ( c_HOL_Otimes__class_Otimes @ SY1174 @ SY1173 @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1324,plain,
! [SV145: $i] :
( ( ! [SY1175: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV145 @ SY1175 @ tc_nat ) @ ( c_Suc @ SV145 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1325,plain,
! [SV146: $i] :
( ( ! [SY1176: $i,SY1177: $i,SY1178: $i] :
( ~ ( class_Orderings_Opreorder @ SV146 )
| ( c_HOL_Oord__class_Oless @ SY1176 @ SY1177 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SY1178 @ SY1177 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SY1176 @ SY1178 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1326,plain,
! [SV147: $i] :
( ( ! [SY1179: $i,SY1180: $i,SY1181: $i] :
( ~ ( class_Orderings_Oorder @ SV147 )
| ( c_HOL_Oord__class_Oless @ SY1179 @ SY1180 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SY1179 @ SY1181 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SY1181 @ SY1180 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1327,plain,
! [SV148: $i] :
( ( ! [SY1182: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV148 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1182 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY1182 @ SV148 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1328,plain,
! [SV149: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV149 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1329,plain,
! [SV150: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV150 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1330,plain,
! [SV151: $i] :
( ( ! [SY1183: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV151 @ ( c_HOL_Oplus__class_Oplus @ SV151 @ SY1183 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1331,plain,
! [SV152: $i] :
( ( ! [SY1184: $i,SY1185: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV152 @ SY1184 @ tc_nat ) @ SY1185 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV152 @ ( c_HOL_Oplus__class_Oplus @ SY1184 @ SY1185 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1332,plain,
! [SV153: $i] :
( ( ! [SY1186: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV153 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SY1186 ) @ SV153 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV153 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1186 @ SV153 ) @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1333,plain,
! [SV154: $i] :
( ( ! [SY1187: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ SV154 ) @ SY1187 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV154 @ ( c_Suc @ SY1187 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1334,plain,
! [SV155: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV155 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1335,plain,
! [SV156: $i] :
( ( ! [SY1188: $i,SY1189: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV156 @ SY1188 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY1189 @ SY1188 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV156 @ SY1189 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1336,plain,
! [SV157: $i] :
( ( ! [SY1190: $i,SY1191: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV157 @ SY1190 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV157 @ SY1191 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SY1190 @ SY1191 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1337,plain,
! [SV158: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV158 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1338,plain,
! [SV159: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV159 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1339,plain,
! [SV160: $i] :
( ( ! [SY1192: $i,SY1193: $i,SY1194: $i,SY1195: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV160 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1192 @ SY1193 @ SV160 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1194 @ SY1193 @ SV160 ) @ SY1195 @ SV160 ) @ SV160 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1192 @ SY1194 @ SV160 ) @ SY1193 @ SV160 ) @ SY1195 @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1340,plain,
! [SV161: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV161 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV161 )
= ( c_HOL_Ozero__class_Ozero @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1341,plain,
! [SV162: $i] :
( ( ! [SY1196: $i,SY1197: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV162 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1196 @ SY1197 @ SV162 ) @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SY1197 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SY1196 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1342,plain,
! [SV163: $i] :
( ( ! [SY1198: $i,SY1199: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV163 @ SY1198 @ tc_nat ) @ SY1199 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV163 @ SY1199 @ tc_nat ) @ SY1198 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1343,plain,
! [SV164: $i] :
( ( ! [SY1200: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1200 @ SY1200 @ SV164 ) @ ( c_HOL_Ozero__class_Ozero @ SV164 ) @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1344,plain,
! [SV165: $i] :
( ( ! [SY1201: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV165 ) @ SY1201 @ tc_nat )
| ( ( c_Suc @ SV165 )
= SY1201 )
| ~ ( c_HOL_Oord__class_Oless @ SV165 @ SY1201 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1345,plain,
! [SV166: $i] :
( ( ! [SY1202: $i,SY1203: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV166 ) @ SY1202 @ tc_nat ) @ ( c_Suc @ SY1203 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV166 @ SY1202 @ tc_nat ) @ SY1203 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1346,plain,
! [SV167: $i] :
( ( ! [SY1204: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV167 @ ( c_Suc @ SY1204 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV167 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SY1204 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1347,plain,
! [SV168: $i] :
( ( ! [SY1205: $i,SY1206: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV168 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1205 @ SY1205 @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SY1206 @ SY1206 @ SV168 ) @ SV168 ) @ SV168 )
| ( SY1205
= ( c_HOL_Ozero__class_Ozero @ SV168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1348,plain,
! [SV169: $i] :
( ( ! [SY1207: $i,SY1208: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV169 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1207 @ SY1207 @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SY1208 @ SY1208 @ SV169 ) @ SV169 ) @ SV169 )
| ( SY1208
= ( c_HOL_Ozero__class_Ozero @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1349,plain,
! [SV170: $i] :
( ( ! [SY1209: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV170 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1209 @ SV170 ) @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1350,plain,
! [SV171: $i] :
( ( ! [SY1210: $i,SY1211: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV171 ) @ SY1210 @ SY1211 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV171 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1211 @ SV171 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1351,plain,
! [SV172: $i] :
( ( ! [SY1212: $i,SY1213: $i] :
( ( ( c_Lambda_Oliftn @ SV172 @ ( c_Lambda_OdB_OVar @ SY1212 ) @ SY1213 )
= ( c_Lambda_OdB_OVar @ SY1212 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1212 @ SY1213 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1352,plain,
! [SV173: $i] :
( ( ! [SY1214: $i,SY1215: $i,SY1216: $i] :
( ( c_Lambda_Oliftn @ SV173 @ ( c_Lambda_OdB_OApp @ SY1214 @ SY1215 ) @ SY1216 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV173 @ SY1214 @ SY1216 ) @ ( c_Lambda_Oliftn @ SV173 @ SY1215 @ SY1216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1353,plain,
! [SV174: $i] :
( ( ! [SY1217: $i,SY1218: $i,SY1219: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV174 )
| ( c_HOL_Oord__class_Oless @ SY1217 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SY1217 @ SV174 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1217 @ SY1218 @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SY1217 @ SY1219 @ SV174 ) @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1354,plain,
! [SV175: $i] :
( ( ! [SY1220: $i,SY1221: $i,SY1222: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV175 )
| ( c_HOL_Oord__class_Oless @ SY1220 @ SY1221 @ SV175 )
| ( c_HOL_Oord__class_Oless @ SY1221 @ SY1220 @ SV175 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1222 @ SY1221 @ SV175 ) @ ( c_HOL_Otimes__class_Otimes @ SY1222 @ SY1220 @ SV175 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1355,plain,
! [SV176: $i] :
( ( ! [SY1223: $i,SY1224: $i,SY1225: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV176 )
| ( c_HOL_Oord__class_Oless @ SY1223 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SY1223 @ SV176 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1224 @ SY1223 @ SV176 ) @ ( c_HOL_Otimes__class_Otimes @ SY1225 @ SY1223 @ SV176 ) @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1356,plain,
! [SV177: $i] :
( ( ! [SY1226: $i,SY1227: $i,SY1228: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV177 )
| ( c_HOL_Oord__class_Oless @ SY1226 @ SY1227 @ SV177 )
| ( c_HOL_Oord__class_Oless @ SY1227 @ SY1226 @ SV177 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1227 @ SY1228 @ SV177 ) @ ( c_HOL_Otimes__class_Otimes @ SY1226 @ SY1228 @ SV177 ) @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1357,plain,
! [SV178: $i] :
( ( ! [SY1229: $i] :
( ( c_HOL_Oord__class_Oless @ SV178 @ SV178 @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV178 ) @ SY1229 @ SV178 )
= ( c_Lambda_Oliftn @ SV178 @ SY1229 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1358,plain,
! [SV179: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV179 @ SV179 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV179 @ ( c_Suc @ SV179 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1359,plain,
! [SV180: $i] :
( ( ! [SY1230: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV180 @ SY1230 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1230 @ ( c_Suc @ SV180 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1360,plain,
! [SV181: $i] :
( ( ! [SY1231: $i] :
( ( c_HOL_Oord__class_Oless @ SV181 @ ( c_Suc @ SY1231 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1231 @ SV181 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1361,plain,
! [SV182: $i] :
( ( ! [SY1232: $i,SY1233: $i,SY1234: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV182 )
| ( c_HOL_Oord__class_Oless @ SY1232 @ SY1233 @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1234 @ SY1233 @ SV182 ) @ ( c_HOL_Otimes__class_Otimes @ SY1234 @ SY1232 @ SV182 ) @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SY1234 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1362,plain,
! [SV183: $i] :
( ( ! [SY1235: $i,SY1236: $i,SY1237: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV183 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1235 @ SY1236 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SY1235 @ SY1237 @ SV183 ) @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SY1237 @ SY1236 @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SY1235 @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1363,plain,
! [SV184: $i] :
( ( ! [SY1238: $i,SY1239: $i,SY1240: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV184 )
| ( c_HOL_Oord__class_Oless @ SY1238 @ SY1239 @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1240 @ SY1238 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SY1240 @ SY1239 @ SV184 ) @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV184 ) @ SY1240 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1364,plain,
! [SV185: $i] :
( ( ! [SY1241: $i,SY1242: $i,SY1243: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV185 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1241 @ SY1242 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SY1241 @ SY1243 @ SV185 ) @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SY1242 @ SY1243 @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV185 ) @ SY1241 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1365,plain,
! [SV186: $i] :
( ( ! [SY1244: $i,SY1245: $i,SY1246: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV186 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1244 @ SY1245 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SY1244 @ SY1246 @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SY1244 @ ( c_HOL_Ozero__class_Ozero @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SY1246 @ SY1245 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1366,plain,
! [SV187: $i] :
( ( ! [SY1247: $i,SY1248: $i,SY1249: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV187 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1247 @ SY1248 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SY1247 @ SY1249 @ SV187 ) @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SY1247 @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ SY1248 @ SY1249 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1367,plain,
! [SV188: $i] :
( ( ! [SY1250: $i,SY1251: $i,SY1252: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV188 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1250 @ SY1251 @ SV188 ) @ ( c_HOL_Otimes__class_Otimes @ SY1250 @ SY1252 @ SV188 ) @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ SY1251 @ SY1252 @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV188 ) @ SY1250 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1368,plain,
! [SV189: $i] :
( ( ! [SY1253: $i,SY1254: $i,SY1255: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV189 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1253 @ SY1254 @ SV189 ) @ ( c_HOL_Otimes__class_Otimes @ SY1253 @ SY1255 @ SV189 ) @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SY1255 @ SY1254 @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SY1253 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1369,plain,
! [SV190: $i] :
( ( ! [SY1256: $i,SY1257: $i,SY1258: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV190 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1256 @ SY1257 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SY1258 @ SY1257 @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SY1257 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SY1258 @ SY1256 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1370,plain,
! [SV191: $i] :
( ( ! [SY1259: $i,SY1260: $i,SY1261: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV191 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1259 @ SY1260 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SY1261 @ SY1260 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SY1260 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SY1259 @ SY1261 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1371,plain,
! [SV192: $i] :
( ( ! [SY1262: $i,SY1263: $i,SY1264: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV192 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1262 @ SY1263 @ SV192 ) @ ( c_HOL_Otimes__class_Otimes @ SY1264 @ SY1263 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SY1262 @ SY1264 @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SY1263 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1372,plain,
! [SV193: $i] :
( ( ! [SY1265: $i,SY1266: $i,SY1267: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV193 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1265 @ SY1266 @ SV193 ) @ ( c_HOL_Otimes__class_Otimes @ SY1267 @ SY1266 @ SV193 ) @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SY1267 @ SY1265 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SY1266 @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1373,plain,
! [SV194: $i] :
( ( ! [SY1268: $i,SY1269: $i,SY1270: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV194 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1268 @ SY1269 @ SV194 ) @ ( c_HOL_Otimes__class_Otimes @ SY1268 @ SY1270 @ SV194 ) @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SY1268 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ SY1269 @ SY1270 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1374,plain,
! [SV195: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV195 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV195 ) @ ( c_HOL_Oone__class_Oone @ SV195 ) @ SV195 ) @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1375,plain,
! [SV196: $i] :
( ( ! [SY1271: $i,SY1272: $i,SY1273: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV196 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1271 @ SY1272 @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SY1273 @ SY1272 @ SV196 ) @ SV196 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1271 @ SY1273 @ SV196 ) @ SY1272 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1376,plain,
! [SV197: $i] :
( ( ! [SY1274: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV197 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SY1274 @ SV197 )
= SY1274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1377,plain,
! [SV198: $i] :
( ( ! [SY1275: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV198 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SY1275 @ SV198 )
= SY1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1378,plain,
! [SV199: $i] :
( ( SV199
= ( c_HOL_Oplus__class_Oplus @ SV199 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1379,plain,
! [SV200: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV200 @ tc_nat )
= SV200 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1380,plain,
! [SV201: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV201 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV201 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1381,plain,
! [SV202: $i] :
( ( ! [SY1276: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV202 )
| ~ ( class_Int_Onumber__ring @ SV202 )
| ( SY1276
= ( c_HOL_Oplus__class_Oplus @ SY1276 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1382,plain,
! [SV203: $i] :
( ( ! [SY1277: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV203 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1277 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
= SY1277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1383,plain,
! [SV204: $i] :
( ( ! [SY1278: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV204 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SY1278 @ SV204 )
= SY1278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1384,plain,
! [SV205: $i] :
( ( ! [SY1279: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV205 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1279 @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV205 )
= SY1279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1385,plain,
! [SV206: $i] :
( ( ! [SY1280: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV206 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1280 @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV206 )
= SY1280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1386,plain,
! [SV207: $i] :
( ( ! [SY1281: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV207 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV207 ) @ SY1281 @ SV207 )
= SY1281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1387,plain,
! [SV208: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV208 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ SV208 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ SV208 ) @ SV208 ) @ SV208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1388,plain,
! [SV209: $i] :
( ( ! [SY1282: $i,SY1283: $i,SY1284: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OApp @ SV209 @ SY1282 ) @ SY1283 @ SY1284 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV209 @ SY1283 @ SY1284 ) @ ( c_Lambda_Osubstn @ SY1282 @ SY1283 @ SY1284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1389,plain,
! [SV210: $i] :
( ( ! [SY1285: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV210 @ SY1285 @ tc_nat ) @ SY1285 @ tc_nat )
= SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1390,plain,
! [SV211: $i] :
( ( ! [SY1286: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV211 @ SY1286 @ tc_nat ) @ SV211 @ tc_nat )
= SY1286 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1391,plain,
! [SV212: $i] :
( ( ! [SY1287: $i,SY1288: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV212 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SY1287 @ SY1288 @ SV212 ) @ SY1288 @ SV212 )
= SY1287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1392,plain,
! [SV213: $i] :
( ( ! [SY1289: $i,SY1290: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV213 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SY1289 @ SY1290 @ SV213 ) @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SY1290 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SY1289 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1393,plain,
! [SV214: $i] :
( ( ! [SY1291: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV214 ) @ ( c_Suc @ SY1291 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV214 @ SY1291 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1394,plain,
! [SV215: $i] :
( ( ! [SY1292: $i] :
( ( c_HOL_Oord__class_Oless @ SV215 @ SY1292 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV215 ) @ ( c_Suc @ SY1292 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1395,plain,
! [SV216: $i] :
( ( ! [SY1293: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV216 ) @ ( c_Suc @ SY1293 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV216 @ SY1293 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1396,plain,
! [SV217: $i] :
( ( ! [SY1294: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV217 @ SY1294 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1294 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1397,plain,
! [SV218: $i] :
( ( ! [SY1295: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV218 @ SY1295 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV218 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1398,plain,
! [SV219: $i] :
( ( ! [SY1296: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV219 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SY1296 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ ( c_HOL_Oplus__class_Oplus @ SY1296 @ SY1296 @ SV219 ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1399,plain,
! [SV220: $i] :
( ( ! [SY1297: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV220 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ ( c_HOL_Oplus__class_Oplus @ SY1297 @ SY1297 @ SV220 ) @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SY1297 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1400,plain,
! [SV221: $i] :
( ( ! [SY1298: $i] :
( ( SV221
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SY1298 @ SV221 ) ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SY1298 ) @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1401,plain,
! [SV222: $i] :
( ( ! [SY1299: $i,SY1300: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV222 @ SY1299 ) @ ( c_Suc @ SY1300 ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV222 @ SY1300 ) @ SY1299 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1299 @ ( c_HOL_Oplus__class_Oplus @ SY1300 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1402,plain,
! [SV223: $i] :
( ( ! [SY1301: $i,SY1302: $i,SY1303: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ SV223 @ SY1301 @ SY1302 ) @ SY1303 )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV223 @ ( c_HOL_Oplus__class_Oplus @ SY1303 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ SY1301 @ SY1303 ) @ SY1302 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1302 @ ( c_HOL_Oplus__class_Oplus @ SY1303 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1403,plain,
! [SV224: $i] :
( ( ! [SY1304: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV224 ) @ SY1304 )
= ( c_Lambda_OdB_OVar @ SV224 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV224 @ SY1304 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1404,plain,
! [SV225: $i] :
( ( ! [SY1305: $i,SY1306: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV225 @ SY1305 ) @ ( c_Lambda_OdB_OApp @ SY1306 @ SY1305 ) )
| ~ ( c_Lambda_Obeta @ SV225 @ SY1306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1405,plain,
! [SV226: $i] :
( ( ! [SY1307: $i,SY1308: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV226 @ SY1307 ) @ ( c_Lambda_OdB_OApp @ SV226 @ SY1308 ) )
| ~ ( c_Lambda_Obeta @ SY1307 @ SY1308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1406,plain,
! [SV227: $i] :
( ( ! [SY1309: $i,SY1310: $i,SY1311: $i,SY1312: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1309 @ SY1310 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SY1311 @ SY1312 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1309 @ SY1311 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SY1310 @ SY1312 @ SV227 ) @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1407,plain,
! [SV228: $i] :
( ( ! [SY1313: $i,SY1314: $i,SY1315: $i,SY1316: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ ( c_Lambda_Olift @ SY1313 @ SY1314 ) @ ( c_Suc @ SY1315 ) ) @ ( c_Lambda_Osubst @ SY1316 @ SY1313 @ SY1315 ) @ SY1314 )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ SY1316 @ SY1314 ) @ SY1313 @ SY1315 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1314 @ ( c_HOL_Oplus__class_Oplus @ SY1315 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1408,plain,
! [SV229: $i] :
( ( ! [SY1317: $i,SY1318: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ SV229 ) @ SY1317 @ SY1318 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ SV229 @ ( c_Lambda_Olift @ SY1317 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Oplus__class_Oplus @ SY1318 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1409,plain,
! [SV230: $i] :
( ( ! [SY1319: $i,SY1320: $i,SY1321: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ SV230 @ SY1319 @ SY1320 ) @ SY1321 )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV230 @ SY1321 ) @ ( c_Lambda_Olift @ SY1319 @ SY1321 ) @ ( c_HOL_Oplus__class_Oplus @ SY1320 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1321 @ ( c_HOL_Oplus__class_Oplus @ SY1320 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1410,plain,
! [SV231: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV231 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV231 )
= ( c_HOL_Oone__class_Oone @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1411,plain,
! [SV232: $i] :
( ( ! [SY1322: $i] :
( ( c_HOL_Oord__class_Oless @ SV232 @ SV232 @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV232 ) @ SY1322 @ SV232 )
= SY1322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1412,plain,
! [SV233: $i] :
( ( ! [SY1323: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV233 ) @ SY1323 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ SV233 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ SV233 @ SY1323 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1413,plain,
! [SV234: $i] :
( ( ! [SY1324: $i,SY1325: $i,SY1326: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV234 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1324 @ SY1325 @ SV234 ) @ SY1326 @ SV234 )
= ( c_HOL_Oplus__class_Oplus @ SY1324 @ ( c_HOL_Oplus__class_Oplus @ SY1325 @ SY1326 @ SV234 ) @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1414,plain,
! [SV235: $i] :
( ( ! [SY1327: $i,SY1328: $i,SY1329: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV235 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1327 @ ( c_HOL_Oplus__class_Oplus @ SY1328 @ SY1329 @ SV235 ) @ SV235 )
= ( c_HOL_Oplus__class_Oplus @ SY1328 @ ( c_HOL_Oplus__class_Oplus @ SY1327 @ SY1329 @ SV235 ) @ SV235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1415,plain,
! [SV236: $i] :
( ( ! [SY1330: $i,SY1331: $i,SY1332: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV236 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1330 @ SY1331 @ SV236 ) @ SY1332 @ SV236 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1330 @ SY1332 @ SV236 ) @ SY1331 @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1416,plain,
! [SV237: $i] :
( ( ! [SY1333: $i,SY1334: $i,SY1335: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1333 @ ( c_HOL_Oplus__class_Oplus @ SY1334 @ SY1335 @ SV237 ) @ SV237 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1333 @ SY1334 @ SV237 ) @ SY1335 @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1417,plain,
! [SV238: $i] :
( ( ! [SY1336: $i,SY1337: $i,SY1338: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV238 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1336 @ SY1337 @ SV238 ) @ SY1338 @ SV238 )
= ( c_HOL_Oplus__class_Oplus @ SY1336 @ ( c_HOL_Oplus__class_Oplus @ SY1337 @ SY1338 @ SV238 ) @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1418,plain,
! [SV239: $i] :
( ( ! [SY1339: $i,SY1340: $i,SY1341: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV239 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1339 @ ( c_HOL_Oplus__class_Oplus @ SY1340 @ SY1341 @ SV239 ) @ SV239 )
= ( c_HOL_Oplus__class_Oplus @ SY1340 @ ( c_HOL_Oplus__class_Oplus @ SY1339 @ SY1341 @ SV239 ) @ SV239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1419,plain,
! [SV240: $i] :
( ( ! [SY1342: $i,SY1343: $i,SY1344: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV240 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1342 @ SY1343 @ SV240 ) @ SY1344 @ SV240 )
= ( c_HOL_Oplus__class_Oplus @ SY1342 @ ( c_HOL_Oplus__class_Oplus @ SY1343 @ SY1344 @ SV240 ) @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1420,plain,
! [SV241: $i] :
( ( ! [SY1345: $i,SY1346: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV241 @ SY1345 @ tc_nat ) @ SY1346 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV241 @ ( c_HOL_Oplus__class_Oplus @ SY1345 @ SY1346 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1421,plain,
! [SV242: $i] :
( ( ! [SY1347: $i,SY1348: $i] :
( ( c_HOL_Oplus__class_Oplus @ SV242 @ ( c_HOL_Oplus__class_Oplus @ SY1347 @ SY1348 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SY1347 @ ( c_HOL_Oplus__class_Oplus @ SV242 @ SY1348 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1422,plain,
! [SV243: $i] :
( ( ! [SY1349: $i,SY1350: $i,SY1351: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV243 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1349 @ ( c_HOL_Oplus__class_Oplus @ SY1350 @ SY1351 @ SV243 ) @ SV243 )
= ( c_HOL_Oplus__class_Oplus @ SY1350 @ ( c_HOL_Oplus__class_Oplus @ SY1349 @ SY1351 @ SV243 ) @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1423,plain,
! [SV244: $i] :
( ( ! [SY1352: $i,SY1353: $i,SY1354: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV244 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1352 @ ( c_HOL_Oplus__class_Oplus @ SY1353 @ SY1354 @ SV244 ) @ SV244 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1352 @ SY1353 @ SV244 ) @ SY1354 @ SV244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1424,plain,
! [SV245: $i] :
( ( ! [SY1355: $i,SY1356: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV245 ) @ SY1355 @ SY1356 )
= ( c_Lambda_OdB_OVar @ SV245 ) )
| ( SV245 = SY1356 )
| ( c_HOL_Oord__class_Oless @ SY1356 @ SV245 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1425,plain,
! [SV246: $i] :
( ( ! [SY1357: $i,SY1358: $i,SY1359: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV246 @ SY1357 @ SY1358 ) @ ( c_Lambda_Osubst @ SY1359 @ SY1357 @ SY1358 ) )
| ~ ( c_Lambda_Obeta @ SV246 @ SY1359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1426,plain,
! [SV247: $i] :
( ( ( c_Suc @ SV247 )
= ( c_HOL_Oplus__class_Oplus @ SV247 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1427,plain,
! [SV248: $i] :
( ( ( c_Suc @ SV248 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV248 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1428,plain,
! [SV249: $i] :
( ( ! [SY1360: $i,SY1361: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ SV249 ) @ SY1360 @ SY1361 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ SV249 @ SY1360 @ ( c_HOL_Oplus__class_Oplus @ SY1361 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1429,plain,
! [SV250: $i] :
( ( ! [SY1362: $i,SY1363: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV250 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1362 @ SY1363 @ SV250 )
= ( c_HOL_Oplus__class_Oplus @ SY1363 @ SY1362 @ SV250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1430,plain,
! [SV251: $i] :
( ( ! [SY1364: $i,SY1365: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV251 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1364 @ SY1365 @ SV251 )
= ( c_HOL_Oplus__class_Oplus @ SY1365 @ SY1364 @ SV251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1431,plain,
! [SV252: $i] :
( ( ! [SY1366: $i] :
( ( c_HOL_Oplus__class_Oplus @ SV252 @ SY1366 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SY1366 @ SV252 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1432,plain,
! [SV253: $i] :
( ( ! [SY1367: $i,SY1368: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV253 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1367 @ SY1368 @ SV253 )
= ( c_HOL_Oplus__class_Oplus @ SY1368 @ SY1367 @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1433,plain,
! [SV254: $i] :
( ( ! [SY1369: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV254 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1369 @ SY1369 @ SV254 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV254 ) @ ( c_HOL_Oone__class_Oone @ SV254 ) @ SV254 ) @ SY1369 @ SV254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1434,plain,
! [SV255: $i] :
( ( ! [SY1370: $i,SY1371: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV255 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1370 @ SY1371 @ SV255 ) @ SY1371 @ SV255 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1370 @ ( c_HOL_Oone__class_Oone @ SV255 ) @ SV255 ) @ SY1371 @ SV255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1435,plain,
! [SV256: $i] :
( ( ! [SY1372: $i,SY1373: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1372 @ ( c_HOL_Otimes__class_Otimes @ SY1373 @ SY1372 @ SV256 ) @ SV256 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1373 @ ( c_HOL_Oone__class_Oone @ SV256 ) @ SV256 ) @ SY1372 @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1436,plain,
! [SV257: $i] :
( ( ! [SY1374: $i] : ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV257 ) @ SY1374 ) @ ( c_Lambda_Osubst @ SV257 @ SY1374 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1437,plain,
! [SV258: $i] :
( ( ! [SY1375: $i,SY1376: $i] :
( ( c_Lambda_Oliftn @ SV258 @ ( c_Lambda_OdB_OAbs @ SY1375 ) @ SY1376 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ SV258 @ SY1375 @ ( c_HOL_Oplus__class_Oplus @ SY1376 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1438,plain,
! [SV259: $i] :
( ( ! [SY1377: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV259 ) @ SY1377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1439,plain,
! [SV260: $i] :
( ( ! [SY1378: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV260 )
| ( c_HOL_Oord__class_Oless @ SY1378 @ ( c_HOL_Oplus__class_Oplus @ SY1378 @ ( c_HOL_Oone__class_Oone @ SV260 ) @ SV260 ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1440,plain,
! [SV261: $i] :
( ( ! [SY1379: $i] :
( ( c_Lambda_Obeta @ SV261 @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV261 @ SY1379 ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV261 ) @ SY1379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1441,plain,
! [SV262: $i] :
( ( ! [SY1380: $i,SY1381: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV262 ) @ SY1380 @ SY1381 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV262 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1381 @ SV262 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1442,plain,
! [SV263: $i] :
( ( ! [SY1382: $i,SY1383: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV263 ) @ SY1382 @ SY1383 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV263 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1383 @ SV263 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1443,plain,
! [SV264: $i] :
( ( ! [SY1384: $i,SY1385: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV264 ) @ SY1384 @ SY1385 )
= ( c_Lambda_OdB_OVar @ SV264 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV264 @ SY1385 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1444,plain,
! [SV265: $i] :
( ( ! [SY1386: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV265 ) @ SY1386 @ SV265 )
= SY1386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1445,plain,
! [SV266: $i] :
( ( ! [SY1387: $i,SY1388: $i,SY1389: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ SV266 @ SY1387 ) @ SY1388 @ SY1389 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV266 @ SY1388 @ SY1389 ) @ ( c_Lambda_Osubst @ SY1387 @ SY1388 @ SY1389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1446,plain,
! [SV267: $i] :
( ( ! [SY1390: $i,SY1391: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV267 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SY1390 @ SY1391 @ tc_nat ) @ SV267 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1390 @ SV267 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1391 @ SV267 ) @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1447,plain,
! [SV268: $i] :
( ( ! [SY1392: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ SV268 ) @ SY1392 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ SV268 @ ( c_HOL_Oplus__class_Oplus @ SY1392 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1448,plain,
! [SV269: $i] :
( ( ! [SY1393: $i,SY1394: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ SV269 @ SY1393 ) @ SY1394 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV269 @ SY1394 ) @ ( c_Lambda_Olift @ SY1393 @ SY1394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1449,plain,
! [SV270: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV270 ) )
| ~ ( c_InductTermi_OIT @ SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1450,plain,
! [SV271: $i] :
( ( ! [SY1395: $i,SY1396: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV271 @ SY1395 ) @ SY1396 @ SY1395 )
= SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1451,plain,
! [SV272: $i] :
( ( ! [SY1397: $i,SY1398: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV272 @ SY1397 ) @ ( c_Lambda_Olift @ SY1398 @ SY1397 ) )
| ~ ( c_Lambda_Obeta @ SV272 @ SY1398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1452,plain,
! [SV273: $i] :
( ( ! [SY1399: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV273 ) @ ( c_Lambda_OdB_OAbs @ SY1399 ) )
| ~ ( c_Lambda_Obeta @ SV273 @ SY1399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1453,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1454,plain,
! [SV274: $i] :
( ( ! [SY1400: $i,SY1401: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV274 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1400 @ SY1401 @ SV274 )
!= ( c_HOL_Ozero__class_Ozero @ SV274 ) )
| ( SY1400 = SY1401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1455,plain,
! [SV275: $i] :
( ( ! [SY1402: $i,SY1403: $i,SY1404: $i,SY1405: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV275 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1402 @ ( c_HOL_Oplus__class_Oplus @ SY1403 @ SY1404 @ SV275 ) @ SV275 )
!= ( c_HOL_Oplus__class_Oplus @ SY1403 @ SY1405 @ SV275 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SY1402 @ SY1404 @ SV275 )
= SY1405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1456,plain,
! [SV276: $i] :
( ( ( c_Suc @ SV276 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1457,plain,
! [SV277: $i] :
( ( ! [SY1406: $i,SY1407: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV277 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY1406 @ SV277 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1407 @ SV277 ) )
| ( SY1406 = SY1407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1458,plain,
! [SV278: $i] :
( ( ! [SY1408: $i,SY1409: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV278 @ SY1408 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV278 @ SY1409 @ tc_nat ) )
| ( SY1408 = SY1409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1459,plain,
! [SV279: $i] :
( ( ( c_Suc @ SV279 )
!= SV279 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1460,plain,
! [SV280: $i] :
( ( ! [SY1410: $i,SY1411: $i,SY1412: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV280 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1410 @ SY1411 @ SV280 )
!= ( c_HOL_Oplus__class_Oplus @ SY1410 @ SY1412 @ SV280 ) )
| ( SY1411 = SY1412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1461,plain,
! [SV281: $i] :
( ( ! [SY1413: $i] :
( ( c_Lambda_OdB_OAbs @ SV281 )
!= ( c_Lambda_OdB_OVar @ SY1413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1462,plain,
! [SV282: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1463,plain,
! [SV283: $i] :
( ( ! [SY1414: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV283 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1414 @ SY1414 @ SV283 )
!= ( c_HOL_Ozero__class_Ozero @ SV283 ) )
| ( SY1414
= ( c_HOL_Ozero__class_Ozero @ SV283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1464,plain,
! [SV284: $i] :
( ( ! [SY1415: $i,SY1416: $i] :
( ( c_Lambda_OdB_OApp @ SV284 @ SY1415 )
!= ( c_Lambda_OdB_OVar @ SY1416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1465,plain,
! [SV285: $i] :
( ( ! [SY1417: $i,SY1418: $i,SY1419: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV285 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1417 @ SY1418 @ SV285 )
!= ( c_HOL_Ominus__class_Ominus @ SY1419 @ SY1419 @ SV285 ) )
| ( SY1417 = SY1418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1466,plain,
! [SV286: $i] :
( ( ! [SY1420: $i,SY1421: $i,SY1422: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV286 @ SY1420 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY1421 @ SY1422 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1421 @ SY1420 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV286 @ SY1422 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1467,plain,
! [SV287: $i] :
( ( ! [SY1423: $i,SY1424: $i,SY1425: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV287 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1423 @ SY1424 @ SV287 )
!= ( c_HOL_Oplus__class_Oplus @ SY1425 @ SY1424 @ SV287 ) )
| ( SY1423 = SY1425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1468,plain,
! [SV288: $i] :
( ( ! [SY1426: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV288 @ SY1426 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1426
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1469,plain,
! [SV289: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1470,plain,
! [SV290: $i] :
( ( ! [SY1427: $i,SY1428: $i,SY1429: $i,SY1430: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV290 )
| ~ ( class_Int_Onumber__ring @ SV290 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1427 @ ( c_HOL_Otimes__class_Otimes @ SY1428 @ SY1429 @ SV290 ) @ SV290 )
!= ( c_HOL_Oplus__class_Oplus @ SY1427 @ ( c_HOL_Otimes__class_Otimes @ SY1428 @ SY1430 @ SV290 ) @ SV290 ) )
| ( SY1429 = SY1430 )
| ( SY1428
= ( c_HOL_Ozero__class_Ozero @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1471,plain,
! [SV291: $i] :
( ( ! [SY1431: $i,SY1432: $i,SY1433: $i,SY1434: $i,SY1435: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV291 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1431 @ SY1432 @ SV291 ) @ SY1433 @ SV291 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1434 @ SY1432 @ SV291 ) @ SY1435 @ SV291 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1431 @ SY1434 @ SV291 ) @ SY1432 @ SV291 ) @ SY1433 @ SV291 )
= SY1435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1472,plain,
! [SV292: $i] :
( ( ! [SY1436: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV292 @ SY1436 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV292
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV292
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1473,plain,
! [SV293: $i] :
( ( ! [SY1437: $i,SY1438: $i,SY1439: $i,SY1440: $i,SY1441: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV293 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1437 @ SY1438 @ SV293 ) @ SY1439 @ SV293 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1440 @ SY1438 @ SV293 ) @ SY1441 @ SV293 ) )
| ( SY1439
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1440 @ SY1437 @ SV293 ) @ SY1438 @ SV293 ) @ SY1441 @ SV293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1474,plain,
! [SV294: $i] :
( ( ! [SY1442: $i,SY1443: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV294 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1442 @ SY1443 @ SV294 )
!= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SY1443
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SY1442
= ( c_HOL_Ozero__class_Ozero @ SV294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1475,plain,
! [SV295: $i] :
( ( ! [SY1444: $i,SY1445: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV295 @ SY1444 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY1445 @ SY1444 @ tc_nat ) )
| ( SV295 = SY1445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1476,plain,
! [SV296: $i] :
( ( ! [SY1446: $i,SY1447: $i] :
( ( c_Lambda_OdB_OApp @ SV296 @ SY1446 )
!= ( c_Lambda_OdB_OAbs @ SY1447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1477,plain,
! [SV297: $i] :
( ( ! [SY1448: $i,SY1449: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV297 )
| ~ ( class_Int_Onumber__ring @ SV297 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1448 @ SY1449 @ SV297 )
!= ( c_HOL_Ozero__class_Ozero @ SV297 ) )
| ( SY1448 = SY1449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1478,plain,
! [SV298: $i] :
( ( ( c_Suc @ SV298 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1479,plain,
! [SV299: $i] :
( ( ! [SY1450: $i,SY1451: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV299 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1450 @ SY1451 @ SV299 )
!= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
| ( SY1450
= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
| ( SY1451
= ( c_HOL_Ozero__class_Ozero @ SV299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1480,plain,
! [SV300: $i] :
( ( ! [SY1452: $i,SY1453: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV300 @ SY1452 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV300 @ SY1453 @ tc_nat ) )
| ( SY1452 = SY1453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1481,plain,
! [SV301: $i] :
( ( ! [SY1454: $i,SY1455: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV301 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1454 @ SY1455 @ SV301 )
!= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
| ( SY1455
= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
| ( SY1454
= ( c_HOL_Ozero__class_Ozero @ SV301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1482,plain,
! [SV302: $i] :
( ( ! [SY1456: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV302 @ SY1456 @ tc_nat ) )
| ( SV302
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV302
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1483,plain,
! [SV303: $i] :
( ( SV303
!= ( c_Suc @ SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1484,plain,
! [SV304: $i] :
( ( ! [SY1457: $i,SY1458: $i] :
( ( c_Lambda_OdB_OAbs @ SV304 )
!= ( c_Lambda_OdB_OApp @ SY1457 @ SY1458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1485,plain,
! [SV305: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV305 )
| ( ( c_HOL_Ozero__class_Ozero @ SV305 )
!= ( c_HOL_Oone__class_Oone @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1486,plain,
! [SV306: $i] :
( ( ! [SY1459: $i,SY1460: $i,SY1461: $i,SY1462: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV306 )
| ~ ( class_Int_Onumber__ring @ SV306 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1459 @ SY1460 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SY1461 @ SY1462 @ SV306 ) @ SV306 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1459 @ SY1462 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SY1461 @ SY1460 @ SV306 ) @ SV306 ) )
| ( SY1460 = SY1462 )
| ( SY1459 = SY1461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1487,plain,
! [SV307: $i] :
( ( ! [SY1463: $i,SY1464: $i,SY1465: $i,SY1466: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV307 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1463 @ SY1464 @ SV307 )
!= ( c_HOL_Ominus__class_Ominus @ SY1465 @ SY1466 @ SV307 ) )
| ( c_HOL_Oord__class_Oless @ SY1463 @ SY1464 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SY1465 @ SY1466 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1488,plain,
! [SV308: $i] :
( ( ! [SY1467: $i,SY1468: $i,SY1469: $i] :
( ( ( c_Lambda_OdB_OApp @ SV308 @ SY1467 )
!= ( c_Lambda_OdB_OApp @ SY1468 @ SY1469 ) )
| ( SY1467 = SY1469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1489,plain,
! [SV309: $i] :
( ( ! [SY1470: $i,SY1471: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1470 @ SY1470 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SY1471 @ SY1471 @ SV309 ) @ SV309 )
!= ( c_HOL_Ozero__class_Ozero @ SV309 ) )
| ( SY1471
= ( c_HOL_Ozero__class_Ozero @ SV309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1490,plain,
! [SV310: $i] :
( ( ! [SY1472: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV310 )
!= ( c_Lambda_OdB_OAbs @ SY1472 ) )
| ( SV310 = SY1472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1491,plain,
! [SV311: $i] :
( ( ! [SY1473: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV311 @ SY1473 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY1473
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV311
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1492,plain,
! [SV312: $i] :
( ( ! [SY1474: $i] :
( ( c_Lambda_OdB_OVar @ SV312 )
!= ( c_Lambda_OdB_OAbs @ SY1474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1493,plain,
! [SV313: $i] :
( ( ! [SY1475: $i,SY1476: $i,SY1477: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV313 )
| ~ ( class_Int_Onumber__ring @ SV313 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1475 @ SY1476 @ SV313 )
!= ( c_HOL_Oplus__class_Oplus @ SY1475 @ SY1477 @ SV313 ) )
| ( SY1476 = SY1477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1494,plain,
! [SV314: $i] :
( ( ! [SY1478: $i,SY1479: $i,SY1480: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV314 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1478 @ SY1478 @ SV314 )
!= ( c_HOL_Ominus__class_Ominus @ SY1479 @ SY1480 @ SV314 ) )
| ( SY1479 = SY1480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1495,plain,
! [SV315: $i] :
( ( ! [SY1481: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV315 @ SY1481 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV315
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1481
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1496,plain,
! [SV316: $i] :
( ( ! [SY1482: $i,SY1483: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV316 )
| ~ ( class_Int_Onumber__ring @ SV316 )
| ( SY1482
!= ( c_HOL_Oplus__class_Oplus @ SY1482 @ SY1483 @ SV316 ) )
| ( SY1483
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1497,plain,
! [SV317: $i] :
( ( ! [SY1484: $i,SY1485: $i,SY1486: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV317 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1484 @ SY1485 @ SV317 )
!= ( c_HOL_Oplus__class_Oplus @ SY1484 @ SY1486 @ SV317 ) )
| ( SY1485 = SY1486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1498,plain,
! [SV318: $i] :
( ( ! [SY1487: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV318 @ SY1487 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY1487
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY1487
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1499,plain,
! [SV319: $i] :
( ( ! [SY1488: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV319 @ SY1488 @ tc_nat ) )
| ( SY1488
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY1488
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1500,plain,
! [SV320: $i] :
( ( ! [SY1489: $i,SY1490: $i] :
( ( c_Lambda_OdB_OVar @ SV320 )
!= ( c_Lambda_OdB_OApp @ SY1489 @ SY1490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1501,plain,
! [SV321: $i] :
( ( ! [SY1491: $i,SY1492: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV321 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1491 @ SY1491 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SY1492 @ SY1492 @ SV321 ) @ SV321 )
!= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SY1491
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1502,plain,
! [SV322: $i] :
( ( ! [SY1493: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV322 @ SY1493 @ tc_nat )
!= SV322 )
| ( SY1493
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1503,plain,
! [SV323: $i] :
( ( ! [SY1494: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV323 @ SY1494 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SY1494 @ SV323 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1494 = SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1504,plain,
! [SV324: $i] :
( ( ! [SY1495: $i] :
( ( SV324
!= ( c_HOL_Oplus__class_Oplus @ SV324 @ SY1495 @ tc_nat ) )
| ( SY1495
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1505,plain,
! [SV325: $i] :
( ( ! [SY1496: $i,SY1497: $i,SY1498: $i,SY1499: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1496 @ SY1497 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SY1498 @ SY1499 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SY1498 @ SY1499 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SY1496 @ SY1497 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1506,plain,
! [SV326: $i] :
( ( ! [SY1500: $i,SY1501: $i,SY1502: $i] :
( ( ( c_Lambda_OdB_OApp @ SV326 @ SY1500 )
!= ( c_Lambda_OdB_OApp @ SY1501 @ SY1502 ) )
| ( SV326 = SY1501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1507,plain,
! [SV327: $i] :
( ( ! [SY1503: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV327 @ SY1503 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV327
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1508,plain,
! [SV328: $i] :
( ( ! [SY1504: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV328 @ SY1504 @ tc_nat ) )
| ( SY1504
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV328
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1509,plain,
! [SV329: $i] :
( ( ! [SY1505: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV329 @ SY1505 @ tc_nat ) )
| ( SV329
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1505
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1510,plain,
! [SV330: $i] :
( ( ! [SY1506: $i] :
( ( ( c_Lambda_OdB_OVar @ SV330 )
!= ( c_Lambda_OdB_OVar @ SY1506 ) )
| ( SV330 = SY1506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1511,plain,
! [SV331: $i] :
( ( ! [SY1507: $i,SY1508: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV331 )
| ( ( c_HOL_Ominus__class_Ominus @ SY1507 @ SY1508 @ SV331 )
!= ( c_HOL_Ozero__class_Ozero @ SV331 ) )
| ( SY1507 = SY1508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1512,plain,
! [SV332: $i] :
( ( ! [SY1509: $i,SY1510: $i,SY1511: $i,SY1512: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV332 )
| ~ ( class_Int_Onumber__ring @ SV332 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1509 @ SY1510 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SY1511 @ SY1512 @ SV332 ) @ SV332 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1509 @ SY1512 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SY1511 @ SY1510 @ SV332 ) @ SV332 ) )
| ( SY1510 = SY1512 )
| ( SY1509 = SY1511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1513,plain,
! [SV333: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV333 )
| ( ( c_HOL_Oone__class_Oone @ SV333 )
!= ( c_HOL_Ozero__class_Ozero @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1514,plain,
! [SV334: $i] :
( ( ! [SY1513: $i] :
( ( ( c_Suc @ SV334 )
!= ( c_Suc @ SY1513 ) )
| ( SV334 = SY1513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1515,plain,
! [SV335: $i] :
( ( ! [SY1514: $i] :
( ( ( c_Suc @ SV335 )
!= ( c_Suc @ SY1514 ) )
| ( SV335 = SY1514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1516,plain,
! [SV336: $i,SV2: $i] :
( ( ! [SY1515: $i,SY1516: $i,SY1517: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SY1515 @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SY1516 @ SY1517 @ SV2 ) @ SV2 )
= ( c_HOL_Otimes__class_Otimes @ SY1516 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SY1515 @ SV2 ) @ SY1517 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1517,plain,
! [SV337: $i,SV3: $i] :
( ( ! [SY1518: $i,SY1519: $i,SY1520: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV3 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV337 @ SY1518 @ SV3 ) @ ( c_HOL_Otimes__class_Otimes @ SY1519 @ SY1520 @ SV3 ) @ SV3 )
= ( c_HOL_Otimes__class_Otimes @ SV337 @ ( c_HOL_Otimes__class_Otimes @ SY1518 @ ( c_HOL_Otimes__class_Otimes @ SY1519 @ SY1520 @ SV3 ) @ SV3 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1518,plain,
! [SV338: $i,SV4: $i] :
( ( ! [SY1521: $i,SY1522: $i,SY1523: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV338 @ SY1521 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SY1522 @ SY1523 @ SV4 ) @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV338 @ SY1522 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SY1521 @ SY1523 @ SV4 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1519,plain,
! [SV339: $i,SV5: $i] :
( ( ( SV5 = SV339 )
| ~ ( c_HOL_Oord__class_Oless @ SV5 @ ( c_Suc @ SV339 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV5 @ SV339 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1520,plain,
! [SV340: $i,SV6: $i] :
( ( ( SV6 = SV340 )
| ~ ( c_HOL_Oord__class_Oless @ SV340 @ ( c_Suc @ SV6 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV340 @ SV6 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1521,plain,
! [SV341: $i,SV7: $i] :
( ( ( SV7 = SV341 )
| ( c_HOL_Oord__class_Oless @ SV7 @ SV341 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV7 @ ( c_Suc @ SV341 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1522,plain,
! [SV342: $i,SV8: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV8 ) @ ( c_Suc @ SV342 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV8 @ SV342 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1523,plain,
! [SV343: $i,SV9: $i] :
( ( ! [SY1524: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV343 @ SV343 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SY1524 @ SY1524 @ SV9 ) @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1524,plain,
! [SV10: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV10 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_HOL_Ozero__class_Ozero @ SV10 ) @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1525,plain,
! [SV344: $i,SV11: $i] :
( ( ! [SY1525: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV11 ) @ SV344 @ SY1525 )
= ( c_Lambda_OdB_OVar @ SV11 ) )
| ( SV11 = SY1525 )
| ( c_HOL_Oord__class_Oless @ SY1525 @ SV11 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1526,plain,
! [SV345: $i,SV12: $i] :
( ( ! [SY1526: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV12 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SV345 @ SY1526 @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SY1526 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SV345 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1527,plain,
! [SV346: $i,SV13: $i] :
( ( ! [SY1527: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV13 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SV346 @ SY1527 @ SV13 ) @ SV13 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SY1527 @ SV13 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV346 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1528,plain,
! [SV347: $i,SV14: $i] :
( ( ! [SY1528: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV14 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV347 @ SV14 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SY1528 @ SV14 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ ( c_HOL_Otimes__class_Otimes @ SY1528 @ SV347 @ SV14 ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1529,plain,
! [SV348: $i,SV15: $i] :
( ( ! [SY1529: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV15 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV348 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SY1529 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ ( c_HOL_Otimes__class_Otimes @ SV348 @ SY1529 @ SV15 ) @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1530,plain,
! [SV349: $i,SV16: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV16 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV349 @ SV349 @ SV16 ) @ ( c_HOL_Ozero__class_Ozero @ SV16 ) @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SV349 @ ( c_HOL_Ozero__class_Ozero @ SV16 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1531,plain,
! [SV350: $i,SV17: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV17 )
| ( c_HOL_Oord__class_Oless @ SV350 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SV350 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1532,plain,
! [SV351: $i,SV18: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV18 )
| ( c_HOL_Oord__class_Oless @ SV351 @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV351 @ SV351 @ SV18 ) @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1533,plain,
! [SV352: $i,SV19: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV19 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV352 @ SV352 @ SV19 ) @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
| ~ ( c_HOL_Oord__class_Oless @ SV352 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1534,plain,
! [SV353: $i,SV20: $i] :
( ( ! [SY1530: $i,SY1531: $i,SY1532: $i,SY1533: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV20 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV353 @ SY1530 @ SV20 ) @ SY1531 @ SV20 ) @ SY1532 @ SV20 ) @ SY1533 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SY1531 @ SV20 ) @ SY1532 @ SV20 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1530 @ SY1531 @ SV20 ) @ SY1533 @ SV20 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1535,plain,
! [SV354: $i,SV21: $i] :
( ( ! [SY1534: $i,SY1535: $i,SY1536: $i,SY1537: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV21 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV354 @ SY1534 @ SV21 ) @ SY1535 @ SV21 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1536 @ SY1534 @ SV21 ) @ SY1537 @ SV21 ) @ SV21 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV354 @ SY1536 @ SV21 ) @ SY1534 @ SV21 ) @ SY1535 @ SV21 ) @ SY1537 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1536,plain,
! [SV355: $i,SV22: $i] :
( ( ! [SY1538: $i,SY1539: $i,SY1540: $i,SY1541: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV22 )
| ( c_HOL_Oord__class_Oless @ SV355 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1538 @ SY1539 @ SV22 ) @ SY1540 @ SV22 ) @ SY1541 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1539 @ SY1540 @ SV22 ) @ SV355 @ SV22 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1538 @ SY1540 @ SV22 ) @ SY1541 @ SV22 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1537,plain,
! [SV356: $i,SV23: $i] :
( ( ! [SY1542: $i,SY1543: $i,SY1544: $i,SY1545: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV23 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV356 @ SY1542 @ SV23 ) @ SY1543 @ SV23 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1544 @ SY1542 @ SV23 ) @ SY1545 @ SV23 ) @ SV23 )
| ~ ( c_HOL_Oord__class_Oless @ SY1543 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1544 @ SV356 @ SV23 ) @ SY1542 @ SV23 ) @ SY1545 @ SV23 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1538,plain,
! [SV357: $i,SV24: $i] :
( ( ! [SY1546: $i] :
( ( c_Lambda_Oliftn @ ( c_Suc @ SV24 ) @ SV357 @ SY1546 )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ SV24 @ SV357 @ SY1546 ) @ SY1546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1539,plain,
! [SV358: $i,SV27: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV27 )
| ~ ( class_Int_Onumber__ring @ SV27 )
| ( ( c_HOL_Ominus__class_Ominus @ SV358 @ SV358 @ SV27 )
= ( c_HOL_Ozero__class_Ozero @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1540,plain,
! [SV359: $i,SV28: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV28 )
| ( ( c_HOL_Ominus__class_Ominus @ SV359 @ SV359 @ SV28 )
= ( c_HOL_Ozero__class_Ozero @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1541,plain,
! [SV360: $i,SV29: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV29 )
| ( ( c_HOL_Ominus__class_Ominus @ SV360 @ ( c_HOL_Ozero__class_Ozero @ SV29 ) @ SV29 )
= SV360 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1542,plain,
! [SV361: $i,SV30: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV30 )
| ( ( c_HOL_Ominus__class_Ominus @ SV361 @ SV361 @ SV30 )
= ( c_HOL_Ozero__class_Ozero @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1543,plain,
! [SV362: $i,SV31: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV31 )
| ( ( c_HOL_Ominus__class_Ominus @ SV362 @ SV362 @ SV31 )
= ( c_HOL_Ozero__class_Ozero @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1544,plain,
! [SV363: $i,SV32: $i] :
( ( ! [SY1547: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV363 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SY1547 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1547 @ SV32 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1547 @ SV363 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1545,plain,
! [SV364: $i,SV34: $i] :
( ( ! [SY1548: $i] :
( ( c_HOL_Oord__class_Oless @ SV34 @ ( c_HOL_Oplus__class_Oplus @ SV364 @ SY1548 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV34 @ SY1548 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1546,plain,
! [SV365: $i,SV35: $i] :
( ( ! [SY1549: $i] :
( ( c_HOL_Oord__class_Oless @ SV35 @ ( c_HOL_Oplus__class_Oplus @ SV365 @ SY1549 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV35 @ SV365 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1547,plain,
! [SV366: $i,SV36: $i] :
( ( ! [SY1550: $i] :
( ( c_HOL_Oord__class_Oless @ SV36 @ SV366 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV36 @ SY1550 @ tc_nat ) @ SV366 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1548,plain,
! [SV367: $i,SV37: $i] :
( ( ! [SY1551: $i] :
( ( c_HOL_Oord__class_Oless @ SV37 @ ( c_HOL_Oplus__class_Oplus @ SV367 @ SY1551 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV37 @ SY1551 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1549,plain,
! [SV368: $i,SV38: $i] :
( ( ! [SY1552: $i] :
( ( c_HOL_Oord__class_Oless @ SV38 @ ( c_HOL_Oplus__class_Oplus @ SV368 @ SY1552 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV38 @ SV368 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1550,plain,
! [SV369: $i,SV39: $i] :
( ( c_HOL_Oord__class_Oless @ SV39 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV39 @ SV369 @ tc_nat ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1551,plain,
! [SV370: $i,SV40: $i] :
( ( c_HOL_Oord__class_Oless @ SV40 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV370 @ SV40 @ tc_nat ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1552,plain,
! [SV371: $i,SV41: $i] :
( ( c_HOL_Oord__class_Oless @ SV41 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV41 @ SV371 @ tc_nat ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1553,plain,
! [SV372: $i,SV42: $i] :
( ( ! [SY1553: $i,SY1554: $i,SY1555: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV42 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV372 @ SY1553 @ SV42 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1554 @ SV372 @ SV42 ) @ SY1553 @ SV42 ) @ SY1555 @ SV42 ) @ SV42 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1554 @ SY1553 @ SV42 ) @ SY1555 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1554,plain,
! [SV373: $i,SV43: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ SV43 ) @ SV373 @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV43 @ SV373 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1555,plain,
! [SV374: $i,SV44: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV44 @ ( c_Suc @ SV374 ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV44 @ SV374 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1556,plain,
! [SV375: $i,SV45: $i] :
( ( ! [SY1556: $i,SY1557: $i,SY1558: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV45 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV375 @ SY1556 @ SV45 ) @ SY1557 @ SV45 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1558 @ SY1556 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV375 @ SY1558 @ SV45 ) @ SY1556 @ SV45 ) @ SY1557 @ SV45 ) @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1557,plain,
! [SV376: $i,SV46: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV46 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV46 ) @ SV376 @ SV46 )
= SV376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1558,plain,
! [SV377: $i,SV47: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV47 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV377 @ SV47 )
= SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1559,plain,
! [SV378: $i,SV48: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV48 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV48 ) @ SV378 @ SV48 )
= SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1560,plain,
! [SV379: $i,SV49: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV379 @ SV49 )
= ( c_HOL_Ozero__class_Ozero @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1561,plain,
! [SV380: $i,SV50: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
| ( ( c_HOL_Otimes__class_Otimes @ SV380 @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV50 )
= ( c_HOL_Ozero__class_Ozero @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1562,plain,
! [SV381: $i,SV51: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV51 )
| ( ( c_HOL_Otimes__class_Otimes @ SV381 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 )
= ( c_HOL_Ozero__class_Ozero @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1563,plain,
! [SV382: $i,SV52: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV52 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV382 @ SV52 )
= ( c_HOL_Ozero__class_Ozero @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1564,plain,
! [SV383: $i,SV53: $i] :
( ( ~ ( class_Ring__and__Field_Omult__zero @ SV53 )
| ( ( c_HOL_Otimes__class_Otimes @ SV383 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
= ( c_HOL_Ozero__class_Ozero @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1565,plain,
! [SV384: $i,SV54: $i] :
( ( ~ ( class_Ring__and__Field_Omult__zero @ SV54 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV384 @ SV54 )
= ( c_HOL_Ozero__class_Ozero @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1566,plain,
! [SV385: $i,SV55: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV385 @ SV55 )
= ( c_HOL_Ozero__class_Ozero @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1567,plain,
! [SV386: $i,SV56: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV56 @ SV386 @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV56 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV386 @ tc_nat ) ) )
| ( SV56
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1568,plain,
! [SV387: $i,SV57: $i] :
( ( ! [SY1559: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV57 @ SV387 @ tc_nat ) @ SY1559 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV57 @ SY1559 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1569,plain,
! [SV58: $i] :
( ( c_HOL_Oord__class_Oless @ SV58 @ SV58 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1570,plain,
! [SV59: $i] :
( ( c_HOL_Oord__class_Oless @ SV59 @ SV59 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1571,plain,
! [SV388: $i,SV60: $i] :
( ( ~ ( class_Orderings_Oorder @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV388 @ SV388 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1572,plain,
! [SV389: $i,SV61: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV61 )
| ~ ( c_HOL_Oord__class_Oless @ SV389 @ SV389 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1573,plain,
! [SV390: $i,SV62: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ SV390 @ SV390 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1574,plain,
! [SV391: $i,SV63: $i] :
( ( ! [SY1560: $i] :
( ( ( c_Lambda_Oliftn @ SV63 @ ( c_Lambda_OdB_OVar @ SV391 ) @ SY1560 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ SV391 @ SV63 @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ SV391 @ SY1560 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1575,plain,
! [SV392: $i,SV64: $i] :
( ( ! [SY1561: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV64 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ ( c_HOL_Oplus__class_Oplus @ SV392 @ SY1561 @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SY1561 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV392 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1576,plain,
! [SV393: $i,SV65: $i] :
( ( ! [SY1562: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV65 )
| ( c_HOL_Oord__class_Oless @ SV393 @ SY1562 @ SV65 )
| ( c_HOL_Oord__class_Oless @ SY1562 @ SV393 @ SV65 )
| ( SY1562 = SV393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1577,plain,
! [SV394: $i,SV66: $i] :
( ( ! [SY1563: $i] :
( ~ ( class_Orderings_Olinorder @ SV66 )
| ( SV394 = SY1563 )
| ( c_HOL_Oord__class_Oless @ SY1563 @ SV394 @ SV66 )
| ( c_HOL_Oord__class_Oless @ SV394 @ SY1563 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1578,plain,
! [SV395: $i,SV67: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV67 @ SV395 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV395 @ SV67 @ tc_nat )
| ( SV395 = SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1579,plain,
! [SV396: $i,SV68: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV68 @ SV396 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV396 @ SV68 @ tc_nat )
| ( SV396 = SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1580,plain,
! [SV397: $i,SV69: $i] :
( ( ! [SY1564: $i] :
( ~ ( class_Orderings_Olinorder @ SV69 )
| ( c_HOL_Oord__class_Oless @ SV397 @ SY1564 @ SV69 )
| ( c_HOL_Oord__class_Oless @ SY1564 @ SV397 @ SV69 )
| ( SY1564 = SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1581,plain,
! [SV398: $i,SV70: $i] :
( ( ! [SY1565: $i] :
( ~ ( class_Orderings_Olinorder @ SV70 )
| ( c_HOL_Oord__class_Oless @ SV398 @ SY1565 @ SV70 )
| ( SY1565 = SV398 )
| ( c_HOL_Oord__class_Oless @ SY1565 @ SV398 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1582,plain,
! [SV399: $i,SV71: $i] :
( ( ! [SY1566: $i] :
( ~ ( class_Orderings_Olinorder @ SV71 )
| ( SV399 = SY1566 )
| ( c_HOL_Oord__class_Oless @ SV399 @ SY1566 @ SV71 )
| ( c_HOL_Oord__class_Oless @ SY1566 @ SV399 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1583,plain,
! [SV72: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV72 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= SV72 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV72 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1584,plain,
! [SV73: $i] :
( ( ( SV73
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV73 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV73 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1585,plain,
! [SV400: $i,SV74: $i] :
( ( ! [SY1567: $i,SY1568: $i,SY1569: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV74 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV400 @ SY1567 @ SV74 ) @ ( c_HOL_Oplus__class_Oplus @ SY1568 @ SY1569 @ SV74 ) @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SY1567 @ SY1569 @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV400 @ SY1568 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1586,plain,
! [SV401: $i,SV75: $i] :
( ( ! [SY1570: $i,SY1571: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV75 @ SV401 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY1570 @ SY1571 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV401 @ SY1571 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV75 @ SY1570 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1587,plain,
! [SV402: $i,SV76: $i] :
( ( ! [SY1572: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV76 )
| ( c_HOL_Oord__class_Oless @ SV402 @ SY1572 @ SV76 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV402 @ SY1572 @ SV76 ) @ ( c_HOL_Ozero__class_Ozero @ SV76 ) @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1588,plain,
! [SV403: $i,SV77: $i] :
( ( ! [SY1573: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV77 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SY1573 @ SV77 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SV403 @ SY1573 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1589,plain,
! [SV404: $i,SV78: $i] :
( ( ! [SY1574: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV78 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV404 @ SV78 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1574 @ SV78 ) @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV404 @ SY1574 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1590,plain,
! [SV405: $i,SV79: $i] :
( ( ! [SY1575: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 )
| ( c_HOL_Oord__class_Oless @ SV405 @ SY1575 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV405 @ SV79 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1575 @ SV79 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1591,plain,
! [SV406: $i,SV82: $i] :
( ( ! [SY1576: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV82 ) @ SV406 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1576 @ SV406 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV82 @ SY1576 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1592,plain,
! [SV83: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV83 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ ( c_HOL_Oone__class_Oone @ SV83 ) @ SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1593,plain,
! [SV407: $i,SV84: $i] :
( ( ! [SY1577: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV84 )
| ( ( c_HOL_Otimes__class_Otimes @ SV407 @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SY1577 @ SV84 ) @ SV84 )
= ( c_HOL_Otimes__class_Otimes @ SV407 @ SY1577 @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1594,plain,
! [SV408: $i,SV85: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV85 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV408 @ SV85 ) @ SV85 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV408 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1595,plain,
! [SV409: $i,SV86: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV86 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV409 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV409 @ SV86 ) @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1596,plain,
! [SV87: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV87 @ tc_nat )
= $true )
| ( ( SV87
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1265]) ).
thf(1597,plain,
! [SV410: $i,SV88: $i] :
( ( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV88 @ SV410 )
= SV88 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1598,plain,
! [SV411: $i,SV89: $i] :
( ( ! [SY1578: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV89 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SY1578 @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SY1578 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1599,plain,
! [SV412: $i,SV90: $i] :
( ( ! [SY1579: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV90 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV412 @ SY1579 @ SV90 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SY1579 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV412 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1600,plain,
! [SV413: $i,SV91: $i] :
( ( ! [SY1580: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV91 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV413 @ SY1580 @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SY1580 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV413 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1601,plain,
! [SV414: $i,SV92: $i] :
( ( ( c_Lambda_Osubstn @ SV92 @ SV414 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Lambda_Osubst @ SV92 @ SV414 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1602,plain,
! [SV415: $i,SV93: $i] :
( ( ! [SY1581: $i,SY1582: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV93 )
| ( c_HOL_Oord__class_Oless @ SV415 @ ( c_HOL_Oplus__class_Oplus @ SY1581 @ SY1582 @ SV93 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV415 @ SY1582 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SY1581 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1603,plain,
! [SV416: $i,SV94: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV94 @ SV416 @ tc_nat ) @ SV94 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1604,plain,
! [SV417: $i,SV95: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV95 @ SV417 @ tc_nat ) @ SV417 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1605,plain,
! [SV418: $i,SV96: $i] :
( ( ! [SY1583: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV96 @ SV418 @ tc_nat ) @ SY1583 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV96 @ ( c_HOL_Ominus__class_Ominus @ SY1583 @ SV418 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1606,plain,
! [SV419: $i,SV97: $i] :
( ( ! [SY1584: $i] :
( ( c_HOL_Oord__class_Oless @ SV97 @ ( c_HOL_Ominus__class_Ominus @ SV419 @ SY1584 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV97 @ SY1584 @ tc_nat ) @ SV419 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1607,plain,
! [SV420: $i,SV98: $i] :
( ( ! [SY1585: $i,SY1586: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV98 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV420 @ SY1585 @ SV98 ) @ ( c_HOL_Oplus__class_Oplus @ SY1586 @ SY1585 @ SV98 ) @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV420 @ SY1586 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1608,plain,
! [SV421: $i,SV99: $i] :
( ( ! [SY1587: $i,SY1588: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV99 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV421 @ SY1587 @ SV99 ) @ ( c_HOL_Oplus__class_Oplus @ SY1588 @ SY1587 @ SV99 ) @ SV99 )
| ~ ( c_HOL_Oord__class_Oless @ SV421 @ SY1588 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1609,plain,
! [SV422: $i,SV100: $i] :
( ( ! [SY1589: $i,SY1590: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV100 )
| ( c_HOL_Oord__class_Oless @ SV422 @ SY1589 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV422 @ SY1590 @ SV100 ) @ ( c_HOL_Oplus__class_Oplus @ SY1589 @ SY1590 @ SV100 ) @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1610,plain,
! [SV423: $i,SV101: $i] :
( ( ! [SY1591: $i,SY1592: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV101 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SY1591 @ SV101 ) @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SY1592 @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SY1591 @ SY1592 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1611,plain,
! [SV424: $i,SV102: $i] :
( ( ! [SY1593: $i,SY1594: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV102 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SY1593 @ SV102 ) @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SY1594 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SY1593 @ SY1594 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1612,plain,
! [SV425: $i,SV103: $i] :
( ( ! [SY1595: $i,SY1596: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV103 )
| ( c_HOL_Oord__class_Oless @ SV425 @ SY1595 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1596 @ SV425 @ SV103 ) @ ( c_HOL_Oplus__class_Oplus @ SY1596 @ SY1595 @ SV103 ) @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1613,plain,
! [SV426: $i,SV104: $i] :
( ( ! [SY1597: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV104 @ SV426 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY1597 @ SV426 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV104 @ SY1597 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1614,plain,
! [SV427: $i,SV105: $i] :
( ( ! [SY1598: $i] :
( ( c_HOL_Oord__class_Oless @ SV105 @ SV427 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1598 @ SV105 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY1598 @ SV427 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1615,plain,
! [SV428: $i,SV106: $i] :
( ( ! [SY1599: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV106 @ SV428 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV106 @ SY1599 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV428 @ SY1599 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1616,plain,
! [SV429: $i,SV107: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV107 )
| ( ( c_HOL_Otimes__class_Otimes @ SV429 @ SV429 @ SV107 )
= SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1617,plain,
! [SV430: $i,SV108: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV108 @ SV430 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV430 @ SV108 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1618,plain,
! [SV431: $i,SV109: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV109 @ SV431 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV431 @ SV109 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1619,plain,
! [SV432: $i,SV110: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV110 @ SV432 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV110 ) @ SV432 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1620,plain,
! [SV433: $i,SV111: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV111 @ ( c_Suc @ SV433 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV111 @ SV433 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1621,plain,
! [SV112: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV112 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ SV112 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ SV112 ) @ SV112 )
= ( c_HOL_Ozero__class_Ozero @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1622,plain,
! [SV434: $i,SV113: $i] :
( ( ! [SY1600: $i,SY1601: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV113 )
| ( c_HOL_Oord__class_Oless @ SV434 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
| ( c_HOL_Oord__class_Oless @ SY1600 @ SY1601 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1600 @ SV434 @ SV113 ) @ ( c_HOL_Otimes__class_Otimes @ SY1601 @ SV434 @ SV113 ) @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1623,plain,
! [SV435: $i,SV114: $i] :
( ( ! [SY1602: $i,SY1603: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV114 )
| ( c_HOL_Oord__class_Oless @ SV435 @ SY1602 @ SV114 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SY1603 @ SV114 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1602 @ SY1603 @ SV114 ) @ ( c_HOL_Otimes__class_Otimes @ SV435 @ SY1603 @ SV114 ) @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1624,plain,
! [SV436: $i,SV115: $i] :
( ( ! [SY1604: $i,SY1605: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV115 )
| ( c_HOL_Oord__class_Oless @ SV436 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
| ( c_HOL_Oord__class_Oless @ SY1604 @ SY1605 @ SV115 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SY1604 @ SV115 ) @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SY1605 @ SV115 ) @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1625,plain,
! [SV437: $i,SV116: $i] :
( ( ! [SY1606: $i,SY1607: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV116 )
| ( c_HOL_Oord__class_Oless @ SV437 @ SY1606 @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SY1607 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1607 @ SY1606 @ SV116 ) @ ( c_HOL_Otimes__class_Otimes @ SY1607 @ SV437 @ SV116 ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1626,plain,
! [SV117: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV117 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV117 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV117 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1627,plain,
! [SV438: $i,SV118: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV118 @ SV438 @ tc_nat ) @ SV118 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV118 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV438 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1628,plain,
! [SV439: $i,SV119: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV119 @ ( c_HOL_Ominus__class_Ominus @ SV439 @ SV119 @ tc_nat ) @ tc_nat )
= SV439 )
| ( c_HOL_Oord__class_Oless @ SV439 @ SV119 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1629,plain,
! [SV440: $i,SV120: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV120 @ ( c_Suc @ SV440 ) @ tc_nat ) @ SV120 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV120 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1630,plain,
! [SV441: $i,SV121: $i] :
( ( ! [SY1608: $i,SY1609: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV121 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV441 @ SY1608 @ SV121 ) @ SY1609 @ SV121 )
= ( c_HOL_Otimes__class_Otimes @ SV441 @ ( c_HOL_Otimes__class_Otimes @ SY1608 @ SY1609 @ SV121 ) @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1631,plain,
! [SV442: $i,SV122: $i] :
( ( ! [SY1610: $i,SY1611: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV122 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV442 @ SY1610 @ SV122 ) @ SY1611 @ SV122 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV442 @ SY1611 @ SV122 ) @ SY1610 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1632,plain,
! [SV443: $i,SV123: $i] :
( ( ! [SY1612: $i,SY1613: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV123 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV443 @ SY1612 @ SV123 ) @ SY1613 @ SV123 )
= ( c_HOL_Otimes__class_Otimes @ SV443 @ ( c_HOL_Otimes__class_Otimes @ SY1612 @ SY1613 @ SV123 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1633,plain,
! [SV444: $i,SV124: $i] :
( ( ! [SY1614: $i,SY1615: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV124 )
| ( ( c_HOL_Otimes__class_Otimes @ SV444 @ ( c_HOL_Otimes__class_Otimes @ SY1614 @ SY1615 @ SV124 ) @ SV124 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV444 @ SY1614 @ SV124 ) @ SY1615 @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1634,plain,
! [SV445: $i,SV125: $i] :
( ( ! [SY1616: $i,SY1617: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
| ( ( c_HOL_Otimes__class_Otimes @ SV445 @ ( c_HOL_Otimes__class_Otimes @ SY1616 @ SY1617 @ SV125 ) @ SV125 )
= ( c_HOL_Otimes__class_Otimes @ SY1616 @ ( c_HOL_Otimes__class_Otimes @ SV445 @ SY1617 @ SV125 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1635,plain,
! [SV446: $i,SV126: $i] :
( ( ! [SY1618: $i,SY1619: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV126 )
| ( ( c_HOL_Otimes__class_Otimes @ SV446 @ ( c_HOL_Otimes__class_Otimes @ SY1618 @ SY1619 @ SV126 ) @ SV126 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV446 @ SY1618 @ SV126 ) @ SY1619 @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1636,plain,
! [SV447: $i,SV127: $i] :
( ( ! [SY1620: $i,SY1621: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV447 @ SY1620 @ SV127 ) @ SY1621 @ SV127 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV447 @ SY1621 @ SV127 ) @ ( c_HOL_Otimes__class_Otimes @ SY1620 @ SY1621 @ SV127 ) @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1637,plain,
! [SV448: $i,SV128: $i] :
( ( ! [SY1622: $i,SY1623: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV128 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV448 @ SY1622 @ SV128 ) @ SY1623 @ SV128 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV448 @ SY1623 @ SV128 ) @ ( c_HOL_Otimes__class_Otimes @ SY1622 @ SY1623 @ SV128 ) @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1638,plain,
! [SV449: $i,SV129: $i] :
( ( ! [SY1624: $i,SY1625: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV129 )
| ( ( c_HOL_Otimes__class_Otimes @ SV449 @ ( c_HOL_Oplus__class_Oplus @ SY1624 @ SY1625 @ SV129 ) @ SV129 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV449 @ SY1624 @ SV129 ) @ ( c_HOL_Otimes__class_Otimes @ SV449 @ SY1625 @ SV129 ) @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1639,plain,
! [SV450: $i,SV130: $i] :
( ( ! [SY1626: $i] :
( ~ ( class_Orderings_Oorder @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV450 @ SY1626 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SY1626 @ SV450 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1640,plain,
! [SV451: $i,SV131: $i] :
( ( ! [SY1627: $i] :
( ~ ( class_Orderings_Olinorder @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ SV451 @ SY1627 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ SY1627 @ SV451 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1641,plain,
! [SV452: $i,SV132: $i] :
( ( ! [SY1628: $i] :
( ~ ( class_Orderings_Opreorder @ SV132 )
| ~ ( c_HOL_Oord__class_Oless @ SV452 @ SY1628 @ SV132 )
| ~ ( c_HOL_Oord__class_Oless @ SY1628 @ SV452 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1642,plain,
! [SV453: $i,SV133: $i] :
( ( ! [SY1629: $i] :
( ~ ( class_Orderings_Opreorder @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SV453 @ SY1629 @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SY1629 @ SV453 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1643,plain,
! [SV454: $i,SV134: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV134 )
| ( ( c_HOL_Otimes__class_Otimes @ SV454 @ ( c_HOL_Oone__class_Oone @ SV134 ) @ SV134 )
= SV454 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1644,plain,
! [SV455: $i,SV135: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV135 )
| ( ( c_HOL_Otimes__class_Otimes @ SV455 @ ( c_HOL_Oone__class_Oone @ SV135 ) @ SV135 )
= SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1645,plain,
! [SV456: $i,SV136: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV136 ) @ SV456 @ SV136 )
= SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1646,plain,
! [SV457: $i,SV137: $i] :
( ( ! [SY1630: $i,SY1631: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV137 )
| ~ ( class_Int_Onumber__ring @ SV137 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SY1630 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SY1631 @ SV137 ) @ SV137 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SY1631 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SY1630 @ SV137 ) @ SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1647,plain,
! [SV458: $i,SV138: $i] :
( ( ! [SY1632: $i,SY1633: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV138 )
| ~ ( class_Int_Onumber__ring @ SV138 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SY1632 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SY1633 @ SV138 ) @ SV138 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SY1633 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SY1632 @ SV138 ) @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1648,plain,
! [SV139: $i] :
( ( ( SV139
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV139 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1649,plain,
! [SV459: $i,SV140: $i] :
( ( ! [SY1634: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV140 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV459 @ SY1634 @ SV140 ) @ SY1634 @ SV140 )
= SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1650,plain,
! [SV460: $i,SV141: $i] :
( ( ! [SY1635: $i] :
( ( c_Lambda_Osubstn @ SV141 @ SV460 @ SY1635 )
= ( c_Lambda_Osubst @ SV141 @ ( c_Lambda_Oliftn @ SY1635 @ SV460 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1651,plain,
! [SV461: $i,SV142: $i] :
( ( ! [SY1636: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV142 )
| ( ( c_HOL_Otimes__class_Otimes @ SV461 @ SY1636 @ SV142 )
= ( c_HOL_Otimes__class_Otimes @ SY1636 @ SV461 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1652,plain,
! [SV143: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV143 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV143 ) @ ( c_HOL_Ozero__class_Ozero @ SV143 ) @ SV143 )
= ( c_HOL_Ozero__class_Ozero @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1653,plain,
! [SV462: $i,SV144: $i] :
( ( ! [SY1637: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
| ( ( c_HOL_Otimes__class_Otimes @ SV462 @ SY1637 @ SV144 )
= ( c_HOL_Otimes__class_Otimes @ SY1637 @ SV462 @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1654,plain,
! [SV463: $i,SV145: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV145 @ SV463 @ tc_nat ) @ ( c_Suc @ SV145 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1655,plain,
! [SV464: $i,SV146: $i] :
( ( ! [SY1638: $i,SY1639: $i] :
( ~ ( class_Orderings_Opreorder @ SV146 )
| ( c_HOL_Oord__class_Oless @ SV464 @ SY1638 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SY1639 @ SY1638 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SV464 @ SY1639 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1656,plain,
! [SV465: $i,SV147: $i] :
( ( ! [SY1640: $i,SY1641: $i] :
( ~ ( class_Orderings_Oorder @ SV147 )
| ( c_HOL_Oord__class_Oless @ SV465 @ SY1640 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SV465 @ SY1641 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SY1641 @ SY1640 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1657,plain,
! [SV466: $i,SV148: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV148 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV466 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV466 @ SV148 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1658,plain,
! [SV149: $i] :
( ( c_HOL_Oord__class_Oless @ SV149 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1659,plain,
! [SV150: $i] :
( ( c_HOL_Oord__class_Oless @ SV150 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1660,plain,
! [SV467: $i,SV151: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV151 @ ( c_HOL_Oplus__class_Oplus @ SV151 @ SV467 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1661,plain,
! [SV468: $i,SV152: $i] :
( ( ! [SY1642: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV152 @ SV468 @ tc_nat ) @ SY1642 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV152 @ ( c_HOL_Oplus__class_Oplus @ SV468 @ SY1642 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1662,plain,
! [SV469: $i,SV153: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV153 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV469 ) @ SV153 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV153 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV469 @ SV153 ) @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1663,plain,
! [SV470: $i,SV154: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ SV154 ) @ SV470 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV154 @ ( c_Suc @ SV470 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1664,plain,
! [SV471: $i,SV156: $i] :
( ( ! [SY1643: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV156 @ SV471 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY1643 @ SV471 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV156 @ SY1643 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1665,plain,
! [SV472: $i,SV157: $i] :
( ( ! [SY1644: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV157 @ SV472 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV157 @ SY1644 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV472 @ SY1644 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1666,plain,
! [SV473: $i,SV160: $i] :
( ( ! [SY1645: $i,SY1646: $i,SY1647: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV160 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV473 @ SY1645 @ SV160 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1646 @ SY1645 @ SV160 ) @ SY1647 @ SV160 ) @ SV160 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV473 @ SY1646 @ SV160 ) @ SY1645 @ SV160 ) @ SY1647 @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1667,plain,
! [SV161: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV161 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV161 )
= ( c_HOL_Ozero__class_Ozero @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1668,plain,
! [SV474: $i,SV162: $i] :
( ( ! [SY1648: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV162 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SY1648 @ SV162 ) @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SY1648 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV474 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1669,plain,
! [SV475: $i,SV163: $i] :
( ( ! [SY1649: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV163 @ SV475 @ tc_nat ) @ SY1649 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV163 @ SY1649 @ tc_nat ) @ SV475 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1670,plain,
! [SV476: $i,SV164: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SV476 @ SV164 ) @ ( c_HOL_Ozero__class_Ozero @ SV164 ) @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1671,plain,
! [SV477: $i,SV165: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV165 ) @ SV477 @ tc_nat )
| ( ( c_Suc @ SV165 )
= SV477 )
| ~ ( c_HOL_Oord__class_Oless @ SV165 @ SV477 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1672,plain,
! [SV478: $i,SV166: $i] :
( ( ! [SY1650: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV166 ) @ SV478 @ tc_nat ) @ ( c_Suc @ SY1650 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV166 @ SV478 @ tc_nat ) @ SY1650 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1673,plain,
! [SV479: $i,SV167: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV167 @ ( c_Suc @ SV479 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV167 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV479 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1674,plain,
! [SV480: $i,SV168: $i] :
( ( ! [SY1651: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV168 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV480 @ SV480 @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SY1651 @ SY1651 @ SV168 ) @ SV168 ) @ SV168 )
| ( SV480
= ( c_HOL_Ozero__class_Ozero @ SV168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1675,plain,
! [SV481: $i,SV169: $i] :
( ( ! [SY1652: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV169 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV481 @ SV481 @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SY1652 @ SY1652 @ SV169 ) @ SV169 ) @ SV169 )
| ( SY1652
= ( c_HOL_Ozero__class_Ozero @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1676,plain,
! [SV482: $i,SV170: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV170 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV482 @ SV170 ) @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1677,plain,
! [SV483: $i,SV171: $i] :
( ( ! [SY1653: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV171 ) @ SV483 @ SY1653 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV171 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1653 @ SV171 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1678,plain,
! [SV484: $i,SV172: $i] :
( ( ! [SY1654: $i] :
( ( ( c_Lambda_Oliftn @ SV172 @ ( c_Lambda_OdB_OVar @ SV484 ) @ SY1654 )
= ( c_Lambda_OdB_OVar @ SV484 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV484 @ SY1654 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1679,plain,
! [SV485: $i,SV173: $i] :
( ( ! [SY1655: $i,SY1656: $i] :
( ( c_Lambda_Oliftn @ SV173 @ ( c_Lambda_OdB_OApp @ SV485 @ SY1655 ) @ SY1656 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV173 @ SV485 @ SY1656 ) @ ( c_Lambda_Oliftn @ SV173 @ SY1655 @ SY1656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1680,plain,
! [SV486: $i,SV174: $i] :
( ( ! [SY1657: $i,SY1658: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV174 )
| ( c_HOL_Oord__class_Oless @ SV486 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV486 @ SV174 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SY1657 @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SY1658 @ SV174 ) @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1681,plain,
! [SV487: $i,SV175: $i] :
( ( ! [SY1659: $i,SY1660: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV175 )
| ( c_HOL_Oord__class_Oless @ SV487 @ SY1659 @ SV175 )
| ( c_HOL_Oord__class_Oless @ SY1659 @ SV487 @ SV175 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1660 @ SY1659 @ SV175 ) @ ( c_HOL_Otimes__class_Otimes @ SY1660 @ SV487 @ SV175 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1682,plain,
! [SV488: $i,SV176: $i] :
( ( ! [SY1661: $i,SY1662: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV176 )
| ( c_HOL_Oord__class_Oless @ SV488 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV488 @ SV176 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1661 @ SV488 @ SV176 ) @ ( c_HOL_Otimes__class_Otimes @ SY1662 @ SV488 @ SV176 ) @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1683,plain,
! [SV489: $i,SV177: $i] :
( ( ! [SY1663: $i,SY1664: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV177 )
| ( c_HOL_Oord__class_Oless @ SV489 @ SY1663 @ SV177 )
| ( c_HOL_Oord__class_Oless @ SY1663 @ SV489 @ SV177 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1663 @ SY1664 @ SV177 ) @ ( c_HOL_Otimes__class_Otimes @ SV489 @ SY1664 @ SV177 ) @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1684,plain,
! [SV490: $i,SV178: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV178 @ SV178 @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV178 ) @ SV490 @ SV178 )
= ( c_Lambda_Oliftn @ SV178 @ SV490 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1685,plain,
! [SV179: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV179 @ SV179 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV179 @ ( c_Suc @ SV179 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1686,plain,
! [SV491: $i,SV180: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV180 @ SV491 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV491 @ ( c_Suc @ SV180 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1687,plain,
! [SV492: $i,SV181: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV181 @ ( c_Suc @ SV492 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV492 @ SV181 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1688,plain,
! [SV493: $i,SV182: $i] :
( ( ! [SY1665: $i,SY1666: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV182 )
| ( c_HOL_Oord__class_Oless @ SV493 @ SY1665 @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1666 @ SY1665 @ SV182 ) @ ( c_HOL_Otimes__class_Otimes @ SY1666 @ SV493 @ SV182 ) @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SY1666 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1689,plain,
! [SV494: $i,SV183: $i] :
( ( ! [SY1667: $i,SY1668: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV183 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SY1667 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SY1668 @ SV183 ) @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SY1668 @ SY1667 @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1690,plain,
! [SV495: $i,SV184: $i] :
( ( ! [SY1669: $i,SY1670: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV184 )
| ( c_HOL_Oord__class_Oless @ SV495 @ SY1669 @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1670 @ SV495 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SY1670 @ SY1669 @ SV184 ) @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV184 ) @ SY1670 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1691,plain,
! [SV496: $i,SV185: $i] :
( ( ! [SY1671: $i,SY1672: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV185 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SY1671 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SY1672 @ SV185 ) @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SY1671 @ SY1672 @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV185 ) @ SV496 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1692,plain,
! [SV497: $i,SV186: $i] :
( ( ! [SY1673: $i,SY1674: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV186 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SY1673 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SY1674 @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SV497 @ ( c_HOL_Ozero__class_Ozero @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SY1674 @ SY1673 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1693,plain,
! [SV498: $i,SV187: $i] :
( ( ! [SY1675: $i,SY1676: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV187 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SY1675 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SY1676 @ SV187 ) @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SV498 @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ SY1675 @ SY1676 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1694,plain,
! [SV499: $i,SV188: $i] :
( ( ! [SY1677: $i,SY1678: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV188 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SY1677 @ SV188 ) @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SY1678 @ SV188 ) @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ SY1677 @ SY1678 @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV188 ) @ SV499 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1695,plain,
! [SV500: $i,SV189: $i] :
( ( ! [SY1679: $i,SY1680: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV189 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SY1679 @ SV189 ) @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SY1680 @ SV189 ) @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SY1680 @ SY1679 @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SV500 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1696,plain,
! [SV501: $i,SV190: $i] :
( ( ! [SY1681: $i,SY1682: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV190 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV501 @ SY1681 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SY1682 @ SY1681 @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SY1681 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SY1682 @ SV501 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1697,plain,
! [SV502: $i,SV191: $i] :
( ( ! [SY1683: $i,SY1684: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV191 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SY1683 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SY1684 @ SY1683 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SY1683 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV502 @ SY1684 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1698,plain,
! [SV503: $i,SV192: $i] :
( ( ! [SY1685: $i,SY1686: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV192 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV503 @ SY1685 @ SV192 ) @ ( c_HOL_Otimes__class_Otimes @ SY1686 @ SY1685 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SV503 @ SY1686 @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SY1685 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1699,plain,
! [SV504: $i,SV193: $i] :
( ( ! [SY1687: $i,SY1688: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV193 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV504 @ SY1687 @ SV193 ) @ ( c_HOL_Otimes__class_Otimes @ SY1688 @ SY1687 @ SV193 ) @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SY1688 @ SV504 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SY1687 @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1700,plain,
! [SV505: $i,SV194: $i] :
( ( ! [SY1689: $i,SY1690: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV194 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SY1689 @ SV194 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SY1690 @ SV194 ) @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV505 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ SY1689 @ SY1690 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1701,plain,
! [SV195: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV195 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV195 ) @ ( c_HOL_Oone__class_Oone @ SV195 ) @ SV195 ) @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1702,plain,
! [SV506: $i,SV196: $i] :
( ( ! [SY1691: $i,SY1692: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV196 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SY1691 @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SY1692 @ SY1691 @ SV196 ) @ SV196 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV506 @ SY1692 @ SV196 ) @ SY1691 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1703,plain,
! [SV507: $i,SV197: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV197 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV507 @ SV197 )
= SV507 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1704,plain,
! [SV508: $i,SV198: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV198 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV508 @ SV198 )
= SV508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1705,plain,
! [SV509: $i,SV202: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV202 )
| ~ ( class_Int_Onumber__ring @ SV202 )
| ( SV509
= ( c_HOL_Oplus__class_Oplus @ SV509 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1706,plain,
! [SV510: $i,SV203: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV203 )
| ( ( c_HOL_Oplus__class_Oplus @ SV510 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
= SV510 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1707,plain,
! [SV511: $i,SV204: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV204 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV511 @ SV204 )
= SV511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1708,plain,
! [SV512: $i,SV205: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV205 )
| ( ( c_HOL_Oplus__class_Oplus @ SV512 @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV205 )
= SV512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1709,plain,
! [SV513: $i,SV206: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV206 )
| ( ( c_HOL_Oplus__class_Oplus @ SV513 @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV206 )
= SV513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1710,plain,
! [SV514: $i,SV207: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV207 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV207 ) @ SV514 @ SV207 )
= SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1711,plain,
! [SV208: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV208 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ SV208 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ SV208 ) @ SV208 ) @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1712,plain,
! [SV515: $i,SV209: $i] :
( ( ! [SY1693: $i,SY1694: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OApp @ SV209 @ SV515 ) @ SY1693 @ SY1694 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV209 @ SY1693 @ SY1694 ) @ ( c_Lambda_Osubstn @ SV515 @ SY1693 @ SY1694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1713,plain,
! [SV516: $i,SV210: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV210 @ SV516 @ tc_nat ) @ SV516 @ tc_nat )
= SV210 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1714,plain,
! [SV517: $i,SV211: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV211 @ SV517 @ tc_nat ) @ SV211 @ tc_nat )
= SV517 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1715,plain,
! [SV518: $i,SV212: $i] :
( ( ! [SY1695: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV212 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV518 @ SY1695 @ SV212 ) @ SY1695 @ SV212 )
= SV518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1716,plain,
! [SV519: $i,SV213: $i] :
( ( ! [SY1696: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV213 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV519 @ SY1696 @ SV213 ) @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SY1696 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV519 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1717,plain,
! [SV520: $i,SV214: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV214 ) @ ( c_Suc @ SV520 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV214 @ SV520 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1718,plain,
! [SV521: $i,SV215: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV215 @ SV521 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV215 ) @ ( c_Suc @ SV521 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1719,plain,
! [SV522: $i,SV216: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV216 ) @ ( c_Suc @ SV522 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV216 @ SV522 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1720,plain,
! [SV523: $i,SV217: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV217 @ SV523 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV523 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1721,plain,
! [SV524: $i,SV218: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV218 @ SV524 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV218 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1722,plain,
! [SV525: $i,SV219: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV219 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV525 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ ( c_HOL_Oplus__class_Oplus @ SV525 @ SV525 @ SV219 ) @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1723,plain,
! [SV526: $i,SV220: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV220 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ ( c_HOL_Oplus__class_Oplus @ SV526 @ SV526 @ SV220 ) @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV526 @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1724,plain,
! [SV527: $i,SV221: $i] :
( ( ( SV221
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV527 @ SV221 ) ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV527 ) @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1725,plain,
! [SV528: $i,SV222: $i] :
( ( ! [SY1697: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV222 @ SV528 ) @ ( c_Suc @ SY1697 ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV222 @ SY1697 ) @ SV528 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV528 @ ( c_HOL_Oplus__class_Oplus @ SY1697 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1726,plain,
! [SV529: $i,SV223: $i] :
( ( ! [SY1698: $i,SY1699: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ SV223 @ SV529 @ SY1698 ) @ SY1699 )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV223 @ ( c_HOL_Oplus__class_Oplus @ SY1699 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ SV529 @ SY1699 ) @ SY1698 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1698 @ ( c_HOL_Oplus__class_Oplus @ SY1699 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1727,plain,
! [SV530: $i,SV224: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV224 ) @ SV530 )
= ( c_Lambda_OdB_OVar @ SV224 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV224 @ SV530 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1728,plain,
! [SV531: $i,SV225: $i] :
( ( ! [SY1700: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV225 @ SV531 ) @ ( c_Lambda_OdB_OApp @ SY1700 @ SV531 ) )
| ~ ( c_Lambda_Obeta @ SV225 @ SY1700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1729,plain,
! [SV532: $i,SV226: $i] :
( ( ! [SY1701: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV226 @ SV532 ) @ ( c_Lambda_OdB_OApp @ SV226 @ SY1701 ) )
| ~ ( c_Lambda_Obeta @ SV532 @ SY1701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1730,plain,
! [SV533: $i,SV227: $i] :
( ( ! [SY1702: $i,SY1703: $i,SY1704: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SY1702 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SY1703 @ SY1704 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SY1703 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SY1702 @ SY1704 @ SV227 ) @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1731,plain,
! [SV534: $i,SV228: $i] :
( ( ! [SY1705: $i,SY1706: $i,SY1707: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ ( c_Lambda_Olift @ SV534 @ SY1705 ) @ ( c_Suc @ SY1706 ) ) @ ( c_Lambda_Osubst @ SY1707 @ SV534 @ SY1706 ) @ SY1705 )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ SY1707 @ SY1705 ) @ SV534 @ SY1706 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1705 @ ( c_HOL_Oplus__class_Oplus @ SY1706 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1732,plain,
! [SV535: $i,SV229: $i] :
( ( ! [SY1708: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ SV229 ) @ SV535 @ SY1708 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ SV229 @ ( c_Lambda_Olift @ SV535 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Oplus__class_Oplus @ SY1708 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1733,plain,
! [SV536: $i,SV230: $i] :
( ( ! [SY1709: $i,SY1710: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ SV230 @ SV536 @ SY1709 ) @ SY1710 )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV230 @ SY1710 ) @ ( c_Lambda_Olift @ SV536 @ SY1710 ) @ ( c_HOL_Oplus__class_Oplus @ SY1709 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1710 @ ( c_HOL_Oplus__class_Oplus @ SY1709 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1734,plain,
! [SV231: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV231 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV231 )
= ( c_HOL_Oone__class_Oone @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1735,plain,
! [SV537: $i,SV232: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV232 @ SV232 @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV232 ) @ SV537 @ SV232 )
= SV537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1736,plain,
! [SV538: $i,SV233: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV233 ) @ SV538 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ SV233 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ SV233 @ SV538 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1737,plain,
! [SV539: $i,SV234: $i] :
( ( ! [SY1711: $i,SY1712: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV234 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV539 @ SY1711 @ SV234 ) @ SY1712 @ SV234 )
= ( c_HOL_Oplus__class_Oplus @ SV539 @ ( c_HOL_Oplus__class_Oplus @ SY1711 @ SY1712 @ SV234 ) @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1738,plain,
! [SV540: $i,SV235: $i] :
( ( ! [SY1713: $i,SY1714: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV235 )
| ( ( c_HOL_Oplus__class_Oplus @ SV540 @ ( c_HOL_Oplus__class_Oplus @ SY1713 @ SY1714 @ SV235 ) @ SV235 )
= ( c_HOL_Oplus__class_Oplus @ SY1713 @ ( c_HOL_Oplus__class_Oplus @ SV540 @ SY1714 @ SV235 ) @ SV235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1739,plain,
! [SV541: $i,SV236: $i] :
( ( ! [SY1715: $i,SY1716: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV236 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV541 @ SY1715 @ SV236 ) @ SY1716 @ SV236 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV541 @ SY1716 @ SV236 ) @ SY1715 @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1740,plain,
! [SV542: $i,SV237: $i] :
( ( ! [SY1717: $i,SY1718: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 )
| ( ( c_HOL_Oplus__class_Oplus @ SV542 @ ( c_HOL_Oplus__class_Oplus @ SY1717 @ SY1718 @ SV237 ) @ SV237 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV542 @ SY1717 @ SV237 ) @ SY1718 @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1741,plain,
! [SV543: $i,SV238: $i] :
( ( ! [SY1719: $i,SY1720: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV238 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV543 @ SY1719 @ SV238 ) @ SY1720 @ SV238 )
= ( c_HOL_Oplus__class_Oplus @ SV543 @ ( c_HOL_Oplus__class_Oplus @ SY1719 @ SY1720 @ SV238 ) @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1742,plain,
! [SV544: $i,SV239: $i] :
( ( ! [SY1721: $i,SY1722: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV239 )
| ( ( c_HOL_Oplus__class_Oplus @ SV544 @ ( c_HOL_Oplus__class_Oplus @ SY1721 @ SY1722 @ SV239 ) @ SV239 )
= ( c_HOL_Oplus__class_Oplus @ SY1721 @ ( c_HOL_Oplus__class_Oplus @ SV544 @ SY1722 @ SV239 ) @ SV239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1743,plain,
! [SV545: $i,SV240: $i] :
( ( ! [SY1723: $i,SY1724: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV240 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV545 @ SY1723 @ SV240 ) @ SY1724 @ SV240 )
= ( c_HOL_Oplus__class_Oplus @ SV545 @ ( c_HOL_Oplus__class_Oplus @ SY1723 @ SY1724 @ SV240 ) @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1744,plain,
! [SV546: $i,SV241: $i] :
( ( ! [SY1725: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV241 @ SV546 @ tc_nat ) @ SY1725 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV241 @ ( c_HOL_Oplus__class_Oplus @ SV546 @ SY1725 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1745,plain,
! [SV547: $i,SV242: $i] :
( ( ! [SY1726: $i] :
( ( c_HOL_Oplus__class_Oplus @ SV242 @ ( c_HOL_Oplus__class_Oplus @ SV547 @ SY1726 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV547 @ ( c_HOL_Oplus__class_Oplus @ SV242 @ SY1726 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1746,plain,
! [SV548: $i,SV243: $i] :
( ( ! [SY1727: $i,SY1728: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV243 )
| ( ( c_HOL_Oplus__class_Oplus @ SV548 @ ( c_HOL_Oplus__class_Oplus @ SY1727 @ SY1728 @ SV243 ) @ SV243 )
= ( c_HOL_Oplus__class_Oplus @ SY1727 @ ( c_HOL_Oplus__class_Oplus @ SV548 @ SY1728 @ SV243 ) @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1747,plain,
! [SV549: $i,SV244: $i] :
( ( ! [SY1729: $i,SY1730: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV244 )
| ( ( c_HOL_Oplus__class_Oplus @ SV549 @ ( c_HOL_Oplus__class_Oplus @ SY1729 @ SY1730 @ SV244 ) @ SV244 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV549 @ SY1729 @ SV244 ) @ SY1730 @ SV244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1748,plain,
! [SV550: $i,SV245: $i] :
( ( ! [SY1731: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV245 ) @ SV550 @ SY1731 )
= ( c_Lambda_OdB_OVar @ SV245 ) )
| ( SV245 = SY1731 )
| ( c_HOL_Oord__class_Oless @ SY1731 @ SV245 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1749,plain,
! [SV551: $i,SV246: $i] :
( ( ! [SY1732: $i,SY1733: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV246 @ SV551 @ SY1732 ) @ ( c_Lambda_Osubst @ SY1733 @ SV551 @ SY1732 ) )
| ~ ( c_Lambda_Obeta @ SV246 @ SY1733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1750,plain,
! [SV552: $i,SV249: $i] :
( ( ! [SY1734: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ SV249 ) @ SV552 @ SY1734 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ SV249 @ SV552 @ ( c_HOL_Oplus__class_Oplus @ SY1734 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1751,plain,
! [SV553: $i,SV250: $i] :
( ( ! [SY1735: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV250 )
| ( ( c_HOL_Oplus__class_Oplus @ SV553 @ SY1735 @ SV250 )
= ( c_HOL_Oplus__class_Oplus @ SY1735 @ SV553 @ SV250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1752,plain,
! [SV554: $i,SV251: $i] :
( ( ! [SY1736: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV251 )
| ( ( c_HOL_Oplus__class_Oplus @ SV554 @ SY1736 @ SV251 )
= ( c_HOL_Oplus__class_Oplus @ SY1736 @ SV554 @ SV251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1753,plain,
! [SV555: $i,SV252: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV252 @ SV555 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV555 @ SV252 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1754,plain,
! [SV556: $i,SV253: $i] :
( ( ! [SY1737: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV253 )
| ( ( c_HOL_Oplus__class_Oplus @ SV556 @ SY1737 @ SV253 )
= ( c_HOL_Oplus__class_Oplus @ SY1737 @ SV556 @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1755,plain,
! [SV557: $i,SV254: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV254 )
| ( ( c_HOL_Oplus__class_Oplus @ SV557 @ SV557 @ SV254 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV254 ) @ ( c_HOL_Oone__class_Oone @ SV254 ) @ SV254 ) @ SV557 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1756,plain,
! [SV558: $i,SV255: $i] :
( ( ! [SY1738: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV255 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV558 @ SY1738 @ SV255 ) @ SY1738 @ SV255 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV558 @ ( c_HOL_Oone__class_Oone @ SV255 ) @ SV255 ) @ SY1738 @ SV255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1757,plain,
! [SV559: $i,SV256: $i] :
( ( ! [SY1739: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
| ( ( c_HOL_Oplus__class_Oplus @ SV559 @ ( c_HOL_Otimes__class_Otimes @ SY1739 @ SV559 @ SV256 ) @ SV256 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY1739 @ ( c_HOL_Oone__class_Oone @ SV256 ) @ SV256 ) @ SV559 @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1758,plain,
! [SV560: $i,SV257: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV257 ) @ SV560 ) @ ( c_Lambda_Osubst @ SV257 @ SV560 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1759,plain,
! [SV561: $i,SV258: $i] :
( ( ! [SY1740: $i] :
( ( c_Lambda_Oliftn @ SV258 @ ( c_Lambda_OdB_OAbs @ SV561 ) @ SY1740 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ SV258 @ SV561 @ ( c_HOL_Oplus__class_Oplus @ SY1740 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1760,plain,
! [SV562: $i,SV259: $i] :
( ( ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV259 ) @ SV562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1761,plain,
! [SV563: $i,SV260: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV260 )
| ( c_HOL_Oord__class_Oless @ SV563 @ ( c_HOL_Oplus__class_Oplus @ SV563 @ ( c_HOL_Oone__class_Oone @ SV260 ) @ SV260 ) @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1762,plain,
! [SV564: $i,SV261: $i] :
( ( ( c_Lambda_Obeta @ SV261 @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV261 @ SV564 ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV261 ) @ SV564 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1763,plain,
! [SV565: $i,SV262: $i] :
( ( ! [SY1741: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV262 ) @ SV565 @ SY1741 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV262 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1741 @ SV262 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1764,plain,
! [SV566: $i,SV263: $i] :
( ( ! [SY1742: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV263 ) @ SV566 @ SY1742 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV263 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1742 @ SV263 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1765,plain,
! [SV567: $i,SV264: $i] :
( ( ! [SY1743: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV264 ) @ SV567 @ SY1743 )
= ( c_Lambda_OdB_OVar @ SV264 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV264 @ SY1743 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1766,plain,
! [SV568: $i,SV265: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV265 ) @ SV568 @ SV265 )
= SV568 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1767,plain,
! [SV569: $i,SV266: $i] :
( ( ! [SY1744: $i,SY1745: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ SV266 @ SV569 ) @ SY1744 @ SY1745 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV266 @ SY1744 @ SY1745 ) @ ( c_Lambda_Osubst @ SV569 @ SY1744 @ SY1745 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1768,plain,
! [SV570: $i,SV267: $i] :
( ( ! [SY1746: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV267 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SV570 @ SY1746 @ tc_nat ) @ SV267 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV570 @ SV267 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1746 @ SV267 ) @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1769,plain,
! [SV571: $i,SV268: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ SV268 ) @ SV571 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Olift @ SV268 @ ( c_HOL_Oplus__class_Oplus @ SV571 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1770,plain,
! [SV572: $i,SV269: $i] :
( ( ! [SY1747: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ SV269 @ SV572 ) @ SY1747 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV269 @ SY1747 ) @ ( c_Lambda_Olift @ SV572 @ SY1747 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1771,plain,
! [SV270: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV270 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1772,plain,
! [SV573: $i,SV271: $i] :
( ( ! [SY1748: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV271 @ SV573 ) @ SY1748 @ SV573 )
= SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1773,plain,
! [SV574: $i,SV272: $i] :
( ( ! [SY1749: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV272 @ SV574 ) @ ( c_Lambda_Olift @ SY1749 @ SV574 ) )
| ~ ( c_Lambda_Obeta @ SV272 @ SY1749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1774,plain,
! [SV575: $i,SV273: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV273 ) @ ( c_Lambda_OdB_OAbs @ SV575 ) )
| ~ ( c_Lambda_Obeta @ SV273 @ SV575 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1775,plain,
! [SV576: $i,SV274: $i] :
( ( ! [SY1750: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV274 )
| ( ( c_HOL_Ominus__class_Ominus @ SV576 @ SY1750 @ SV274 )
!= ( c_HOL_Ozero__class_Ozero @ SV274 ) )
| ( SV576 = SY1750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1776,plain,
! [SV577: $i,SV275: $i] :
( ( ! [SY1751: $i,SY1752: $i,SY1753: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV275 )
| ( ( c_HOL_Oplus__class_Oplus @ SV577 @ ( c_HOL_Oplus__class_Oplus @ SY1751 @ SY1752 @ SV275 ) @ SV275 )
!= ( c_HOL_Oplus__class_Oplus @ SY1751 @ SY1753 @ SV275 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV577 @ SY1752 @ SV275 )
= SY1753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1777,plain,
! [SV276: $i] :
( ( ( c_Suc @ SV276 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1778,plain,
! [SV578: $i,SV277: $i] :
( ( ! [SY1754: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV277 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV578 @ SV277 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1754 @ SV277 ) )
| ( SV578 = SY1754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1779,plain,
! [SV579: $i,SV278: $i] :
( ( ! [SY1755: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV278 @ SV579 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV278 @ SY1755 @ tc_nat ) )
| ( SV579 = SY1755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1780,plain,
! [SV279: $i] :
( ( ( c_Suc @ SV279 )
= SV279 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1781,plain,
! [SV580: $i,SV280: $i] :
( ( ! [SY1756: $i,SY1757: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV280 )
| ( ( c_HOL_Oplus__class_Oplus @ SV580 @ SY1756 @ SV280 )
!= ( c_HOL_Oplus__class_Oplus @ SV580 @ SY1757 @ SV280 ) )
| ( SY1756 = SY1757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1782,plain,
! [SV581: $i,SV281: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV281 )
!= ( c_Lambda_OdB_OVar @ SV581 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1783,plain,
! [SV282: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV282 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1462]) ).
thf(1784,plain,
! [SV582: $i,SV283: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV283 )
| ( ( c_HOL_Oplus__class_Oplus @ SV582 @ SV582 @ SV283 )
!= ( c_HOL_Ozero__class_Ozero @ SV283 ) )
| ( SV582
= ( c_HOL_Ozero__class_Ozero @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1785,plain,
! [SV583: $i,SV284: $i] :
( ( ! [SY1758: $i] :
( ( c_Lambda_OdB_OApp @ SV284 @ SV583 )
!= ( c_Lambda_OdB_OVar @ SY1758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1786,plain,
! [SV584: $i,SV285: $i] :
( ( ! [SY1759: $i,SY1760: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV285 )
| ( ( c_HOL_Ominus__class_Ominus @ SV584 @ SY1759 @ SV285 )
!= ( c_HOL_Ominus__class_Ominus @ SY1760 @ SY1760 @ SV285 ) )
| ( SV584 = SY1759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1787,plain,
! [SV585: $i,SV286: $i] :
( ( ! [SY1761: $i,SY1762: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV286 @ SV585 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY1761 @ SY1762 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1761 @ SV585 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV286 @ SY1762 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1788,plain,
! [SV586: $i,SV287: $i] :
( ( ! [SY1763: $i,SY1764: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV287 )
| ( ( c_HOL_Oplus__class_Oplus @ SV586 @ SY1763 @ SV287 )
!= ( c_HOL_Oplus__class_Oplus @ SY1764 @ SY1763 @ SV287 ) )
| ( SV586 = SY1764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1789,plain,
! [SV587: $i,SV288: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV288 @ SV587 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV587
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1790,plain,
! [SV289: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV289 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1791,plain,
! [SV588: $i,SV290: $i] :
( ( ! [SY1765: $i,SY1766: $i,SY1767: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV290 )
| ~ ( class_Int_Onumber__ring @ SV290 )
| ( ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SY1765 @ SY1766 @ SV290 ) @ SV290 )
!= ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SY1765 @ SY1767 @ SV290 ) @ SV290 ) )
| ( SY1766 = SY1767 )
| ( SY1765
= ( c_HOL_Ozero__class_Ozero @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1792,plain,
! [SV589: $i,SV291: $i] :
( ( ! [SY1768: $i,SY1769: $i,SY1770: $i,SY1771: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV291 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV589 @ SY1768 @ SV291 ) @ SY1769 @ SV291 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1770 @ SY1768 @ SV291 ) @ SY1771 @ SV291 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV589 @ SY1770 @ SV291 ) @ SY1768 @ SV291 ) @ SY1769 @ SV291 )
= SY1771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1793,plain,
! [SV590: $i,SV292: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV292 @ SV590 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV292
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV292
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1794,plain,
! [SV591: $i,SV293: $i] :
( ( ! [SY1772: $i,SY1773: $i,SY1774: $i,SY1775: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV293 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV591 @ SY1772 @ SV293 ) @ SY1773 @ SV293 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1774 @ SY1772 @ SV293 ) @ SY1775 @ SV293 ) )
| ( SY1773
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1774 @ SV591 @ SV293 ) @ SY1772 @ SV293 ) @ SY1775 @ SV293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1795,plain,
! [SV592: $i,SV294: $i] :
( ( ! [SY1776: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV294 )
| ( ( c_HOL_Otimes__class_Otimes @ SV592 @ SY1776 @ SV294 )
!= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SY1776
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SV592
= ( c_HOL_Ozero__class_Ozero @ SV294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1796,plain,
! [SV593: $i,SV295: $i] :
( ( ! [SY1777: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV295 @ SV593 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY1777 @ SV593 @ tc_nat ) )
| ( SV295 = SY1777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1797,plain,
! [SV594: $i,SV296: $i] :
( ( ! [SY1778: $i] :
( ( c_Lambda_OdB_OApp @ SV296 @ SV594 )
!= ( c_Lambda_OdB_OAbs @ SY1778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1798,plain,
! [SV595: $i,SV297: $i] :
( ( ! [SY1779: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV297 )
| ~ ( class_Int_Onumber__ring @ SV297 )
| ( ( c_HOL_Ominus__class_Ominus @ SV595 @ SY1779 @ SV297 )
!= ( c_HOL_Ozero__class_Ozero @ SV297 ) )
| ( SV595 = SY1779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1799,plain,
! [SV298: $i] :
( ( ( c_Suc @ SV298 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1800,plain,
! [SV596: $i,SV299: $i] :
( ( ! [SY1780: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV299 )
| ( ( c_HOL_Otimes__class_Otimes @ SV596 @ SY1780 @ SV299 )
!= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
| ( SV596
= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
| ( SY1780
= ( c_HOL_Ozero__class_Ozero @ SV299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1801,plain,
! [SV597: $i,SV300: $i] :
( ( ! [SY1781: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV300 @ SV597 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV300 @ SY1781 @ tc_nat ) )
| ( SV597 = SY1781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1802,plain,
! [SV598: $i,SV301: $i] :
( ( ! [SY1782: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV301 )
| ( ( c_HOL_Otimes__class_Otimes @ SV598 @ SY1782 @ SV301 )
!= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
| ( SY1782
= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
| ( SV598
= ( c_HOL_Ozero__class_Ozero @ SV301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1803,plain,
! [SV599: $i,SV302: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV302 @ SV599 @ tc_nat ) )
| ( SV302
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV302
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1804,plain,
! [SV303: $i] :
( ( SV303
= ( c_Suc @ SV303 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1805,plain,
! [SV600: $i,SV304: $i] :
( ( ! [SY1783: $i] :
( ( c_Lambda_OdB_OAbs @ SV304 )
!= ( c_Lambda_OdB_OApp @ SV600 @ SY1783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1806,plain,
! [SV305: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV305 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV305 )
!= ( c_HOL_Oone__class_Oone @ SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1807,plain,
! [SV601: $i,SV306: $i] :
( ( ! [SY1784: $i,SY1785: $i,SY1786: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV306 )
| ~ ( class_Int_Onumber__ring @ SV306 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SY1784 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SY1785 @ SY1786 @ SV306 ) @ SV306 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SY1786 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SY1785 @ SY1784 @ SV306 ) @ SV306 ) )
| ( SY1784 = SY1786 )
| ( SV601 = SY1785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1808,plain,
! [SV602: $i,SV307: $i] :
( ( ! [SY1787: $i,SY1788: $i,SY1789: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV307 )
| ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SY1787 @ SV307 )
!= ( c_HOL_Ominus__class_Ominus @ SY1788 @ SY1789 @ SV307 ) )
| ( c_HOL_Oord__class_Oless @ SV602 @ SY1787 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SY1788 @ SY1789 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1809,plain,
! [SV603: $i,SV308: $i] :
( ( ! [SY1790: $i,SY1791: $i] :
( ( ( c_Lambda_OdB_OApp @ SV308 @ SV603 )
!= ( c_Lambda_OdB_OApp @ SY1790 @ SY1791 ) )
| ( SV603 = SY1791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1810,plain,
! [SV604: $i,SV309: $i] :
( ( ! [SY1792: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV604 @ SV604 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SY1792 @ SY1792 @ SV309 ) @ SV309 )
!= ( c_HOL_Ozero__class_Ozero @ SV309 ) )
| ( SY1792
= ( c_HOL_Ozero__class_Ozero @ SV309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1811,plain,
! [SV605: $i,SV310: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV310 )
!= ( c_Lambda_OdB_OAbs @ SV605 ) )
| ( SV310 = SV605 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1812,plain,
! [SV606: $i,SV311: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV311 @ SV606 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV606
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV311
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1813,plain,
! [SV607: $i,SV312: $i] :
( ( ( c_Lambda_OdB_OVar @ SV312 )
!= ( c_Lambda_OdB_OAbs @ SV607 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1814,plain,
! [SV608: $i,SV313: $i] :
( ( ! [SY1793: $i,SY1794: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV313 )
| ~ ( class_Int_Onumber__ring @ SV313 )
| ( ( c_HOL_Oplus__class_Oplus @ SV608 @ SY1793 @ SV313 )
!= ( c_HOL_Oplus__class_Oplus @ SV608 @ SY1794 @ SV313 ) )
| ( SY1793 = SY1794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1815,plain,
! [SV609: $i,SV314: $i] :
( ( ! [SY1795: $i,SY1796: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV314 )
| ( ( c_HOL_Ominus__class_Ominus @ SV609 @ SV609 @ SV314 )
!= ( c_HOL_Ominus__class_Ominus @ SY1795 @ SY1796 @ SV314 ) )
| ( SY1795 = SY1796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1816,plain,
! [SV610: $i,SV315: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV315 @ SV610 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV315
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV610
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1817,plain,
! [SV611: $i,SV316: $i] :
( ( ! [SY1797: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV316 )
| ~ ( class_Int_Onumber__ring @ SV316 )
| ( SV611
!= ( c_HOL_Oplus__class_Oplus @ SV611 @ SY1797 @ SV316 ) )
| ( SY1797
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1818,plain,
! [SV612: $i,SV317: $i] :
( ( ! [SY1798: $i,SY1799: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV317 )
| ( ( c_HOL_Oplus__class_Oplus @ SV612 @ SY1798 @ SV317 )
!= ( c_HOL_Oplus__class_Oplus @ SV612 @ SY1799 @ SV317 ) )
| ( SY1798 = SY1799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1819,plain,
! [SV613: $i,SV318: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV318 @ SV613 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV613
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV613
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1820,plain,
! [SV614: $i,SV319: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV319 @ SV614 @ tc_nat ) )
| ( SV614
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV614
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1821,plain,
! [SV615: $i,SV320: $i] :
( ( ! [SY1800: $i] :
( ( c_Lambda_OdB_OVar @ SV320 )
!= ( c_Lambda_OdB_OApp @ SV615 @ SY1800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1822,plain,
! [SV616: $i,SV321: $i] :
( ( ! [SY1801: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV321 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV616 @ SV616 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SY1801 @ SY1801 @ SV321 ) @ SV321 )
!= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV616
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1823,plain,
! [SV617: $i,SV322: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV322 @ SV617 @ tc_nat )
!= SV322 )
| ( SV617
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1824,plain,
! [SV618: $i,SV323: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV323 @ SV618 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV618 @ SV323 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV618 = SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1825,plain,
! [SV619: $i,SV324: $i] :
( ( ( SV324
!= ( c_HOL_Oplus__class_Oplus @ SV324 @ SV619 @ tc_nat ) )
| ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1826,plain,
! [SV620: $i,SV325: $i] :
( ( ! [SY1802: $i,SY1803: $i,SY1804: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SY1802 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SY1803 @ SY1804 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SY1803 @ SY1804 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV620 @ SY1802 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1827,plain,
! [SV621: $i,SV326: $i] :
( ( ! [SY1805: $i,SY1806: $i] :
( ( ( c_Lambda_OdB_OApp @ SV326 @ SV621 )
!= ( c_Lambda_OdB_OApp @ SY1805 @ SY1806 ) )
| ( SV326 = SY1805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1828,plain,
! [SV622: $i,SV327: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV327 @ SV622 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV327
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1829,plain,
! [SV623: $i,SV328: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV328 @ SV623 @ tc_nat ) )
| ( SV623
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV328
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1830,plain,
! [SV624: $i,SV329: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV329 @ SV624 @ tc_nat ) )
| ( SV329
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV624
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1831,plain,
! [SV625: $i,SV330: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV330 )
!= ( c_Lambda_OdB_OVar @ SV625 ) )
| ( SV330 = SV625 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1832,plain,
! [SV626: $i,SV331: $i] :
( ( ! [SY1807: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV331 )
| ( ( c_HOL_Ominus__class_Ominus @ SV626 @ SY1807 @ SV331 )
!= ( c_HOL_Ozero__class_Ozero @ SV331 ) )
| ( SV626 = SY1807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1833,plain,
! [SV627: $i,SV332: $i] :
( ( ! [SY1808: $i,SY1809: $i,SY1810: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV332 )
| ~ ( class_Int_Onumber__ring @ SV332 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SY1808 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SY1809 @ SY1810 @ SV332 ) @ SV332 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SY1810 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SY1809 @ SY1808 @ SV332 ) @ SV332 ) )
| ( SY1808 = SY1810 )
| ( SV627 = SY1809 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1834,plain,
! [SV333: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV333 ) )
= $true )
| ( ( ( c_HOL_Oone__class_Oone @ SV333 )
!= ( c_HOL_Ozero__class_Ozero @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1835,plain,
! [SV628: $i,SV334: $i] :
( ( ( ( c_Suc @ SV334 )
!= ( c_Suc @ SV628 ) )
| ( SV334 = SV628 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1836,plain,
! [SV629: $i,SV335: $i] :
( ( ( ( c_Suc @ SV335 )
!= ( c_Suc @ SV629 ) )
| ( SV335 = SV629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1837,plain,
! [SV630: $i,SV336: $i,SV2: $i] :
( ( ! [SY1811: $i,SY1812: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV630 @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SY1811 @ SY1812 @ SV2 ) @ SV2 )
= ( c_HOL_Otimes__class_Otimes @ SY1811 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV630 @ SV2 ) @ SY1812 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1838,plain,
! [SV631: $i,SV337: $i,SV3: $i] :
( ( ! [SY1813: $i,SY1814: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV3 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV337 @ SV631 @ SV3 ) @ ( c_HOL_Otimes__class_Otimes @ SY1813 @ SY1814 @ SV3 ) @ SV3 )
= ( c_HOL_Otimes__class_Otimes @ SV337 @ ( c_HOL_Otimes__class_Otimes @ SV631 @ ( c_HOL_Otimes__class_Otimes @ SY1813 @ SY1814 @ SV3 ) @ SV3 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1839,plain,
! [SV632: $i,SV338: $i,SV4: $i] :
( ( ! [SY1815: $i,SY1816: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV338 @ SV632 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SY1815 @ SY1816 @ SV4 ) @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV338 @ SY1815 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SV632 @ SY1816 @ SV4 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1840,plain,
! [SV339: $i,SV5: $i] :
( ( ( SV5 = SV339 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV5 @ ( c_Suc @ SV339 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV5 @ SV339 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1841,plain,
! [SV340: $i,SV6: $i] :
( ( ( SV6 = SV340 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV340 @ ( c_Suc @ SV6 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV340 @ SV6 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1842,plain,
! [SV341: $i,SV7: $i] :
( ( ( SV7 = SV341 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV7 @ SV341 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV7 @ ( c_Suc @ SV341 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1843,plain,
! [SV633: $i,SV343: $i,SV9: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV343 @ SV343 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV633 @ SV633 @ SV9 ) @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1844,plain,
! [SV10: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV10 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_HOL_Ozero__class_Ozero @ SV10 ) @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1845,plain,
! [SV634: $i,SV344: $i,SV11: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV11 ) @ SV344 @ SV634 )
= ( c_Lambda_OdB_OVar @ SV11 ) )
| ( SV11 = SV634 )
| ( c_HOL_Oord__class_Oless @ SV634 @ SV11 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1846,plain,
! [SV635: $i,SV345: $i,SV12: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV12 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SV345 @ SV635 @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SV635 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SV345 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1847,plain,
! [SV636: $i,SV346: $i,SV13: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV13 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SV346 @ SV636 @ SV13 ) @ SV13 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV636 @ SV13 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV346 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1848,plain,
! [SV637: $i,SV347: $i,SV14: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV14 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV347 @ SV14 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV637 @ SV14 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ ( c_HOL_Otimes__class_Otimes @ SV637 @ SV347 @ SV14 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1849,plain,
! [SV638: $i,SV348: $i,SV15: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV15 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV348 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV638 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ ( c_HOL_Otimes__class_Otimes @ SV348 @ SV638 @ SV15 ) @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1850,plain,
! [SV349: $i,SV16: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV16 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV349 @ SV349 @ SV16 ) @ ( c_HOL_Ozero__class_Ozero @ SV16 ) @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SV349 @ ( c_HOL_Ozero__class_Ozero @ SV16 ) @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1851,plain,
! [SV350: $i,SV17: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV17 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV350 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SV350 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1852,plain,
! [SV351: $i,SV18: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV18 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV351 @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV351 @ SV351 @ SV18 ) @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1853,plain,
! [SV352: $i,SV19: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV19 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV352 @ SV352 @ SV19 ) @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
| ~ ( c_HOL_Oord__class_Oless @ SV352 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1533]) ).
thf(1854,plain,
! [SV639: $i,SV353: $i,SV20: $i] :
( ( ! [SY1817: $i,SY1818: $i,SY1819: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV20 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV353 @ SV639 @ SV20 ) @ SY1817 @ SV20 ) @ SY1818 @ SV20 ) @ SY1819 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SY1817 @ SV20 ) @ SY1818 @ SV20 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV639 @ SY1817 @ SV20 ) @ SY1819 @ SV20 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1855,plain,
! [SV640: $i,SV354: $i,SV21: $i] :
( ( ! [SY1820: $i,SY1821: $i,SY1822: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV21 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV354 @ SV640 @ SV21 ) @ SY1820 @ SV21 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1821 @ SV640 @ SV21 ) @ SY1822 @ SV21 ) @ SV21 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV354 @ SY1821 @ SV21 ) @ SV640 @ SV21 ) @ SY1820 @ SV21 ) @ SY1822 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1856,plain,
! [SV641: $i,SV355: $i,SV22: $i] :
( ( ! [SY1823: $i,SY1824: $i,SY1825: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV22 )
| ( c_HOL_Oord__class_Oless @ SV355 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SY1823 @ SV22 ) @ SY1824 @ SV22 ) @ SY1825 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1823 @ SY1824 @ SV22 ) @ SV355 @ SV22 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV641 @ SY1824 @ SV22 ) @ SY1825 @ SV22 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1857,plain,
! [SV642: $i,SV356: $i,SV23: $i] :
( ( ! [SY1826: $i,SY1827: $i,SY1828: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV23 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV356 @ SV642 @ SV23 ) @ SY1826 @ SV23 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1827 @ SV642 @ SV23 ) @ SY1828 @ SV23 ) @ SV23 )
| ~ ( c_HOL_Oord__class_Oless @ SY1826 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1827 @ SV356 @ SV23 ) @ SV642 @ SV23 ) @ SY1828 @ SV23 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1858,plain,
! [SV643: $i,SV357: $i,SV24: $i] :
( ( ( c_Lambda_Oliftn @ ( c_Suc @ SV24 ) @ SV357 @ SV643 )
= ( c_Lambda_Olift @ ( c_Lambda_Oliftn @ SV24 @ SV357 @ SV643 ) @ SV643 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1859,plain,
! [SV358: $i,SV27: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV27 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV27 )
| ( ( c_HOL_Ominus__class_Ominus @ SV358 @ SV358 @ SV27 )
= ( c_HOL_Ozero__class_Ozero @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1539]) ).
thf(1860,plain,
! [SV359: $i,SV28: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV28 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV359 @ SV359 @ SV28 )
= ( c_HOL_Ozero__class_Ozero @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1861,plain,
! [SV360: $i,SV29: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV29 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV360 @ ( c_HOL_Ozero__class_Ozero @ SV29 ) @ SV29 )
= SV360 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1862,plain,
! [SV361: $i,SV30: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV30 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV361 @ SV361 @ SV30 )
= ( c_HOL_Ozero__class_Ozero @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1542]) ).
thf(1863,plain,
! [SV362: $i,SV31: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV31 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV362 @ SV362 @ SV31 )
= ( c_HOL_Ozero__class_Ozero @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1864,plain,
! [SV644: $i,SV363: $i,SV32: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV363 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV644 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV644 @ SV32 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV644 @ SV363 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1865,plain,
! [SV645: $i,SV364: $i,SV34: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV34 @ ( c_HOL_Oplus__class_Oplus @ SV364 @ SV645 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV34 @ SV645 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1866,plain,
! [SV646: $i,SV365: $i,SV35: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV35 @ ( c_HOL_Oplus__class_Oplus @ SV365 @ SV646 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV35 @ SV365 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1867,plain,
! [SV647: $i,SV366: $i,SV36: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV36 @ SV366 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV36 @ SV647 @ tc_nat ) @ SV366 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1868,plain,
! [SV648: $i,SV367: $i,SV37: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV37 @ ( c_HOL_Oplus__class_Oplus @ SV367 @ SV648 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV37 @ SV648 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1869,plain,
! [SV649: $i,SV368: $i,SV38: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV38 @ ( c_HOL_Oplus__class_Oplus @ SV368 @ SV649 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV38 @ SV368 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1870,plain,
! [SV650: $i,SV372: $i,SV42: $i] :
( ( ! [SY1829: $i,SY1830: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV42 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV372 @ SV650 @ SV42 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1829 @ SV372 @ SV42 ) @ SV650 @ SV42 ) @ SY1830 @ SV42 ) @ SV42 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1829 @ SV650 @ SV42 ) @ SY1830 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1871,plain,
! [SV651: $i,SV375: $i,SV45: $i] :
( ( ! [SY1831: $i,SY1832: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV45 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV375 @ SV651 @ SV45 ) @ SY1831 @ SV45 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1832 @ SV651 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV375 @ SY1832 @ SV45 ) @ SV651 @ SV45 ) @ SY1831 @ SV45 ) @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1872,plain,
! [SV376: $i,SV46: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV46 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV46 ) @ SV376 @ SV46 )
= SV376 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1557]) ).
thf(1873,plain,
! [SV377: $i,SV47: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV47 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV377 @ SV47 )
= SV377 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1558]) ).
thf(1874,plain,
! [SV378: $i,SV48: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV48 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV48 ) @ SV378 @ SV48 )
= SV378 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1875,plain,
! [SV379: $i,SV49: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV379 @ SV49 )
= ( c_HOL_Ozero__class_Ozero @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1560]) ).
thf(1876,plain,
! [SV380: $i,SV50: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV380 @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV50 )
= ( c_HOL_Ozero__class_Ozero @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1877,plain,
! [SV381: $i,SV51: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV51 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV381 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 )
= ( c_HOL_Ozero__class_Ozero @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1878,plain,
! [SV382: $i,SV52: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV52 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV382 @ SV52 )
= ( c_HOL_Ozero__class_Ozero @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1879,plain,
! [SV383: $i,SV53: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV53 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV383 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
= ( c_HOL_Ozero__class_Ozero @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1564]) ).
thf(1880,plain,
! [SV384: $i,SV54: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV54 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV384 @ SV54 )
= ( c_HOL_Ozero__class_Ozero @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1565]) ).
thf(1881,plain,
! [SV385: $i,SV55: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV385 @ SV55 )
= ( c_HOL_Ozero__class_Ozero @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1882,plain,
! [SV386: $i,SV56: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV56 @ SV386 @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV56 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ SV386 @ tc_nat ) ) )
= $true )
| ( ( SV56
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1883,plain,
! [SV652: $i,SV387: $i,SV57: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV57 @ SV387 @ tc_nat ) @ SV652 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV57 @ SV652 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1884,plain,
! [SV388: $i,SV60: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV60 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV388 @ SV388 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1885,plain,
! [SV389: $i,SV61: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV61 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV389 @ SV389 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1886,plain,
! [SV390: $i,SV62: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV62 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV390 @ SV390 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1573]) ).
thf(1887,plain,
! [SV653: $i,SV391: $i,SV63: $i] :
( ( ( ( c_Lambda_Oliftn @ SV63 @ ( c_Lambda_OdB_OVar @ SV391 ) @ SV653 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ SV391 @ SV63 @ tc_nat ) ) )
| ( c_HOL_Oord__class_Oless @ SV391 @ SV653 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1888,plain,
! [SV654: $i,SV392: $i,SV64: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV64 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ ( c_HOL_Oplus__class_Oplus @ SV392 @ SV654 @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV654 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV392 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1889,plain,
! [SV655: $i,SV393: $i,SV65: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV65 )
| ( c_HOL_Oord__class_Oless @ SV393 @ SV655 @ SV65 )
| ( c_HOL_Oord__class_Oless @ SV655 @ SV393 @ SV65 )
| ( SV655 = SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1890,plain,
! [SV656: $i,SV394: $i,SV66: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV66 )
| ( SV394 = SV656 )
| ( c_HOL_Oord__class_Oless @ SV656 @ SV394 @ SV66 )
| ( c_HOL_Oord__class_Oless @ SV394 @ SV656 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1891,plain,
! [SV395: $i,SV67: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV67 @ SV395 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV395 @ SV67 @ tc_nat )
| ( SV395 = SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1578]) ).
thf(1892,plain,
! [SV396: $i,SV68: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV68 @ SV396 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV396 @ SV68 @ tc_nat )
| ( SV396 = SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1893,plain,
! [SV657: $i,SV397: $i,SV69: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV69 )
| ( c_HOL_Oord__class_Oless @ SV397 @ SV657 @ SV69 )
| ( c_HOL_Oord__class_Oless @ SV657 @ SV397 @ SV69 )
| ( SV657 = SV397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1894,plain,
! [SV658: $i,SV398: $i,SV70: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV70 )
| ( c_HOL_Oord__class_Oless @ SV398 @ SV658 @ SV70 )
| ( SV658 = SV398 )
| ( c_HOL_Oord__class_Oless @ SV658 @ SV398 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1895,plain,
! [SV659: $i,SV399: $i,SV71: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV71 )
| ( SV399 = SV659 )
| ( c_HOL_Oord__class_Oless @ SV399 @ SV659 @ SV71 )
| ( c_HOL_Oord__class_Oless @ SV659 @ SV399 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1896,plain,
! [SV72: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV72 @ tc_nat )
= $false )
| ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV72 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1897,plain,
! [SV73: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV73 @ tc_nat )
= $false )
| ( ( SV73
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV73 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1584]) ).
thf(1898,plain,
! [SV660: $i,SV400: $i,SV74: $i] :
( ( ! [SY1833: $i,SY1834: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV74 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV400 @ SV660 @ SV74 ) @ ( c_HOL_Oplus__class_Oplus @ SY1833 @ SY1834 @ SV74 ) @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV660 @ SY1834 @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV400 @ SY1833 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1899,plain,
! [SV661: $i,SV401: $i,SV75: $i] :
( ( ! [SY1835: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV75 @ SV401 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV661 @ SY1835 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV401 @ SY1835 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV75 @ SV661 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1900,plain,
! [SV662: $i,SV402: $i,SV76: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV76 )
| ( c_HOL_Oord__class_Oless @ SV402 @ SV662 @ SV76 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV402 @ SV662 @ SV76 ) @ ( c_HOL_Ozero__class_Ozero @ SV76 ) @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1901,plain,
! [SV663: $i,SV403: $i,SV77: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV77 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SV663 @ SV77 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SV403 @ SV663 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(1902,plain,
! [SV664: $i,SV404: $i,SV78: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV78 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV404 @ SV78 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV664 @ SV78 ) @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV404 @ SV664 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1903,plain,
! [SV665: $i,SV405: $i,SV79: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 )
| ( c_HOL_Oord__class_Oless @ SV405 @ SV665 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV405 @ SV79 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV665 @ SV79 ) @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1904,plain,
! [SV666: $i,SV406: $i,SV82: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV82 ) @ SV406 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV666 @ SV406 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV82 @ SV666 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1905,plain,
! [SV83: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV83 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV83 ) @ ( c_HOL_Oone__class_Oone @ SV83 ) @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1906,plain,
! [SV667: $i,SV407: $i,SV84: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV84 )
| ( ( c_HOL_Otimes__class_Otimes @ SV407 @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SV667 @ SV84 ) @ SV84 )
= ( c_HOL_Otimes__class_Otimes @ SV407 @ SV667 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1907,plain,
! [SV408: $i,SV85: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV85 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV408 @ SV85 ) @ SV85 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV408 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1594]) ).
thf(1908,plain,
! [SV409: $i,SV86: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV86 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV409 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV409 @ SV86 ) @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1909,plain,
! [SV668: $i,SV411: $i,SV89: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV89 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SV668 @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV668 @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1910,plain,
! [SV669: $i,SV412: $i,SV90: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV90 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV412 @ SV669 @ SV90 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV412 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(1911,plain,
! [SV670: $i,SV413: $i,SV91: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV91 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV413 @ SV670 @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV670 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV413 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1912,plain,
! [SV671: $i,SV415: $i,SV93: $i] :
( ( ! [SY1836: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV93 )
| ( c_HOL_Oord__class_Oless @ SV415 @ ( c_HOL_Oplus__class_Oplus @ SV671 @ SY1836 @ SV93 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV415 @ SY1836 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV671 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1913,plain,
! [SV416: $i,SV94: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV94 @ SV416 @ tc_nat ) @ SV94 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1914,plain,
! [SV417: $i,SV95: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV95 @ SV417 @ tc_nat ) @ SV417 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1915,plain,
! [SV672: $i,SV418: $i,SV96: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV96 @ SV418 @ tc_nat ) @ SV672 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV96 @ ( c_HOL_Ominus__class_Ominus @ SV672 @ SV418 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1916,plain,
! [SV673: $i,SV419: $i,SV97: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV97 @ ( c_HOL_Ominus__class_Ominus @ SV419 @ SV673 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV97 @ SV673 @ tc_nat ) @ SV419 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1917,plain,
! [SV674: $i,SV420: $i,SV98: $i] :
( ( ! [SY1837: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV98 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV420 @ SV674 @ SV98 ) @ ( c_HOL_Oplus__class_Oplus @ SY1837 @ SV674 @ SV98 ) @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV420 @ SY1837 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(1918,plain,
! [SV675: $i,SV421: $i,SV99: $i] :
( ( ! [SY1838: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV99 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV421 @ SV675 @ SV99 ) @ ( c_HOL_Oplus__class_Oplus @ SY1838 @ SV675 @ SV99 ) @ SV99 )
| ~ ( c_HOL_Oord__class_Oless @ SV421 @ SY1838 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1919,plain,
! [SV676: $i,SV422: $i,SV100: $i] :
( ( ! [SY1839: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV100 )
| ( c_HOL_Oord__class_Oless @ SV422 @ SV676 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV422 @ SY1839 @ SV100 ) @ ( c_HOL_Oplus__class_Oplus @ SV676 @ SY1839 @ SV100 ) @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1920,plain,
! [SV677: $i,SV423: $i,SV101: $i] :
( ( ! [SY1840: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV101 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SV677 @ SV101 ) @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SY1840 @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SY1840 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(1921,plain,
! [SV678: $i,SV424: $i,SV102: $i] :
( ( ! [SY1841: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV102 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SV678 @ SV102 ) @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SY1841 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SV678 @ SY1841 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1922,plain,
! [SV679: $i,SV425: $i,SV103: $i] :
( ( ! [SY1842: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV103 )
| ( c_HOL_Oord__class_Oless @ SV425 @ SV679 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1842 @ SV425 @ SV103 ) @ ( c_HOL_Oplus__class_Oplus @ SY1842 @ SV679 @ SV103 ) @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1923,plain,
! [SV680: $i,SV426: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV104 @ SV426 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV680 @ SV426 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV104 @ SV680 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1924,plain,
! [SV681: $i,SV427: $i,SV105: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV105 @ SV427 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV681 @ SV105 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV681 @ SV427 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1925,plain,
! [SV682: $i,SV428: $i,SV106: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV106 @ SV428 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV106 @ SV682 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV428 @ SV682 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1926,plain,
! [SV429: $i,SV107: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV107 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV429 @ SV429 @ SV107 )
= SV429 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1927,plain,
! [SV430: $i,SV108: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV108 @ SV430 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV430 @ SV108 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(1928,plain,
! [SV431: $i,SV109: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV109 @ SV431 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV431 @ SV109 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1618]) ).
thf(1929,plain,
! [SV432: $i,SV110: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV110 @ SV432 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV110 ) @ SV432 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1619]) ).
thf(1930,plain,
! [SV433: $i,SV111: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV111 @ ( c_Suc @ SV433 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV111 @ SV433 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1620]) ).
thf(1931,plain,
! [SV112: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV112 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ SV112 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ SV112 ) @ SV112 )
= ( c_HOL_Ozero__class_Ozero @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1932,plain,
! [SV683: $i,SV434: $i,SV113: $i] :
( ( ! [SY1843: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV113 )
| ( c_HOL_Oord__class_Oless @ SV434 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
| ( c_HOL_Oord__class_Oless @ SV683 @ SY1843 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV683 @ SV434 @ SV113 ) @ ( c_HOL_Otimes__class_Otimes @ SY1843 @ SV434 @ SV113 ) @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1933,plain,
! [SV684: $i,SV435: $i,SV114: $i] :
( ( ! [SY1844: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV114 )
| ( c_HOL_Oord__class_Oless @ SV435 @ SV684 @ SV114 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SY1844 @ SV114 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV684 @ SY1844 @ SV114 ) @ ( c_HOL_Otimes__class_Otimes @ SV435 @ SY1844 @ SV114 ) @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1934,plain,
! [SV685: $i,SV436: $i,SV115: $i] :
( ( ! [SY1845: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV115 )
| ( c_HOL_Oord__class_Oless @ SV436 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
| ( c_HOL_Oord__class_Oless @ SV685 @ SY1845 @ SV115 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV685 @ SV115 ) @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SY1845 @ SV115 ) @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1935,plain,
! [SV686: $i,SV437: $i,SV116: $i] :
( ( ! [SY1846: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV116 )
| ( c_HOL_Oord__class_Oless @ SV437 @ SV686 @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SY1846 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1846 @ SV686 @ SV116 ) @ ( c_HOL_Otimes__class_Otimes @ SY1846 @ SV437 @ SV116 ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1936,plain,
! [SV117: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV117 @ tc_nat )
= $false )
| ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV117 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1937,plain,
! [SV438: $i,SV118: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV118 @ SV438 @ tc_nat ) @ SV118 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV118 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV438 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1938,plain,
! [SV439: $i,SV119: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV119 @ ( c_HOL_Ominus__class_Ominus @ SV439 @ SV119 @ tc_nat ) @ tc_nat )
= SV439 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV439 @ SV119 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1628]) ).
thf(1939,plain,
! [SV440: $i,SV120: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV120 @ ( c_Suc @ SV440 ) @ tc_nat ) @ SV120 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV120 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1940,plain,
! [SV687: $i,SV441: $i,SV121: $i] :
( ( ! [SY1847: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV121 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV441 @ SV687 @ SV121 ) @ SY1847 @ SV121 )
= ( c_HOL_Otimes__class_Otimes @ SV441 @ ( c_HOL_Otimes__class_Otimes @ SV687 @ SY1847 @ SV121 ) @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1941,plain,
! [SV688: $i,SV442: $i,SV122: $i] :
( ( ! [SY1848: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV122 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV442 @ SV688 @ SV122 ) @ SY1848 @ SV122 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV442 @ SY1848 @ SV122 ) @ SV688 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1942,plain,
! [SV689: $i,SV443: $i,SV123: $i] :
( ( ! [SY1849: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV123 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV443 @ SV689 @ SV123 ) @ SY1849 @ SV123 )
= ( c_HOL_Otimes__class_Otimes @ SV443 @ ( c_HOL_Otimes__class_Otimes @ SV689 @ SY1849 @ SV123 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1943,plain,
! [SV690: $i,SV444: $i,SV124: $i] :
( ( ! [SY1850: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV124 )
| ( ( c_HOL_Otimes__class_Otimes @ SV444 @ ( c_HOL_Otimes__class_Otimes @ SV690 @ SY1850 @ SV124 ) @ SV124 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV444 @ SV690 @ SV124 ) @ SY1850 @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1944,plain,
! [SV691: $i,SV445: $i,SV125: $i] :
( ( ! [SY1851: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
| ( ( c_HOL_Otimes__class_Otimes @ SV445 @ ( c_HOL_Otimes__class_Otimes @ SV691 @ SY1851 @ SV125 ) @ SV125 )
= ( c_HOL_Otimes__class_Otimes @ SV691 @ ( c_HOL_Otimes__class_Otimes @ SV445 @ SY1851 @ SV125 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1945,plain,
! [SV692: $i,SV446: $i,SV126: $i] :
( ( ! [SY1852: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV126 )
| ( ( c_HOL_Otimes__class_Otimes @ SV446 @ ( c_HOL_Otimes__class_Otimes @ SV692 @ SY1852 @ SV126 ) @ SV126 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV446 @ SV692 @ SV126 ) @ SY1852 @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(1946,plain,
! [SV693: $i,SV447: $i,SV127: $i] :
( ( ! [SY1853: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV447 @ SV693 @ SV127 ) @ SY1853 @ SV127 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV447 @ SY1853 @ SV127 ) @ ( c_HOL_Otimes__class_Otimes @ SV693 @ SY1853 @ SV127 ) @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1947,plain,
! [SV694: $i,SV448: $i,SV128: $i] :
( ( ! [SY1854: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV128 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV448 @ SV694 @ SV128 ) @ SY1854 @ SV128 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV448 @ SY1854 @ SV128 ) @ ( c_HOL_Otimes__class_Otimes @ SV694 @ SY1854 @ SV128 ) @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1948,plain,
! [SV695: $i,SV449: $i,SV129: $i] :
( ( ! [SY1855: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV129 )
| ( ( c_HOL_Otimes__class_Otimes @ SV449 @ ( c_HOL_Oplus__class_Oplus @ SV695 @ SY1855 @ SV129 ) @ SV129 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV449 @ SV695 @ SV129 ) @ ( c_HOL_Otimes__class_Otimes @ SV449 @ SY1855 @ SV129 ) @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1949,plain,
! [SV696: $i,SV450: $i,SV130: $i] :
( ( ~ ( class_Orderings_Oorder @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV450 @ SV696 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV696 @ SV450 @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1950,plain,
! [SV697: $i,SV451: $i,SV131: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ SV451 @ SV697 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ SV697 @ SV451 @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1951,plain,
! [SV698: $i,SV452: $i,SV132: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV132 )
| ~ ( c_HOL_Oord__class_Oless @ SV452 @ SV698 @ SV132 )
| ~ ( c_HOL_Oord__class_Oless @ SV698 @ SV452 @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(1952,plain,
! [SV699: $i,SV453: $i,SV133: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SV453 @ SV699 @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SV699 @ SV453 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1953,plain,
! [SV454: $i,SV134: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV134 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV454 @ ( c_HOL_Oone__class_Oone @ SV134 ) @ SV134 )
= SV454 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1954,plain,
! [SV455: $i,SV135: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV135 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV455 @ ( c_HOL_Oone__class_Oone @ SV135 ) @ SV135 )
= SV455 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1644]) ).
thf(1955,plain,
! [SV456: $i,SV136: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV136 ) @ SV456 @ SV136 )
= SV456 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1645]) ).
thf(1956,plain,
! [SV700: $i,SV457: $i,SV137: $i] :
( ( ! [SY1856: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV137 )
| ~ ( class_Int_Onumber__ring @ SV137 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV700 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SY1856 @ SV137 ) @ SV137 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SY1856 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV700 @ SV137 ) @ SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(1957,plain,
! [SV701: $i,SV458: $i,SV138: $i] :
( ( ! [SY1857: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV138 )
| ~ ( class_Int_Onumber__ring @ SV138 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV701 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SY1857 @ SV138 ) @ SV138 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SY1857 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV701 @ SV138 ) @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1958,plain,
! [SV139: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV139 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( SV139
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1959,plain,
! [SV702: $i,SV459: $i,SV140: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV140 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV459 @ SV702 @ SV140 ) @ SV702 @ SV140 )
= SV459 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1960,plain,
! [SV703: $i,SV460: $i,SV141: $i] :
( ( ( c_Lambda_Osubstn @ SV141 @ SV460 @ SV703 )
= ( c_Lambda_Osubst @ SV141 @ ( c_Lambda_Oliftn @ SV703 @ SV460 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV703 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1961,plain,
! [SV704: $i,SV461: $i,SV142: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV142 )
| ( ( c_HOL_Otimes__class_Otimes @ SV461 @ SV704 @ SV142 )
= ( c_HOL_Otimes__class_Otimes @ SV704 @ SV461 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1962,plain,
! [SV143: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV143 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV143 ) @ ( c_HOL_Ozero__class_Ozero @ SV143 ) @ SV143 )
= ( c_HOL_Ozero__class_Ozero @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1963,plain,
! [SV705: $i,SV462: $i,SV144: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
| ( ( c_HOL_Otimes__class_Otimes @ SV462 @ SV705 @ SV144 )
= ( c_HOL_Otimes__class_Otimes @ SV705 @ SV462 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1964,plain,
! [SV706: $i,SV464: $i,SV146: $i] :
( ( ! [SY1858: $i] :
( ~ ( class_Orderings_Opreorder @ SV146 )
| ( c_HOL_Oord__class_Oless @ SV464 @ SV706 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SY1858 @ SV706 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SV464 @ SY1858 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1965,plain,
! [SV707: $i,SV465: $i,SV147: $i] :
( ( ! [SY1859: $i] :
( ~ ( class_Orderings_Oorder @ SV147 )
| ( c_HOL_Oord__class_Oless @ SV465 @ SV707 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SV465 @ SY1859 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SY1859 @ SV707 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1966,plain,
! [SV466: $i,SV148: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV148 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV466 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV466 @ SV148 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1967,plain,
! [SV708: $i,SV468: $i,SV152: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV152 @ SV468 @ tc_nat ) @ SV708 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV152 @ ( c_HOL_Oplus__class_Oplus @ SV468 @ SV708 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1968,plain,
! [SV469: $i,SV153: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV153 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV469 ) @ SV153 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV153 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV469 @ SV153 ) @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1969,plain,
! [SV709: $i,SV471: $i,SV156: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV156 @ SV471 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV709 @ SV471 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV156 @ SV709 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(1970,plain,
! [SV710: $i,SV472: $i,SV157: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV157 @ SV472 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV157 @ SV710 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV472 @ SV710 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1971,plain,
! [SV711: $i,SV473: $i,SV160: $i] :
( ( ! [SY1860: $i,SY1861: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV160 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV473 @ SV711 @ SV160 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1860 @ SV711 @ SV160 ) @ SY1861 @ SV160 ) @ SV160 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV473 @ SY1860 @ SV160 ) @ SV711 @ SV160 ) @ SY1861 @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1972,plain,
! [SV161: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV161 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV161 )
= ( c_HOL_Ozero__class_Ozero @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1973,plain,
! [SV712: $i,SV474: $i,SV162: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV162 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SV712 @ SV162 ) @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV712 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV474 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1974,plain,
! [SV713: $i,SV475: $i,SV163: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV163 @ SV475 @ tc_nat ) @ SV713 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV163 @ SV713 @ tc_nat ) @ SV475 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1975,plain,
! [SV476: $i,SV164: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV164 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SV476 @ SV164 ) @ ( c_HOL_Ozero__class_Ozero @ SV164 ) @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1976,plain,
! [SV477: $i,SV165: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV165 ) @ SV477 @ tc_nat )
= $true )
| ( ( ( ( c_Suc @ SV165 )
= SV477 )
| ~ ( c_HOL_Oord__class_Oless @ SV165 @ SV477 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1977,plain,
! [SV714: $i,SV478: $i,SV166: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV166 ) @ SV478 @ tc_nat ) @ ( c_Suc @ SV714 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV166 @ SV478 @ tc_nat ) @ SV714 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(1978,plain,
! [SV715: $i,SV480: $i,SV168: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV168 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV480 @ SV480 @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SV715 @ SV715 @ SV168 ) @ SV168 ) @ SV168 )
| ( SV480
= ( c_HOL_Ozero__class_Ozero @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1979,plain,
! [SV716: $i,SV481: $i,SV169: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV169 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV481 @ SV481 @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SV716 @ SV716 @ SV169 ) @ SV169 ) @ SV169 )
| ( SV716
= ( c_HOL_Ozero__class_Ozero @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(1980,plain,
! [SV482: $i,SV170: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV170 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV482 @ SV170 ) @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1676]) ).
thf(1981,plain,
! [SV717: $i,SV483: $i,SV171: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV171 ) @ SV483 @ SV717 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV171 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV717 @ SV171 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(1982,plain,
! [SV718: $i,SV484: $i,SV172: $i] :
( ( ( ( c_Lambda_Oliftn @ SV172 @ ( c_Lambda_OdB_OVar @ SV484 ) @ SV718 )
= ( c_Lambda_OdB_OVar @ SV484 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV484 @ SV718 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(1983,plain,
! [SV719: $i,SV485: $i,SV173: $i] :
( ( ! [SY1862: $i] :
( ( c_Lambda_Oliftn @ SV173 @ ( c_Lambda_OdB_OApp @ SV485 @ SV719 ) @ SY1862 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV173 @ SV485 @ SY1862 ) @ ( c_Lambda_Oliftn @ SV173 @ SV719 @ SY1862 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(1984,plain,
! [SV720: $i,SV486: $i,SV174: $i] :
( ( ! [SY1863: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV174 )
| ( c_HOL_Oord__class_Oless @ SV486 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV486 @ SV174 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV720 @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SY1863 @ SV174 ) @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(1985,plain,
! [SV721: $i,SV487: $i,SV175: $i] :
( ( ! [SY1864: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV175 )
| ( c_HOL_Oord__class_Oless @ SV487 @ SV721 @ SV175 )
| ( c_HOL_Oord__class_Oless @ SV721 @ SV487 @ SV175 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1864 @ SV721 @ SV175 ) @ ( c_HOL_Otimes__class_Otimes @ SY1864 @ SV487 @ SV175 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(1986,plain,
! [SV722: $i,SV488: $i,SV176: $i] :
( ( ! [SY1865: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV176 )
| ( c_HOL_Oord__class_Oless @ SV488 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV488 @ SV176 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV722 @ SV488 @ SV176 ) @ ( c_HOL_Otimes__class_Otimes @ SY1865 @ SV488 @ SV176 ) @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1987,plain,
! [SV723: $i,SV489: $i,SV177: $i] :
( ( ! [SY1866: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV177 )
| ( c_HOL_Oord__class_Oless @ SV489 @ SV723 @ SV177 )
| ( c_HOL_Oord__class_Oless @ SV723 @ SV489 @ SV177 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV723 @ SY1866 @ SV177 ) @ ( c_HOL_Otimes__class_Otimes @ SV489 @ SY1866 @ SV177 ) @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(1988,plain,
! [SV490: $i,SV178: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV178 @ SV178 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV178 ) @ SV490 @ SV178 )
= ( c_Lambda_Oliftn @ SV178 @ SV490 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1989,plain,
! [SV491: $i,SV180: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV180 @ SV491 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV491 @ ( c_Suc @ SV180 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1686]) ).
thf(1990,plain,
! [SV492: $i,SV181: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV181 @ ( c_Suc @ SV492 ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV492 @ SV181 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1991,plain,
! [SV724: $i,SV493: $i,SV182: $i] :
( ( ! [SY1867: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV182 )
| ( c_HOL_Oord__class_Oless @ SV493 @ SV724 @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1867 @ SV724 @ SV182 ) @ ( c_HOL_Otimes__class_Otimes @ SY1867 @ SV493 @ SV182 ) @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SY1867 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(1992,plain,
! [SV725: $i,SV494: $i,SV183: $i] :
( ( ! [SY1868: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV183 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV725 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SY1868 @ SV183 ) @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SY1868 @ SV725 @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(1993,plain,
! [SV726: $i,SV495: $i,SV184: $i] :
( ( ! [SY1869: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV184 )
| ( c_HOL_Oord__class_Oless @ SV495 @ SV726 @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY1869 @ SV495 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SY1869 @ SV726 @ SV184 ) @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV184 ) @ SY1869 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(1994,plain,
! [SV727: $i,SV496: $i,SV185: $i] :
( ( ! [SY1870: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV185 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV727 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SY1870 @ SV185 ) @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SV727 @ SY1870 @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV185 ) @ SV496 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(1995,plain,
! [SV728: $i,SV497: $i,SV186: $i] :
( ( ! [SY1871: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV186 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV728 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SY1871 @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SV497 @ ( c_HOL_Ozero__class_Ozero @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SY1871 @ SV728 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(1996,plain,
! [SV729: $i,SV498: $i,SV187: $i] :
( ( ! [SY1872: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV187 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV729 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SY1872 @ SV187 ) @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SV498 @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ SV729 @ SY1872 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(1997,plain,
! [SV730: $i,SV499: $i,SV188: $i] :
( ( ! [SY1873: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV188 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV730 @ SV188 ) @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SY1873 @ SV188 ) @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ SV730 @ SY1873 @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV188 ) @ SV499 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(1998,plain,
! [SV731: $i,SV500: $i,SV189: $i] :
( ( ! [SY1874: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV189 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV731 @ SV189 ) @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SY1874 @ SV189 ) @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SY1874 @ SV731 @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SV500 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(1999,plain,
! [SV732: $i,SV501: $i,SV190: $i] :
( ( ! [SY1875: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV190 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV501 @ SV732 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SY1875 @ SV732 @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SV732 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SY1875 @ SV501 @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2000,plain,
! [SV733: $i,SV502: $i,SV191: $i] :
( ( ! [SY1876: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV191 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SV733 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SY1876 @ SV733 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV733 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV502 @ SY1876 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2001,plain,
! [SV734: $i,SV503: $i,SV192: $i] :
( ( ! [SY1877: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV192 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV503 @ SV734 @ SV192 ) @ ( c_HOL_Otimes__class_Otimes @ SY1877 @ SV734 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SV503 @ SY1877 @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV734 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2002,plain,
! [SV735: $i,SV504: $i,SV193: $i] :
( ( ! [SY1878: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV193 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV504 @ SV735 @ SV193 ) @ ( c_HOL_Otimes__class_Otimes @ SY1878 @ SV735 @ SV193 ) @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SY1878 @ SV504 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SV735 @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2003,plain,
! [SV736: $i,SV505: $i,SV194: $i] :
( ( ! [SY1879: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV194 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV736 @ SV194 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SY1879 @ SV194 ) @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV505 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ SV736 @ SY1879 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2004,plain,
! [SV195: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV195 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV195 ) @ ( c_HOL_Oone__class_Oone @ SV195 ) @ SV195 ) @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(2005,plain,
! [SV737: $i,SV506: $i,SV196: $i] :
( ( ! [SY1880: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV196 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV737 @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SY1880 @ SV737 @ SV196 ) @ SV196 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV506 @ SY1880 @ SV196 ) @ SV737 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2006,plain,
! [SV507: $i,SV197: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV197 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV507 @ SV197 )
= SV507 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(2007,plain,
! [SV508: $i,SV198: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV198 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV508 @ SV198 )
= SV508 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(2008,plain,
! [SV509: $i,SV202: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV202 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV202 )
| ( SV509
= ( c_HOL_Oplus__class_Oplus @ SV509 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1705]) ).
thf(2009,plain,
! [SV510: $i,SV203: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV203 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV510 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
= SV510 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(2010,plain,
! [SV511: $i,SV204: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV204 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV511 @ SV204 )
= SV511 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(2011,plain,
! [SV512: $i,SV205: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV205 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV512 @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV205 )
= SV512 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(2012,plain,
! [SV513: $i,SV206: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV206 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV513 @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV206 )
= SV513 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1709]) ).
thf(2013,plain,
! [SV514: $i,SV207: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV207 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV207 ) @ SV514 @ SV207 )
= SV514 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(2014,plain,
! [SV208: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV208 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ SV208 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ SV208 ) @ SV208 ) @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(2015,plain,
! [SV738: $i,SV515: $i,SV209: $i] :
( ( ! [SY1881: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OApp @ SV209 @ SV515 ) @ SV738 @ SY1881 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV209 @ SV738 @ SY1881 ) @ ( c_Lambda_Osubstn @ SV515 @ SV738 @ SY1881 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2016,plain,
! [SV739: $i,SV518: $i,SV212: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV212 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV518 @ SV739 @ SV212 ) @ SV739 @ SV212 )
= SV518 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2017,plain,
! [SV740: $i,SV519: $i,SV213: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV213 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV519 @ SV740 @ SV213 ) @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV740 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV519 @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2018,plain,
! [SV520: $i,SV214: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV214 ) @ ( c_Suc @ SV520 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV214 @ SV520 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(2019,plain,
! [SV521: $i,SV215: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV215 @ SV521 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV215 ) @ ( c_Suc @ SV521 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(2020,plain,
! [SV522: $i,SV216: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV216 ) @ ( c_Suc @ SV522 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV216 @ SV522 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(2021,plain,
! [SV523: $i,SV217: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV217 @ SV523 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV523 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(2022,plain,
! [SV524: $i,SV218: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV218 @ SV524 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV218 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(2023,plain,
! [SV525: $i,SV219: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV219 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV525 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ ( c_HOL_Oplus__class_Oplus @ SV525 @ SV525 @ SV219 ) @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(2024,plain,
! [SV526: $i,SV220: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV220 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ ( c_HOL_Oplus__class_Oplus @ SV526 @ SV526 @ SV220 ) @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV526 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(2025,plain,
! [SV527: $i,SV221: $i] :
( ( ( SV221
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV527 @ SV221 ) ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV527 ) @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(2026,plain,
! [SV741: $i,SV528: $i,SV222: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV222 @ SV528 ) @ ( c_Suc @ SV741 ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV222 @ SV741 ) @ SV528 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV528 @ ( c_HOL_Oplus__class_Oplus @ SV741 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2027,plain,
! [SV742: $i,SV529: $i,SV223: $i] :
( ( ! [SY1882: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ SV223 @ SV529 @ SV742 ) @ SY1882 )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV223 @ ( c_HOL_Oplus__class_Oplus @ SY1882 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ SV529 @ SY1882 ) @ SV742 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV742 @ ( c_HOL_Oplus__class_Oplus @ SY1882 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2028,plain,
! [SV530: $i,SV224: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV224 ) @ SV530 )
= ( c_Lambda_OdB_OVar @ SV224 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV224 @ SV530 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(2029,plain,
! [SV743: $i,SV531: $i,SV225: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV225 @ SV531 ) @ ( c_Lambda_OdB_OApp @ SV743 @ SV531 ) )
| ~ ( c_Lambda_Obeta @ SV225 @ SV743 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2030,plain,
! [SV744: $i,SV532: $i,SV226: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV226 @ SV532 ) @ ( c_Lambda_OdB_OApp @ SV226 @ SV744 ) )
| ~ ( c_Lambda_Obeta @ SV532 @ SV744 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2031,plain,
! [SV745: $i,SV533: $i,SV227: $i] :
( ( ! [SY1883: $i,SY1884: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV745 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SY1883 @ SY1884 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SY1883 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV745 @ SY1884 @ SV227 ) @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2032,plain,
! [SV746: $i,SV534: $i,SV228: $i] :
( ( ! [SY1885: $i,SY1886: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ ( c_Lambda_Olift @ SV534 @ SV746 ) @ ( c_Suc @ SY1885 ) ) @ ( c_Lambda_Osubst @ SY1886 @ SV534 @ SY1885 ) @ SV746 )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ SY1886 @ SV746 ) @ SV534 @ SY1885 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV746 @ ( c_HOL_Oplus__class_Oplus @ SY1885 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2033,plain,
! [SV747: $i,SV535: $i,SV229: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ SV229 ) @ SV535 @ SV747 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubst @ SV229 @ ( c_Lambda_Olift @ SV535 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Oplus__class_Oplus @ SV747 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2034,plain,
! [SV748: $i,SV536: $i,SV230: $i] :
( ( ! [SY1887: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ SV230 @ SV536 @ SV748 ) @ SY1887 )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV230 @ SY1887 ) @ ( c_Lambda_Olift @ SV536 @ SY1887 ) @ ( c_HOL_Oplus__class_Oplus @ SV748 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1887 @ ( c_HOL_Oplus__class_Oplus @ SV748 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2035,plain,
! [SV231: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV231 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV231 )
= ( c_HOL_Oone__class_Oone @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(2036,plain,
! [SV537: $i,SV232: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV232 @ SV232 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV232 ) @ SV537 @ SV232 )
= SV537 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1735]) ).
thf(2037,plain,
! [SV538: $i,SV233: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV233 ) @ SV538 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ SV233 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV233 @ SV538 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(2038,plain,
! [SV749: $i,SV539: $i,SV234: $i] :
( ( ! [SY1888: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV234 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV539 @ SV749 @ SV234 ) @ SY1888 @ SV234 )
= ( c_HOL_Oplus__class_Oplus @ SV539 @ ( c_HOL_Oplus__class_Oplus @ SV749 @ SY1888 @ SV234 ) @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2039,plain,
! [SV750: $i,SV540: $i,SV235: $i] :
( ( ! [SY1889: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV235 )
| ( ( c_HOL_Oplus__class_Oplus @ SV540 @ ( c_HOL_Oplus__class_Oplus @ SV750 @ SY1889 @ SV235 ) @ SV235 )
= ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Oplus__class_Oplus @ SV540 @ SY1889 @ SV235 ) @ SV235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2040,plain,
! [SV751: $i,SV541: $i,SV236: $i] :
( ( ! [SY1890: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV236 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV541 @ SV751 @ SV236 ) @ SY1890 @ SV236 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV541 @ SY1890 @ SV236 ) @ SV751 @ SV236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2041,plain,
! [SV752: $i,SV542: $i,SV237: $i] :
( ( ! [SY1891: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 )
| ( ( c_HOL_Oplus__class_Oplus @ SV542 @ ( c_HOL_Oplus__class_Oplus @ SV752 @ SY1891 @ SV237 ) @ SV237 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV542 @ SV752 @ SV237 ) @ SY1891 @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2042,plain,
! [SV753: $i,SV543: $i,SV238: $i] :
( ( ! [SY1892: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV238 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV543 @ SV753 @ SV238 ) @ SY1892 @ SV238 )
= ( c_HOL_Oplus__class_Oplus @ SV543 @ ( c_HOL_Oplus__class_Oplus @ SV753 @ SY1892 @ SV238 ) @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2043,plain,
! [SV754: $i,SV544: $i,SV239: $i] :
( ( ! [SY1893: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV239 )
| ( ( c_HOL_Oplus__class_Oplus @ SV544 @ ( c_HOL_Oplus__class_Oplus @ SV754 @ SY1893 @ SV239 ) @ SV239 )
= ( c_HOL_Oplus__class_Oplus @ SV754 @ ( c_HOL_Oplus__class_Oplus @ SV544 @ SY1893 @ SV239 ) @ SV239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2044,plain,
! [SV755: $i,SV545: $i,SV240: $i] :
( ( ! [SY1894: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV240 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV545 @ SV755 @ SV240 ) @ SY1894 @ SV240 )
= ( c_HOL_Oplus__class_Oplus @ SV545 @ ( c_HOL_Oplus__class_Oplus @ SV755 @ SY1894 @ SV240 ) @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2045,plain,
! [SV756: $i,SV546: $i,SV241: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV241 @ SV546 @ tc_nat ) @ SV756 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV241 @ ( c_HOL_Oplus__class_Oplus @ SV546 @ SV756 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2046,plain,
! [SV757: $i,SV547: $i,SV242: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV242 @ ( c_HOL_Oplus__class_Oplus @ SV547 @ SV757 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV547 @ ( c_HOL_Oplus__class_Oplus @ SV242 @ SV757 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2047,plain,
! [SV758: $i,SV548: $i,SV243: $i] :
( ( ! [SY1895: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV243 )
| ( ( c_HOL_Oplus__class_Oplus @ SV548 @ ( c_HOL_Oplus__class_Oplus @ SV758 @ SY1895 @ SV243 ) @ SV243 )
= ( c_HOL_Oplus__class_Oplus @ SV758 @ ( c_HOL_Oplus__class_Oplus @ SV548 @ SY1895 @ SV243 ) @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2048,plain,
! [SV759: $i,SV549: $i,SV244: $i] :
( ( ! [SY1896: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV244 )
| ( ( c_HOL_Oplus__class_Oplus @ SV549 @ ( c_HOL_Oplus__class_Oplus @ SV759 @ SY1896 @ SV244 ) @ SV244 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV549 @ SV759 @ SV244 ) @ SY1896 @ SV244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2049,plain,
! [SV760: $i,SV550: $i,SV245: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV245 ) @ SV550 @ SV760 )
= ( c_Lambda_OdB_OVar @ SV245 ) )
| ( SV245 = SV760 )
| ( c_HOL_Oord__class_Oless @ SV760 @ SV245 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2050,plain,
! [SV761: $i,SV551: $i,SV246: $i] :
( ( ! [SY1897: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV246 @ SV551 @ SV761 ) @ ( c_Lambda_Osubst @ SY1897 @ SV551 @ SV761 ) )
| ~ ( c_Lambda_Obeta @ SV246 @ SY1897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2051,plain,
! [SV762: $i,SV552: $i,SV249: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ SV249 ) @ SV552 @ SV762 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ SV249 @ SV552 @ ( c_HOL_Oplus__class_Oplus @ SV762 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2052,plain,
! [SV763: $i,SV553: $i,SV250: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV250 )
| ( ( c_HOL_Oplus__class_Oplus @ SV553 @ SV763 @ SV250 )
= ( c_HOL_Oplus__class_Oplus @ SV763 @ SV553 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2053,plain,
! [SV764: $i,SV554: $i,SV251: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV251 )
| ( ( c_HOL_Oplus__class_Oplus @ SV554 @ SV764 @ SV251 )
= ( c_HOL_Oplus__class_Oplus @ SV764 @ SV554 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2054,plain,
! [SV765: $i,SV556: $i,SV253: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV253 )
| ( ( c_HOL_Oplus__class_Oplus @ SV556 @ SV765 @ SV253 )
= ( c_HOL_Oplus__class_Oplus @ SV765 @ SV556 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2055,plain,
! [SV557: $i,SV254: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV254 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV557 @ SV557 @ SV254 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV254 ) @ ( c_HOL_Oone__class_Oone @ SV254 ) @ SV254 ) @ SV557 @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(2056,plain,
! [SV766: $i,SV558: $i,SV255: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV255 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV558 @ SV766 @ SV255 ) @ SV766 @ SV255 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV558 @ ( c_HOL_Oone__class_Oone @ SV255 ) @ SV255 ) @ SV766 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2057,plain,
! [SV767: $i,SV559: $i,SV256: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
| ( ( c_HOL_Oplus__class_Oplus @ SV559 @ ( c_HOL_Otimes__class_Otimes @ SV767 @ SV559 @ SV256 ) @ SV256 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV767 @ ( c_HOL_Oone__class_Oone @ SV256 ) @ SV256 ) @ SV559 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2058,plain,
! [SV768: $i,SV561: $i,SV258: $i] :
( ( ( c_Lambda_Oliftn @ SV258 @ ( c_Lambda_OdB_OAbs @ SV561 ) @ SV768 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ SV258 @ SV561 @ ( c_HOL_Oplus__class_Oplus @ SV768 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2059,plain,
! [SV562: $i,SV259: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV259 ) @ SV562 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(2060,plain,
! [SV563: $i,SV260: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV260 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV563 @ ( c_HOL_Oplus__class_Oplus @ SV563 @ ( c_HOL_Oone__class_Oone @ SV260 ) @ SV260 ) @ SV260 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1761]) ).
thf(2061,plain,
! [SV564: $i,SV261: $i] :
( ( ( c_Lambda_Obeta @ SV261 @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV261 @ SV564 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV261 ) @ SV564 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1762]) ).
thf(2062,plain,
! [SV769: $i,SV565: $i,SV262: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV262 ) @ SV565 @ SV769 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV262 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV769 @ SV262 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2063,plain,
! [SV770: $i,SV566: $i,SV263: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV263 ) @ SV566 @ SV770 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV263 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV770 @ SV263 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2064,plain,
! [SV771: $i,SV567: $i,SV264: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV264 ) @ SV567 @ SV771 )
= ( c_Lambda_OdB_OVar @ SV264 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV264 @ SV771 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2065,plain,
! [SV772: $i,SV569: $i,SV266: $i] :
( ( ! [SY1898: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ SV266 @ SV569 ) @ SV772 @ SY1898 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV266 @ SV772 @ SY1898 ) @ ( c_Lambda_Osubst @ SV569 @ SV772 @ SY1898 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2066,plain,
! [SV773: $i,SV570: $i,SV267: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV267 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SV570 @ SV773 @ tc_nat ) @ SV267 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV570 @ SV267 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV773 @ SV267 ) @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2067,plain,
! [SV774: $i,SV572: $i,SV269: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ SV269 @ SV572 ) @ SV774 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV269 @ SV774 ) @ ( c_Lambda_Olift @ SV572 @ SV774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2068,plain,
! [SV270: $i] :
( ( ( c_InductTermi_OIT @ SV270 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(2069,plain,
! [SV775: $i,SV573: $i,SV271: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV271 @ SV573 ) @ SV775 @ SV573 )
= SV271 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2070,plain,
! [SV776: $i,SV574: $i,SV272: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV272 @ SV574 ) @ ( c_Lambda_Olift @ SV776 @ SV574 ) )
| ~ ( c_Lambda_Obeta @ SV272 @ SV776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2071,plain,
! [SV575: $i,SV273: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV273 ) @ ( c_Lambda_OdB_OAbs @ SV575 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV273 @ SV575 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(2072,plain,
! [SV777: $i,SV576: $i,SV274: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV274 )
| ( ( c_HOL_Ominus__class_Ominus @ SV576 @ SV777 @ SV274 )
!= ( c_HOL_Ozero__class_Ozero @ SV274 ) )
| ( SV576 = SV777 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2073,plain,
! [SV778: $i,SV577: $i,SV275: $i] :
( ( ! [SY1899: $i,SY1900: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV275 )
| ( ( c_HOL_Oplus__class_Oplus @ SV577 @ ( c_HOL_Oplus__class_Oplus @ SV778 @ SY1899 @ SV275 ) @ SV275 )
!= ( c_HOL_Oplus__class_Oplus @ SV778 @ SY1900 @ SV275 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV577 @ SY1899 @ SV275 )
= SY1900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2074,plain,
! [SV779: $i,SV578: $i,SV277: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV277 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV578 @ SV277 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV779 @ SV277 ) )
| ( SV578 = SV779 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2075,plain,
! [SV780: $i,SV579: $i,SV278: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV278 @ SV579 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV278 @ SV780 @ tc_nat ) )
| ( SV579 = SV780 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2076,plain,
! [SV781: $i,SV580: $i,SV280: $i] :
( ( ! [SY1901: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV280 )
| ( ( c_HOL_Oplus__class_Oplus @ SV580 @ SV781 @ SV280 )
!= ( c_HOL_Oplus__class_Oplus @ SV580 @ SY1901 @ SV280 ) )
| ( SV781 = SY1901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2077,plain,
! [SV581: $i,SV281: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV281 )
= ( c_Lambda_OdB_OVar @ SV581 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(2078,plain,
! [SV582: $i,SV283: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV283 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV582 @ SV582 @ SV283 )
!= ( c_HOL_Ozero__class_Ozero @ SV283 ) )
| ( SV582
= ( c_HOL_Ozero__class_Ozero @ SV283 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(2079,plain,
! [SV782: $i,SV583: $i,SV284: $i] :
( ( ( c_Lambda_OdB_OApp @ SV284 @ SV583 )
!= ( c_Lambda_OdB_OVar @ SV782 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2080,plain,
! [SV783: $i,SV584: $i,SV285: $i] :
( ( ! [SY1902: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV285 )
| ( ( c_HOL_Ominus__class_Ominus @ SV584 @ SV783 @ SV285 )
!= ( c_HOL_Ominus__class_Ominus @ SY1902 @ SY1902 @ SV285 ) )
| ( SV584 = SV783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2081,plain,
! [SV784: $i,SV585: $i,SV286: $i] :
( ( ! [SY1903: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV286 @ SV585 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV784 @ SY1903 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV784 @ SV585 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV286 @ SY1903 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2082,plain,
! [SV785: $i,SV586: $i,SV287: $i] :
( ( ! [SY1904: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV287 )
| ( ( c_HOL_Oplus__class_Oplus @ SV586 @ SV785 @ SV287 )
!= ( c_HOL_Oplus__class_Oplus @ SY1904 @ SV785 @ SV287 ) )
| ( SV586 = SY1904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2083,plain,
! [SV587: $i,SV288: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV288 @ SV587 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV587
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(2084,plain,
! [SV786: $i,SV588: $i,SV290: $i] :
( ( ! [SY1905: $i,SY1906: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV290 )
| ~ ( class_Int_Onumber__ring @ SV290 )
| ( ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SY1905 @ SV290 ) @ SV290 )
!= ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SY1906 @ SV290 ) @ SV290 ) )
| ( SY1905 = SY1906 )
| ( SV786
= ( c_HOL_Ozero__class_Ozero @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2085,plain,
! [SV787: $i,SV589: $i,SV291: $i] :
( ( ! [SY1907: $i,SY1908: $i,SY1909: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV291 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV589 @ SV787 @ SV291 ) @ SY1907 @ SV291 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1908 @ SV787 @ SV291 ) @ SY1909 @ SV291 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV589 @ SY1908 @ SV291 ) @ SV787 @ SV291 ) @ SY1907 @ SV291 )
= SY1909 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2086,plain,
! [SV590: $i,SV292: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV292 @ SV590 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV292
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV292
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(2087,plain,
! [SV788: $i,SV591: $i,SV293: $i] :
( ( ! [SY1910: $i,SY1911: $i,SY1912: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV293 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV591 @ SV788 @ SV293 ) @ SY1910 @ SV293 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1911 @ SV788 @ SV293 ) @ SY1912 @ SV293 ) )
| ( SY1910
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1911 @ SV591 @ SV293 ) @ SV788 @ SV293 ) @ SY1912 @ SV293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2088,plain,
! [SV789: $i,SV592: $i,SV294: $i] :
( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV294 )
| ( ( c_HOL_Otimes__class_Otimes @ SV592 @ SV789 @ SV294 )
!= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SV592
= ( c_HOL_Ozero__class_Ozero @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2089,plain,
! [SV790: $i,SV593: $i,SV295: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV295 @ SV593 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV790 @ SV593 @ tc_nat ) )
| ( SV295 = SV790 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2090,plain,
! [SV791: $i,SV594: $i,SV296: $i] :
( ( ( c_Lambda_OdB_OApp @ SV296 @ SV594 )
!= ( c_Lambda_OdB_OAbs @ SV791 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2091,plain,
! [SV792: $i,SV595: $i,SV297: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV297 )
| ~ ( class_Int_Onumber__ring @ SV297 )
| ( ( c_HOL_Ominus__class_Ominus @ SV595 @ SV792 @ SV297 )
!= ( c_HOL_Ozero__class_Ozero @ SV297 ) )
| ( SV595 = SV792 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2092,plain,
! [SV793: $i,SV596: $i,SV299: $i] :
( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV299 )
| ( ( c_HOL_Otimes__class_Otimes @ SV596 @ SV793 @ SV299 )
!= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
| ( SV596
= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
| ( SV793
= ( c_HOL_Ozero__class_Ozero @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2093,plain,
! [SV794: $i,SV597: $i,SV300: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV300 @ SV597 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV300 @ SV794 @ tc_nat ) )
| ( SV597 = SV794 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2094,plain,
! [SV795: $i,SV598: $i,SV301: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV301 )
| ( ( c_HOL_Otimes__class_Otimes @ SV598 @ SV795 @ SV301 )
!= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
| ( SV795
= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
| ( SV598
= ( c_HOL_Ozero__class_Ozero @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2095,plain,
! [SV599: $i,SV302: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV302 @ SV599 @ tc_nat ) )
= $true )
| ( ( ( SV302
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV302
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1803]) ).
thf(2096,plain,
! [SV796: $i,SV600: $i,SV304: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV304 )
!= ( c_Lambda_OdB_OApp @ SV600 @ SV796 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2097,plain,
! [SV305: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV305 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV305 )
!= ( c_HOL_Oone__class_Oone @ SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(2098,plain,
! [SV797: $i,SV601: $i,SV306: $i] :
( ( ! [SY1913: $i,SY1914: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV306 )
| ~ ( class_Int_Onumber__ring @ SV306 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV797 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SY1913 @ SY1914 @ SV306 ) @ SV306 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SY1914 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SY1913 @ SV797 @ SV306 ) @ SV306 ) )
| ( SV797 = SY1914 )
| ( SV601 = SY1913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2099,plain,
! [SV798: $i,SV602: $i,SV307: $i] :
( ( ! [SY1915: $i,SY1916: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV307 )
| ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV798 @ SV307 )
!= ( c_HOL_Ominus__class_Ominus @ SY1915 @ SY1916 @ SV307 ) )
| ( c_HOL_Oord__class_Oless @ SV602 @ SV798 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SY1915 @ SY1916 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2100,plain,
! [SV799: $i,SV603: $i,SV308: $i] :
( ( ! [SY1917: $i] :
( ( ( c_Lambda_OdB_OApp @ SV308 @ SV603 )
!= ( c_Lambda_OdB_OApp @ SV799 @ SY1917 ) )
| ( SV603 = SY1917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2101,plain,
! [SV800: $i,SV604: $i,SV309: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV604 @ SV604 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV800 @ SV800 @ SV309 ) @ SV309 )
!= ( c_HOL_Ozero__class_Ozero @ SV309 ) )
| ( SV800
= ( c_HOL_Ozero__class_Ozero @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2102,plain,
! [SV605: $i,SV310: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV310 )
!= ( c_Lambda_OdB_OAbs @ SV605 ) )
= $true )
| ( ( SV310 = SV605 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(2103,plain,
! [SV606: $i,SV311: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV311 @ SV606 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV606
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV311
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(2104,plain,
! [SV607: $i,SV312: $i] :
( ( ( c_Lambda_OdB_OVar @ SV312 )
= ( c_Lambda_OdB_OAbs @ SV607 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(2105,plain,
! [SV801: $i,SV608: $i,SV313: $i] :
( ( ! [SY1918: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV313 )
| ~ ( class_Int_Onumber__ring @ SV313 )
| ( ( c_HOL_Oplus__class_Oplus @ SV608 @ SV801 @ SV313 )
!= ( c_HOL_Oplus__class_Oplus @ SV608 @ SY1918 @ SV313 ) )
| ( SV801 = SY1918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2106,plain,
! [SV802: $i,SV609: $i,SV314: $i] :
( ( ! [SY1919: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV314 )
| ( ( c_HOL_Ominus__class_Ominus @ SV609 @ SV609 @ SV314 )
!= ( c_HOL_Ominus__class_Ominus @ SV802 @ SY1919 @ SV314 ) )
| ( SV802 = SY1919 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2107,plain,
! [SV610: $i,SV315: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV315 @ SV610 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV315
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV610
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(2108,plain,
! [SV803: $i,SV611: $i,SV316: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV316 )
| ~ ( class_Int_Onumber__ring @ SV316 )
| ( SV611
!= ( c_HOL_Oplus__class_Oplus @ SV611 @ SV803 @ SV316 ) )
| ( SV803
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2109,plain,
! [SV804: $i,SV612: $i,SV317: $i] :
( ( ! [SY1920: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV317 )
| ( ( c_HOL_Oplus__class_Oplus @ SV612 @ SV804 @ SV317 )
!= ( c_HOL_Oplus__class_Oplus @ SV612 @ SY1920 @ SV317 ) )
| ( SV804 = SY1920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2110,plain,
! [SV613: $i,SV318: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV318 @ SV613 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV613
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV613
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(2111,plain,
! [SV614: $i,SV319: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV319 @ SV614 @ tc_nat ) )
= $true )
| ( ( ( SV614
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV614
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(2112,plain,
! [SV805: $i,SV615: $i,SV320: $i] :
( ( ( c_Lambda_OdB_OVar @ SV320 )
!= ( c_Lambda_OdB_OApp @ SV615 @ SV805 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2113,plain,
! [SV806: $i,SV616: $i,SV321: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV321 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV616 @ SV616 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SV806 @ SV806 @ SV321 ) @ SV321 )
!= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV616
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2114,plain,
! [SV617: $i,SV322: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV322 @ SV617 @ tc_nat )
!= SV322 )
= $true )
| ( ( SV617
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(2115,plain,
! [SV618: $i,SV323: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV323 @ SV618 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV618 @ SV323 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV618 = SV323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(2116,plain,
! [SV619: $i,SV324: $i] :
( ( ( SV324
!= ( c_HOL_Oplus__class_Oplus @ SV324 @ SV619 @ tc_nat ) )
= $true )
| ( ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(2117,plain,
! [SV807: $i,SV620: $i,SV325: $i] :
( ( ! [SY1921: $i,SY1922: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV807 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SY1921 @ SY1922 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SY1921 @ SY1922 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV620 @ SV807 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2118,plain,
! [SV808: $i,SV621: $i,SV326: $i] :
( ( ! [SY1923: $i] :
( ( ( c_Lambda_OdB_OApp @ SV326 @ SV621 )
!= ( c_Lambda_OdB_OApp @ SV808 @ SY1923 ) )
| ( SV326 = SV808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2119,plain,
! [SV622: $i,SV327: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV327 @ SV622 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV327
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2120,plain,
! [SV623: $i,SV328: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV328 @ SV623 @ tc_nat ) )
= $true )
| ( ( ( SV623
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV328
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(2121,plain,
! [SV624: $i,SV329: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV329 @ SV624 @ tc_nat ) )
= $true )
| ( ( ( SV329
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV624
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2122,plain,
! [SV625: $i,SV330: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV330 )
!= ( c_Lambda_OdB_OVar @ SV625 ) )
= $true )
| ( ( SV330 = SV625 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(2123,plain,
! [SV809: $i,SV626: $i,SV331: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV331 )
| ( ( c_HOL_Ominus__class_Ominus @ SV626 @ SV809 @ SV331 )
!= ( c_HOL_Ozero__class_Ozero @ SV331 ) )
| ( SV626 = SV809 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2124,plain,
! [SV810: $i,SV627: $i,SV332: $i] :
( ( ! [SY1924: $i,SY1925: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV332 )
| ~ ( class_Int_Onumber__ring @ SV332 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV810 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SY1924 @ SY1925 @ SV332 ) @ SV332 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SY1925 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SY1924 @ SV810 @ SV332 ) @ SV332 ) )
| ( SV810 = SY1925 )
| ( SV627 = SY1924 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2125,plain,
! [SV333: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV333 )
= $false )
| ( ( ( c_HOL_Oone__class_Oone @ SV333 )
!= ( c_HOL_Ozero__class_Ozero @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(2126,plain,
! [SV628: $i,SV334: $i] :
( ( ( ( c_Suc @ SV334 )
!= ( c_Suc @ SV628 ) )
= $true )
| ( ( SV334 = SV628 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(2127,plain,
! [SV629: $i,SV335: $i] :
( ( ( ( c_Suc @ SV335 )
!= ( c_Suc @ SV629 ) )
= $true )
| ( ( SV335 = SV629 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(2128,plain,
! [SV811: $i,SV630: $i,SV336: $i,SV2: $i] :
( ( ! [SY1926: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV630 @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SV811 @ SY1926 @ SV2 ) @ SV2 )
= ( c_HOL_Otimes__class_Otimes @ SV811 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV630 @ SV2 ) @ SY1926 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2129,plain,
! [SV812: $i,SV631: $i,SV337: $i,SV3: $i] :
( ( ! [SY1927: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV3 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV337 @ SV631 @ SV3 ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SY1927 @ SV3 ) @ SV3 )
= ( c_HOL_Otimes__class_Otimes @ SV337 @ ( c_HOL_Otimes__class_Otimes @ SV631 @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SY1927 @ SV3 ) @ SV3 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2130,plain,
! [SV813: $i,SV632: $i,SV338: $i,SV4: $i] :
( ( ! [SY1928: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV338 @ SV632 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SY1928 @ SV4 ) @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV338 @ SV813 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SV632 @ SY1928 @ SV4 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2131,plain,
! [SV339: $i,SV5: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV5 @ ( c_Suc @ SV339 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV5 @ SV339 @ tc_nat )
= $true )
| ( ( SV5 = SV339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(2132,plain,
! [SV6: $i,SV340: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV340 @ ( c_Suc @ SV6 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV340 @ SV6 @ tc_nat )
= $true )
| ( ( SV6 = SV340 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(2133,plain,
! [SV341: $i,SV7: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV7 @ SV341 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV7 @ ( c_Suc @ SV341 ) @ tc_nat ) )
= $true )
| ( ( SV7 = SV341 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(2134,plain,
! [SV633: $i,SV343: $i,SV9: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV9 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV343 @ SV343 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV633 @ SV633 @ SV9 ) @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(2135,plain,
! [SV10: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_HOL_Ozero__class_Ozero @ SV10 ) @ SV10 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(2136,plain,
! [SV634: $i,SV344: $i,SV11: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV11 ) @ SV344 @ SV634 )
= ( c_Lambda_OdB_OVar @ SV11 ) )
= $true )
| ( ( ( SV11 = SV634 )
| ( c_HOL_Oord__class_Oless @ SV634 @ SV11 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(2137,plain,
! [SV635: $i,SV345: $i,SV12: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV12 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SV345 @ SV635 @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SV635 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SV345 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(2138,plain,
! [SV636: $i,SV346: $i,SV13: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV13 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SV346 @ SV636 @ SV13 ) @ SV13 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV636 @ SV13 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV346 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(2139,plain,
! [SV637: $i,SV347: $i,SV14: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV14 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV347 @ SV14 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV637 @ SV14 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ ( c_HOL_Otimes__class_Otimes @ SV637 @ SV347 @ SV14 ) @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(2140,plain,
! [SV638: $i,SV348: $i,SV15: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV15 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV348 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV638 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ ( c_HOL_Otimes__class_Otimes @ SV348 @ SV638 @ SV15 ) @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(2141,plain,
! [SV349: $i,SV16: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV16 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV349 @ SV349 @ SV16 ) @ ( c_HOL_Ozero__class_Ozero @ SV16 ) @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SV349 @ ( c_HOL_Ozero__class_Ozero @ SV16 ) @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(2142,plain,
! [SV350: $i,SV17: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV17 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV350 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SV350 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(2143,plain,
! [SV351: $i,SV18: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV18 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV351 @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV351 @ SV351 @ SV18 ) @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(2144,plain,
! [SV352: $i,SV19: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV19 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV352 @ SV352 @ SV19 ) @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
| ~ ( c_HOL_Oord__class_Oless @ SV352 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(2145,plain,
! [SV814: $i,SV639: $i,SV353: $i,SV20: $i] :
( ( ! [SY1929: $i,SY1930: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV20 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV353 @ SV639 @ SV20 ) @ SV814 @ SV20 ) @ SY1929 @ SV20 ) @ SY1930 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV814 @ SV20 ) @ SY1929 @ SV20 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV639 @ SV814 @ SV20 ) @ SY1930 @ SV20 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2146,plain,
! [SV815: $i,SV640: $i,SV354: $i,SV21: $i] :
( ( ! [SY1931: $i,SY1932: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV21 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV354 @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1931 @ SV640 @ SV21 ) @ SY1932 @ SV21 ) @ SV21 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV354 @ SY1931 @ SV21 ) @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ SY1932 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2147,plain,
! [SV816: $i,SV641: $i,SV355: $i,SV22: $i] :
( ( ! [SY1933: $i,SY1934: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV22 )
| ( c_HOL_Oord__class_Oless @ SV355 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SV816 @ SV22 ) @ SY1933 @ SV22 ) @ SY1934 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SY1933 @ SV22 ) @ SV355 @ SV22 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV641 @ SY1933 @ SV22 ) @ SY1934 @ SV22 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2148,plain,
! [SV817: $i,SV642: $i,SV356: $i,SV23: $i] :
( ( ! [SY1935: $i,SY1936: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV23 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV356 @ SV642 @ SV23 ) @ SV817 @ SV23 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1935 @ SV642 @ SV23 ) @ SY1936 @ SV23 ) @ SV23 )
| ~ ( c_HOL_Oord__class_Oless @ SV817 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1935 @ SV356 @ SV23 ) @ SV642 @ SV23 ) @ SY1936 @ SV23 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2149,plain,
! [SV358: $i,SV27: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV27 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV27 )
| ( ( c_HOL_Ominus__class_Ominus @ SV358 @ SV358 @ SV27 )
= ( c_HOL_Ozero__class_Ozero @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2150,plain,
! [SV359: $i,SV28: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV28 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV359 @ SV359 @ SV28 )
= ( c_HOL_Ozero__class_Ozero @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(2151,plain,
! [SV360: $i,SV29: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV29 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV360 @ ( c_HOL_Ozero__class_Ozero @ SV29 ) @ SV29 )
= SV360 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(2152,plain,
! [SV361: $i,SV30: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV30 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV361 @ SV361 @ SV30 )
= ( c_HOL_Ozero__class_Ozero @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1862]) ).
thf(2153,plain,
! [SV362: $i,SV31: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV31 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV362 @ SV362 @ SV31 )
= ( c_HOL_Ozero__class_Ozero @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(2154,plain,
! [SV644: $i,SV363: $i,SV32: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV363 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV644 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV644 @ SV32 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV644 @ SV363 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(2155,plain,
! [SV645: $i,SV364: $i,SV34: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV34 @ ( c_HOL_Oplus__class_Oplus @ SV364 @ SV645 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV34 @ SV645 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(2156,plain,
! [SV646: $i,SV365: $i,SV35: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV35 @ ( c_HOL_Oplus__class_Oplus @ SV365 @ SV646 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV35 @ SV365 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(2157,plain,
! [SV647: $i,SV366: $i,SV36: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV36 @ SV366 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV36 @ SV647 @ tc_nat ) @ SV366 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(2158,plain,
! [SV648: $i,SV367: $i,SV37: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV37 @ ( c_HOL_Oplus__class_Oplus @ SV367 @ SV648 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV37 @ SV648 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(2159,plain,
! [SV649: $i,SV368: $i,SV38: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV38 @ ( c_HOL_Oplus__class_Oplus @ SV368 @ SV649 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV38 @ SV368 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(2160,plain,
! [SV818: $i,SV650: $i,SV372: $i,SV42: $i] :
( ( ! [SY1937: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV42 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV372 @ SV650 @ SV42 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV818 @ SV372 @ SV42 ) @ SV650 @ SV42 ) @ SY1937 @ SV42 ) @ SV42 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV818 @ SV650 @ SV42 ) @ SY1937 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2161,plain,
! [SV819: $i,SV651: $i,SV375: $i,SV45: $i] :
( ( ! [SY1938: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV45 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV375 @ SV651 @ SV45 ) @ SV819 @ SV45 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1938 @ SV651 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV375 @ SY1938 @ SV45 ) @ SV651 @ SV45 ) @ SV819 @ SV45 ) @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2162,plain,
! [SV376: $i,SV46: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV46 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV46 ) @ SV376 @ SV46 )
= SV376 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(2163,plain,
! [SV377: $i,SV47: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV47 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV47 ) @ SV377 @ SV47 )
= SV377 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(2164,plain,
! [SV378: $i,SV48: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV48 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV48 ) @ SV378 @ SV48 )
= SV378 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(2165,plain,
! [SV379: $i,SV49: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV49 ) @ SV379 @ SV49 )
= ( c_HOL_Ozero__class_Ozero @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(2166,plain,
! [SV380: $i,SV50: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV380 @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV50 )
= ( c_HOL_Ozero__class_Ozero @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(2167,plain,
! [SV381: $i,SV51: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV51 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV381 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 )
= ( c_HOL_Ozero__class_Ozero @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1877]) ).
thf(2168,plain,
! [SV382: $i,SV52: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV52 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV382 @ SV52 )
= ( c_HOL_Ozero__class_Ozero @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(2169,plain,
! [SV383: $i,SV53: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV53 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV383 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
= ( c_HOL_Ozero__class_Ozero @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(2170,plain,
! [SV384: $i,SV54: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV54 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV54 ) @ SV384 @ SV54 )
= ( c_HOL_Ozero__class_Ozero @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(2171,plain,
! [SV385: $i,SV55: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV55 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV55 ) @ SV385 @ SV55 )
= ( c_HOL_Ozero__class_Ozero @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(2172,plain,
! [SV652: $i,SV387: $i,SV57: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV57 @ SV387 @ tc_nat ) @ SV652 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV57 @ SV652 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2173,plain,
! [SV388: $i,SV60: $i] :
( ( ( class_Orderings_Oorder @ SV60 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV388 @ SV388 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(2174,plain,
! [SV389: $i,SV61: $i] :
( ( ( class_Orderings_Olinorder @ SV61 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV389 @ SV389 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(2175,plain,
! [SV390: $i,SV62: $i] :
( ( ( class_Orderings_Opreorder @ SV62 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV390 @ SV390 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2176,plain,
! [SV653: $i,SV391: $i,SV63: $i] :
( ( ( ( c_Lambda_Oliftn @ SV63 @ ( c_Lambda_OdB_OVar @ SV391 ) @ SV653 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Oplus__class_Oplus @ SV391 @ SV63 @ tc_nat ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV391 @ SV653 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(2177,plain,
! [SV654: $i,SV392: $i,SV64: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV64 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ ( c_HOL_Oplus__class_Oplus @ SV392 @ SV654 @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV654 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV392 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(2178,plain,
! [SV655: $i,SV393: $i,SV65: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV65 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV393 @ SV655 @ SV65 )
| ( c_HOL_Oord__class_Oless @ SV655 @ SV393 @ SV65 )
| ( SV655 = SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(2179,plain,
! [SV656: $i,SV394: $i,SV66: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV66 ) )
= $true )
| ( ( ( SV394 = SV656 )
| ( c_HOL_Oord__class_Oless @ SV656 @ SV394 @ SV66 )
| ( c_HOL_Oord__class_Oless @ SV394 @ SV656 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(2180,plain,
! [SV67: $i,SV395: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV395 @ SV67 @ tc_nat )
= $true )
| ( ( SV395 = SV67 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV67 @ SV395 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(2181,plain,
! [SV68: $i,SV396: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV396 @ SV68 @ tc_nat )
= $true )
| ( ( SV396 = SV68 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV68 @ SV396 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2182,plain,
! [SV657: $i,SV397: $i,SV69: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV69 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV397 @ SV657 @ SV69 )
| ( c_HOL_Oord__class_Oless @ SV657 @ SV397 @ SV69 )
| ( SV657 = SV397 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(2183,plain,
! [SV658: $i,SV398: $i,SV70: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV70 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV398 @ SV658 @ SV70 )
| ( SV658 = SV398 )
| ( c_HOL_Oord__class_Oless @ SV658 @ SV398 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(2184,plain,
! [SV659: $i,SV399: $i,SV71: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV71 ) )
= $true )
| ( ( ( SV399 = SV659 )
| ( c_HOL_Oord__class_Oless @ SV399 @ SV659 @ SV71 )
| ( c_HOL_Oord__class_Oless @ SV659 @ SV399 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(2185,plain,
! [SV820: $i,SV660: $i,SV400: $i,SV74: $i] :
( ( ! [SY1939: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV74 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV400 @ SV660 @ SV74 ) @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SY1939 @ SV74 ) @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV660 @ SY1939 @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV400 @ SV820 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2186,plain,
! [SV821: $i,SV661: $i,SV401: $i,SV75: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV75 @ SV401 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV661 @ SV821 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV401 @ SV821 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV75 @ SV661 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2187,plain,
! [SV662: $i,SV402: $i,SV76: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV76 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV402 @ SV662 @ SV76 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV402 @ SV662 @ SV76 ) @ ( c_HOL_Ozero__class_Ozero @ SV76 ) @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(2188,plain,
! [SV663: $i,SV403: $i,SV77: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV77 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SV663 @ SV77 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SV403 @ SV663 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(2189,plain,
! [SV664: $i,SV404: $i,SV78: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV78 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV404 @ SV78 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV664 @ SV78 ) @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV404 @ SV664 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(2190,plain,
! [SV665: $i,SV405: $i,SV79: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV405 @ SV665 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV405 @ SV79 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV665 @ SV79 ) @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(2191,plain,
! [SV666: $i,SV406: $i,SV82: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV82 ) @ SV406 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV666 @ SV406 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV82 @ SV666 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2192,plain,
! [SV667: $i,SV407: $i,SV84: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV84 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV407 @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SV667 @ SV84 ) @ SV84 )
= ( c_HOL_Otimes__class_Otimes @ SV407 @ SV667 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(2193,plain,
! [SV408: $i,SV85: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV85 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV408 @ SV85 ) @ SV85 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV408 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(2194,plain,
! [SV409: $i,SV86: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV86 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV409 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV409 @ SV86 ) @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(2195,plain,
! [SV668: $i,SV411: $i,SV89: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV89 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SV668 @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV668 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(2196,plain,
! [SV669: $i,SV412: $i,SV90: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV90 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV412 @ SV669 @ SV90 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV412 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(2197,plain,
! [SV670: $i,SV413: $i,SV91: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV91 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV413 @ SV670 @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV670 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV413 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2198,plain,
! [SV822: $i,SV671: $i,SV415: $i,SV93: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV93 )
| ( c_HOL_Oord__class_Oless @ SV415 @ ( c_HOL_Oplus__class_Oplus @ SV671 @ SV822 @ SV93 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV415 @ SV822 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV671 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2199,plain,
! [SV672: $i,SV418: $i,SV96: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV96 @ SV418 @ tc_nat ) @ SV672 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV96 @ ( c_HOL_Ominus__class_Ominus @ SV672 @ SV418 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(2200,plain,
! [SV673: $i,SV419: $i,SV97: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV97 @ ( c_HOL_Ominus__class_Ominus @ SV419 @ SV673 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV97 @ SV673 @ tc_nat ) @ SV419 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(2201,plain,
! [SV823: $i,SV674: $i,SV420: $i,SV98: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV98 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV420 @ SV674 @ SV98 ) @ ( c_HOL_Oplus__class_Oplus @ SV823 @ SV674 @ SV98 ) @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV420 @ SV823 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2202,plain,
! [SV824: $i,SV675: $i,SV421: $i,SV99: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV99 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV421 @ SV675 @ SV99 ) @ ( c_HOL_Oplus__class_Oplus @ SV824 @ SV675 @ SV99 ) @ SV99 )
| ~ ( c_HOL_Oord__class_Oless @ SV421 @ SV824 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2203,plain,
! [SV825: $i,SV676: $i,SV422: $i,SV100: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV100 )
| ( c_HOL_Oord__class_Oless @ SV422 @ SV676 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV422 @ SV825 @ SV100 ) @ ( c_HOL_Oplus__class_Oplus @ SV676 @ SV825 @ SV100 ) @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2204,plain,
! [SV826: $i,SV677: $i,SV423: $i,SV101: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV101 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SV677 @ SV101 ) @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SV826 @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV826 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2205,plain,
! [SV827: $i,SV678: $i,SV424: $i,SV102: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV102 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SV678 @ SV102 ) @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SV827 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SV678 @ SV827 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2206,plain,
! [SV828: $i,SV679: $i,SV425: $i,SV103: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV103 )
| ( c_HOL_Oord__class_Oless @ SV425 @ SV679 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV828 @ SV425 @ SV103 ) @ ( c_HOL_Oplus__class_Oplus @ SV828 @ SV679 @ SV103 ) @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2207,plain,
! [SV680: $i,SV426: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV104 @ SV426 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV680 @ SV426 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV104 @ SV680 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(2208,plain,
! [SV681: $i,SV427: $i,SV105: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV105 @ SV427 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV681 @ SV105 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV681 @ SV427 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(2209,plain,
! [SV682: $i,SV428: $i,SV106: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV106 @ SV428 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV106 @ SV682 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV428 @ SV682 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(2210,plain,
! [SV429: $i,SV107: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV107 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV429 @ SV429 @ SV107 )
= SV429 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1926]) ).
thf(2211,plain,
! [SV108: $i,SV430: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV430 @ SV108 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV108 @ SV430 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1927]) ).
thf(2212,plain,
! [SV109: $i,SV431: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV431 @ SV109 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV109 @ SV431 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(2213,plain,
! [SV432: $i,SV110: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV110 ) @ SV432 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV110 @ SV432 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(2214,plain,
! [SV433: $i,SV111: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV111 @ SV433 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV111 @ ( c_Suc @ SV433 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(2215,plain,
! [SV829: $i,SV683: $i,SV434: $i,SV113: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV113 )
| ( c_HOL_Oord__class_Oless @ SV434 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
| ( c_HOL_Oord__class_Oless @ SV683 @ SV829 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV683 @ SV434 @ SV113 ) @ ( c_HOL_Otimes__class_Otimes @ SV829 @ SV434 @ SV113 ) @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2216,plain,
! [SV830: $i,SV684: $i,SV435: $i,SV114: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV114 )
| ( c_HOL_Oord__class_Oless @ SV435 @ SV684 @ SV114 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV830 @ SV114 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV684 @ SV830 @ SV114 ) @ ( c_HOL_Otimes__class_Otimes @ SV435 @ SV830 @ SV114 ) @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2217,plain,
! [SV831: $i,SV685: $i,SV436: $i,SV115: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV115 )
| ( c_HOL_Oord__class_Oless @ SV436 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
| ( c_HOL_Oord__class_Oless @ SV685 @ SV831 @ SV115 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV685 @ SV115 ) @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV831 @ SV115 ) @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2218,plain,
! [SV832: $i,SV686: $i,SV437: $i,SV116: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV116 )
| ( c_HOL_Oord__class_Oless @ SV437 @ SV686 @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV832 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV832 @ SV686 @ SV116 ) @ ( c_HOL_Otimes__class_Otimes @ SV832 @ SV437 @ SV116 ) @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2219,plain,
! [SV438: $i,SV118: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV118 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV438 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV118 @ SV438 @ tc_nat ) @ SV118 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1937]) ).
thf(2220,plain,
! [SV440: $i,SV120: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV120 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV120 @ ( c_Suc @ SV440 ) @ tc_nat ) @ SV120 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(2221,plain,
! [SV833: $i,SV687: $i,SV441: $i,SV121: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV121 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV441 @ SV687 @ SV121 ) @ SV833 @ SV121 )
= ( c_HOL_Otimes__class_Otimes @ SV441 @ ( c_HOL_Otimes__class_Otimes @ SV687 @ SV833 @ SV121 ) @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2222,plain,
! [SV834: $i,SV688: $i,SV442: $i,SV122: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV122 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV442 @ SV688 @ SV122 ) @ SV834 @ SV122 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV442 @ SV834 @ SV122 ) @ SV688 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2223,plain,
! [SV835: $i,SV689: $i,SV443: $i,SV123: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV123 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV443 @ SV689 @ SV123 ) @ SV835 @ SV123 )
= ( c_HOL_Otimes__class_Otimes @ SV443 @ ( c_HOL_Otimes__class_Otimes @ SV689 @ SV835 @ SV123 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2224,plain,
! [SV836: $i,SV690: $i,SV444: $i,SV124: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV124 )
| ( ( c_HOL_Otimes__class_Otimes @ SV444 @ ( c_HOL_Otimes__class_Otimes @ SV690 @ SV836 @ SV124 ) @ SV124 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV444 @ SV690 @ SV124 ) @ SV836 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2225,plain,
! [SV837: $i,SV691: $i,SV445: $i,SV125: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
| ( ( c_HOL_Otimes__class_Otimes @ SV445 @ ( c_HOL_Otimes__class_Otimes @ SV691 @ SV837 @ SV125 ) @ SV125 )
= ( c_HOL_Otimes__class_Otimes @ SV691 @ ( c_HOL_Otimes__class_Otimes @ SV445 @ SV837 @ SV125 ) @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2226,plain,
! [SV838: $i,SV692: $i,SV446: $i,SV126: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV126 )
| ( ( c_HOL_Otimes__class_Otimes @ SV446 @ ( c_HOL_Otimes__class_Otimes @ SV692 @ SV838 @ SV126 ) @ SV126 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV446 @ SV692 @ SV126 ) @ SV838 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2227,plain,
! [SV839: $i,SV693: $i,SV447: $i,SV127: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV447 @ SV693 @ SV127 ) @ SV839 @ SV127 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV447 @ SV839 @ SV127 ) @ ( c_HOL_Otimes__class_Otimes @ SV693 @ SV839 @ SV127 ) @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2228,plain,
! [SV840: $i,SV694: $i,SV448: $i,SV128: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV128 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV448 @ SV694 @ SV128 ) @ SV840 @ SV128 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV448 @ SV840 @ SV128 ) @ ( c_HOL_Otimes__class_Otimes @ SV694 @ SV840 @ SV128 ) @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2229,plain,
! [SV841: $i,SV695: $i,SV449: $i,SV129: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV129 )
| ( ( c_HOL_Otimes__class_Otimes @ SV449 @ ( c_HOL_Oplus__class_Oplus @ SV695 @ SV841 @ SV129 ) @ SV129 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV449 @ SV695 @ SV129 ) @ ( c_HOL_Otimes__class_Otimes @ SV449 @ SV841 @ SV129 ) @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2230,plain,
! [SV696: $i,SV450: $i,SV130: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV130 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV450 @ SV696 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV696 @ SV450 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1949]) ).
thf(2231,plain,
! [SV697: $i,SV451: $i,SV131: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV131 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV451 @ SV697 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ SV697 @ SV451 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1950]) ).
thf(2232,plain,
! [SV698: $i,SV452: $i,SV132: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV132 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV452 @ SV698 @ SV132 )
| ~ ( c_HOL_Oord__class_Oless @ SV698 @ SV452 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(2233,plain,
! [SV699: $i,SV453: $i,SV133: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV133 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV453 @ SV699 @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SV699 @ SV453 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1952]) ).
thf(2234,plain,
! [SV454: $i,SV134: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV134 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV454 @ ( c_HOL_Oone__class_Oone @ SV134 ) @ SV134 )
= SV454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2235,plain,
! [SV455: $i,SV135: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV135 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV455 @ ( c_HOL_Oone__class_Oone @ SV135 ) @ SV135 )
= SV455 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(2236,plain,
! [SV456: $i,SV136: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV136 ) @ SV456 @ SV136 )
= SV456 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1955]) ).
thf(2237,plain,
! [SV842: $i,SV700: $i,SV457: $i,SV137: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV137 )
| ~ ( class_Int_Onumber__ring @ SV137 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV700 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV842 @ SV137 ) @ SV137 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV842 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV700 @ SV137 ) @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2238,plain,
! [SV843: $i,SV701: $i,SV458: $i,SV138: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV138 )
| ~ ( class_Int_Onumber__ring @ SV138 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV701 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV843 @ SV138 ) @ SV138 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV843 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV701 @ SV138 ) @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2239,plain,
! [SV702: $i,SV459: $i,SV140: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV140 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV459 @ SV702 @ SV140 ) @ SV702 @ SV140 )
= SV459 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2240,plain,
! [SV704: $i,SV461: $i,SV142: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV142 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV461 @ SV704 @ SV142 )
= ( c_HOL_Otimes__class_Otimes @ SV704 @ SV461 @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2241,plain,
! [SV705: $i,SV462: $i,SV144: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV462 @ SV705 @ SV144 )
= ( c_HOL_Otimes__class_Otimes @ SV705 @ SV462 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2242,plain,
! [SV844: $i,SV706: $i,SV464: $i,SV146: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV146 )
| ( c_HOL_Oord__class_Oless @ SV464 @ SV706 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SV844 @ SV706 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SV464 @ SV844 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2243,plain,
! [SV845: $i,SV707: $i,SV465: $i,SV147: $i] :
( ( ~ ( class_Orderings_Oorder @ SV147 )
| ( c_HOL_Oord__class_Oless @ SV465 @ SV707 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SV465 @ SV845 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SV845 @ SV707 @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2244,plain,
! [SV148: $i,SV466: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV466 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV466 @ SV148 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV148 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2245,plain,
! [SV469: $i,SV153: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV153 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV469 ) @ SV153 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV153 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV469 @ SV153 ) @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2246,plain,
! [SV846: $i,SV711: $i,SV473: $i,SV160: $i] :
( ( ! [SY1940: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV160 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV473 @ SV711 @ SV160 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV846 @ SV711 @ SV160 ) @ SY1940 @ SV160 ) @ SV160 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV473 @ SV846 @ SV160 ) @ SV711 @ SV160 ) @ SY1940 @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2247,plain,
! [SV712: $i,SV474: $i,SV162: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV162 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SV712 @ SV162 ) @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV712 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV474 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2248,plain,
! [SV476: $i,SV164: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV164 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SV476 @ SV164 ) @ ( c_HOL_Ozero__class_Ozero @ SV164 ) @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1975]) ).
thf(2249,plain,
! [SV477: $i,SV165: $i] :
( ( ( ( c_Suc @ SV165 )
= SV477 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV165 @ SV477 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV165 ) @ SV477 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1976]) ).
thf(2250,plain,
! [SV715: $i,SV480: $i,SV168: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV168 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV480 @ SV480 @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SV715 @ SV715 @ SV168 ) @ SV168 ) @ SV168 )
| ( SV480
= ( c_HOL_Ozero__class_Ozero @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1978]) ).
thf(2251,plain,
! [SV716: $i,SV481: $i,SV169: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV169 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV481 @ SV481 @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SV716 @ SV716 @ SV169 ) @ SV169 ) @ SV169 )
| ( SV716
= ( c_HOL_Ozero__class_Ozero @ SV169 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1979]) ).
thf(2252,plain,
! [SV482: $i,SV170: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV170 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV482 @ SV170 ) @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2253,plain,
! [SV717: $i,SV483: $i,SV171: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV171 ) @ SV483 @ SV717 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV171 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV717 @ SV171 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1981]) ).
thf(2254,plain,
! [SV718: $i,SV484: $i,SV172: $i] :
( ( ( ( c_Lambda_Oliftn @ SV172 @ ( c_Lambda_OdB_OVar @ SV484 ) @ SV718 )
= ( c_Lambda_OdB_OVar @ SV484 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV484 @ SV718 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1982]) ).
thf(2255,plain,
! [SV847: $i,SV719: $i,SV485: $i,SV173: $i] :
( ( ( c_Lambda_Oliftn @ SV173 @ ( c_Lambda_OdB_OApp @ SV485 @ SV719 ) @ SV847 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV173 @ SV485 @ SV847 ) @ ( c_Lambda_Oliftn @ SV173 @ SV719 @ SV847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2256,plain,
! [SV848: $i,SV720: $i,SV486: $i,SV174: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV174 )
| ( c_HOL_Oord__class_Oless @ SV486 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV486 @ SV174 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV720 @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV848 @ SV174 ) @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2257,plain,
! [SV849: $i,SV721: $i,SV487: $i,SV175: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV175 )
| ( c_HOL_Oord__class_Oless @ SV487 @ SV721 @ SV175 )
| ( c_HOL_Oord__class_Oless @ SV721 @ SV487 @ SV175 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV849 @ SV721 @ SV175 ) @ ( c_HOL_Otimes__class_Otimes @ SV849 @ SV487 @ SV175 ) @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2258,plain,
! [SV850: $i,SV722: $i,SV488: $i,SV176: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV176 )
| ( c_HOL_Oord__class_Oless @ SV488 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV488 @ SV176 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV722 @ SV488 @ SV176 ) @ ( c_HOL_Otimes__class_Otimes @ SV850 @ SV488 @ SV176 ) @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2259,plain,
! [SV851: $i,SV723: $i,SV489: $i,SV177: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV177 )
| ( c_HOL_Oord__class_Oless @ SV489 @ SV723 @ SV177 )
| ( c_HOL_Oord__class_Oless @ SV723 @ SV489 @ SV177 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV723 @ SV851 @ SV177 ) @ ( c_HOL_Otimes__class_Otimes @ SV489 @ SV851 @ SV177 ) @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2260,plain,
! [SV491: $i,SV180: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV180 @ SV491 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV491 @ ( c_Suc @ SV180 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2261,plain,
! [SV852: $i,SV724: $i,SV493: $i,SV182: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV182 )
| ( c_HOL_Oord__class_Oless @ SV493 @ SV724 @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV724 @ SV182 ) @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV493 @ SV182 ) @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2262,plain,
! [SV853: $i,SV725: $i,SV494: $i,SV183: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV183 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV725 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV853 @ SV183 ) @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SV853 @ SV725 @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2263,plain,
! [SV854: $i,SV726: $i,SV495: $i,SV184: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV184 )
| ( c_HOL_Oord__class_Oless @ SV495 @ SV726 @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV495 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV726 @ SV184 ) @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV184 ) @ SV854 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2264,plain,
! [SV855: $i,SV727: $i,SV496: $i,SV185: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV185 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV727 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV855 @ SV185 ) @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SV727 @ SV855 @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV185 ) @ SV496 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2265,plain,
! [SV856: $i,SV728: $i,SV497: $i,SV186: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV186 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV728 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV856 @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SV497 @ ( c_HOL_Ozero__class_Ozero @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SV856 @ SV728 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2266,plain,
! [SV857: $i,SV729: $i,SV498: $i,SV187: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV187 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV729 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV857 @ SV187 ) @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SV498 @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ SV729 @ SV857 @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2267,plain,
! [SV858: $i,SV730: $i,SV499: $i,SV188: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV188 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV730 @ SV188 ) @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV858 @ SV188 ) @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ SV730 @ SV858 @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV188 ) @ SV499 @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2268,plain,
! [SV859: $i,SV731: $i,SV500: $i,SV189: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV189 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV731 @ SV189 ) @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV859 @ SV189 ) @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SV859 @ SV731 @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SV500 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2269,plain,
! [SV860: $i,SV732: $i,SV501: $i,SV190: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV190 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV501 @ SV732 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SV860 @ SV732 @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SV732 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SV860 @ SV501 @ SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2270,plain,
! [SV861: $i,SV733: $i,SV502: $i,SV191: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV191 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SV733 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SV861 @ SV733 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV733 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV502 @ SV861 @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2271,plain,
! [SV862: $i,SV734: $i,SV503: $i,SV192: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV192 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV503 @ SV734 @ SV192 ) @ ( c_HOL_Otimes__class_Otimes @ SV862 @ SV734 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SV503 @ SV862 @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV734 @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2272,plain,
! [SV863: $i,SV735: $i,SV504: $i,SV193: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV193 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV504 @ SV735 @ SV193 ) @ ( c_HOL_Otimes__class_Otimes @ SV863 @ SV735 @ SV193 ) @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV504 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SV735 @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2273,plain,
! [SV864: $i,SV736: $i,SV505: $i,SV194: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV194 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV736 @ SV194 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV864 @ SV194 ) @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV505 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ SV736 @ SV864 @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2274,plain,
! [SV865: $i,SV737: $i,SV506: $i,SV196: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV196 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV737 @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SV865 @ SV737 @ SV196 ) @ SV196 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV506 @ SV865 @ SV196 ) @ SV737 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2275,plain,
! [SV507: $i,SV197: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV197 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV507 @ SV197 )
= SV507 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2276,plain,
! [SV508: $i,SV198: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV198 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV508 @ SV198 )
= SV508 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2277,plain,
! [SV509: $i,SV202: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV202 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV202 )
| ( SV509
= ( c_HOL_Oplus__class_Oplus @ SV509 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2008]) ).
thf(2278,plain,
! [SV510: $i,SV203: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV203 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV510 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
= SV510 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2279,plain,
! [SV511: $i,SV204: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV204 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV511 @ SV204 )
= SV511 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2280,plain,
! [SV512: $i,SV205: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV205 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV512 @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV205 )
= SV512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2011]) ).
thf(2281,plain,
! [SV513: $i,SV206: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV206 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV513 @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV206 )
= SV513 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2282,plain,
! [SV514: $i,SV207: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV207 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV207 ) @ SV514 @ SV207 )
= SV514 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2283,plain,
! [SV208: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ SV208 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ ( c_HOL_Ozero__class_Ozero @ SV208 ) @ SV208 ) @ SV208 ) @ SV208 )
= $false )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2284,plain,
! [SV866: $i,SV738: $i,SV515: $i,SV209: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OApp @ SV209 @ SV515 ) @ SV738 @ SV866 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV209 @ SV738 @ SV866 ) @ ( c_Lambda_Osubstn @ SV515 @ SV738 @ SV866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2285,plain,
! [SV739: $i,SV518: $i,SV212: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV212 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV518 @ SV739 @ SV212 ) @ SV739 @ SV212 )
= SV518 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2286,plain,
! [SV740: $i,SV519: $i,SV213: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV213 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV519 @ SV740 @ SV213 ) @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV740 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV519 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2287,plain,
! [SV520: $i,SV214: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV214 @ SV520 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV214 ) @ ( c_Suc @ SV520 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2288,plain,
! [SV521: $i,SV215: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV215 ) @ ( c_Suc @ SV521 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV215 @ SV521 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2289,plain,
! [SV522: $i,SV216: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV216 @ SV522 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV216 ) @ ( c_Suc @ SV522 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2290,plain,
! [SV217: $i,SV523: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV523 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV217 @ SV523 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2291,plain,
! [SV524: $i,SV218: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV218 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV218 @ SV524 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2292,plain,
! [SV525: $i,SV219: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV219 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV525 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ ( c_HOL_Oplus__class_Oplus @ SV525 @ SV525 @ SV219 ) @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2293,plain,
! [SV526: $i,SV220: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV220 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ ( c_HOL_Oplus__class_Oplus @ SV526 @ SV526 @ SV220 ) @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV526 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2294,plain,
! [SV221: $i,SV527: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV527 ) @ SV221 )
= $false )
| ( ( SV221
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV527 @ SV221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2295,plain,
! [SV741: $i,SV528: $i,SV222: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV222 @ SV528 ) @ ( c_Suc @ SV741 ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV222 @ SV741 ) @ SV528 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV528 @ ( c_HOL_Oplus__class_Oplus @ SV741 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2296,plain,
! [SV867: $i,SV742: $i,SV529: $i,SV223: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ SV223 @ SV529 @ SV742 ) @ SV867 )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV223 @ ( c_HOL_Oplus__class_Oplus @ SV867 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ SV529 @ SV867 ) @ SV742 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV742 @ ( c_HOL_Oplus__class_Oplus @ SV867 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2297,plain,
! [SV530: $i,SV224: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV224 @ SV530 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV224 ) @ SV530 )
= ( c_Lambda_OdB_OVar @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2298,plain,
! [SV743: $i,SV531: $i,SV225: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV225 @ SV531 ) @ ( c_Lambda_OdB_OApp @ SV743 @ SV531 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV225 @ SV743 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2029]) ).
thf(2299,plain,
! [SV744: $i,SV532: $i,SV226: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV226 @ SV532 ) @ ( c_Lambda_OdB_OApp @ SV226 @ SV744 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV532 @ SV744 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2030]) ).
thf(2300,plain,
! [SV868: $i,SV745: $i,SV533: $i,SV227: $i] :
( ( ! [SY1941: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV745 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV868 @ SY1941 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV868 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV745 @ SY1941 @ SV227 ) @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2301,plain,
! [SV869: $i,SV746: $i,SV534: $i,SV228: $i] :
( ( ! [SY1942: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ ( c_Lambda_Olift @ SV534 @ SV746 ) @ ( c_Suc @ SV869 ) ) @ ( c_Lambda_Osubst @ SY1942 @ SV534 @ SV869 ) @ SV746 )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ SY1942 @ SV746 ) @ SV534 @ SV869 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV746 @ ( c_HOL_Oplus__class_Oplus @ SV869 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2302,plain,
! [SV870: $i,SV748: $i,SV536: $i,SV230: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ SV230 @ SV536 @ SV748 ) @ SV870 )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV230 @ SV870 ) @ ( c_Lambda_Olift @ SV536 @ SV870 ) @ ( c_HOL_Oplus__class_Oplus @ SV748 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV870 @ ( c_HOL_Oplus__class_Oplus @ SV748 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2303,plain,
! [SV871: $i,SV749: $i,SV539: $i,SV234: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV234 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV539 @ SV749 @ SV234 ) @ SV871 @ SV234 )
= ( c_HOL_Oplus__class_Oplus @ SV539 @ ( c_HOL_Oplus__class_Oplus @ SV749 @ SV871 @ SV234 ) @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2304,plain,
! [SV872: $i,SV750: $i,SV540: $i,SV235: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV235 )
| ( ( c_HOL_Oplus__class_Oplus @ SV540 @ ( c_HOL_Oplus__class_Oplus @ SV750 @ SV872 @ SV235 ) @ SV235 )
= ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Oplus__class_Oplus @ SV540 @ SV872 @ SV235 ) @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2305,plain,
! [SV873: $i,SV751: $i,SV541: $i,SV236: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV236 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV541 @ SV751 @ SV236 ) @ SV873 @ SV236 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV541 @ SV873 @ SV236 ) @ SV751 @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2306,plain,
! [SV874: $i,SV752: $i,SV542: $i,SV237: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 )
| ( ( c_HOL_Oplus__class_Oplus @ SV542 @ ( c_HOL_Oplus__class_Oplus @ SV752 @ SV874 @ SV237 ) @ SV237 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV542 @ SV752 @ SV237 ) @ SV874 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2307,plain,
! [SV875: $i,SV753: $i,SV543: $i,SV238: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV238 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV543 @ SV753 @ SV238 ) @ SV875 @ SV238 )
= ( c_HOL_Oplus__class_Oplus @ SV543 @ ( c_HOL_Oplus__class_Oplus @ SV753 @ SV875 @ SV238 ) @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2308,plain,
! [SV876: $i,SV754: $i,SV544: $i,SV239: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV239 )
| ( ( c_HOL_Oplus__class_Oplus @ SV544 @ ( c_HOL_Oplus__class_Oplus @ SV754 @ SV876 @ SV239 ) @ SV239 )
= ( c_HOL_Oplus__class_Oplus @ SV754 @ ( c_HOL_Oplus__class_Oplus @ SV544 @ SV876 @ SV239 ) @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2309,plain,
! [SV877: $i,SV755: $i,SV545: $i,SV240: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV240 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV545 @ SV755 @ SV240 ) @ SV877 @ SV240 )
= ( c_HOL_Oplus__class_Oplus @ SV545 @ ( c_HOL_Oplus__class_Oplus @ SV755 @ SV877 @ SV240 ) @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2310,plain,
! [SV878: $i,SV758: $i,SV548: $i,SV243: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV243 )
| ( ( c_HOL_Oplus__class_Oplus @ SV548 @ ( c_HOL_Oplus__class_Oplus @ SV758 @ SV878 @ SV243 ) @ SV243 )
= ( c_HOL_Oplus__class_Oplus @ SV758 @ ( c_HOL_Oplus__class_Oplus @ SV548 @ SV878 @ SV243 ) @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2311,plain,
! [SV879: $i,SV759: $i,SV549: $i,SV244: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV244 )
| ( ( c_HOL_Oplus__class_Oplus @ SV549 @ ( c_HOL_Oplus__class_Oplus @ SV759 @ SV879 @ SV244 ) @ SV244 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV549 @ SV759 @ SV244 ) @ SV879 @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2312,plain,
! [SV760: $i,SV550: $i,SV245: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV245 ) @ SV550 @ SV760 )
= ( c_Lambda_OdB_OVar @ SV245 ) )
= $true )
| ( ( ( SV245 = SV760 )
| ( c_HOL_Oord__class_Oless @ SV760 @ SV245 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2049]) ).
thf(2313,plain,
! [SV880: $i,SV761: $i,SV551: $i,SV246: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV246 @ SV551 @ SV761 ) @ ( c_Lambda_Osubst @ SV880 @ SV551 @ SV761 ) )
| ~ ( c_Lambda_Obeta @ SV246 @ SV880 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2314,plain,
! [SV763: $i,SV553: $i,SV250: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV250 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV553 @ SV763 @ SV250 )
= ( c_HOL_Oplus__class_Oplus @ SV763 @ SV553 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2315,plain,
! [SV764: $i,SV554: $i,SV251: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV251 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV554 @ SV764 @ SV251 )
= ( c_HOL_Oplus__class_Oplus @ SV764 @ SV554 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2053]) ).
thf(2316,plain,
! [SV765: $i,SV556: $i,SV253: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV253 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV556 @ SV765 @ SV253 )
= ( c_HOL_Oplus__class_Oplus @ SV765 @ SV556 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2054]) ).
thf(2317,plain,
! [SV557: $i,SV254: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV254 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV557 @ SV557 @ SV254 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV254 ) @ ( c_HOL_Oone__class_Oone @ SV254 ) @ SV254 ) @ SV557 @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2318,plain,
! [SV766: $i,SV558: $i,SV255: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV255 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV558 @ SV766 @ SV255 ) @ SV766 @ SV255 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV558 @ ( c_HOL_Oone__class_Oone @ SV255 ) @ SV255 ) @ SV766 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2056]) ).
thf(2319,plain,
! [SV767: $i,SV559: $i,SV256: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV559 @ ( c_HOL_Otimes__class_Otimes @ SV767 @ SV559 @ SV256 ) @ SV256 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV767 @ ( c_HOL_Oone__class_Oone @ SV256 ) @ SV256 ) @ SV559 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2057]) ).
thf(2320,plain,
! [SV563: $i,SV260: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV260 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV563 @ ( c_HOL_Oplus__class_Oplus @ SV563 @ ( c_HOL_Oone__class_Oone @ SV260 ) @ SV260 ) @ SV260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2321,plain,
! [SV564: $i,SV261: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV261 ) @ SV564 )
= $false )
| ( ( c_Lambda_Obeta @ SV261 @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV261 @ SV564 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2061]) ).
thf(2322,plain,
! [SV769: $i,SV565: $i,SV262: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV262 ) @ SV565 @ SV769 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV262 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV769 @ SV262 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2323,plain,
! [SV770: $i,SV566: $i,SV263: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV263 ) @ SV566 @ SV770 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV263 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV770 @ SV263 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2324,plain,
! [SV771: $i,SV567: $i,SV264: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV264 ) @ SV567 @ SV771 )
= ( c_Lambda_OdB_OVar @ SV264 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV264 @ SV771 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2064]) ).
thf(2325,plain,
! [SV881: $i,SV772: $i,SV569: $i,SV266: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ SV266 @ SV569 ) @ SV772 @ SV881 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV266 @ SV772 @ SV881 ) @ ( c_Lambda_Osubst @ SV569 @ SV772 @ SV881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2326,plain,
! [SV773: $i,SV570: $i,SV267: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV267 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SV570 @ SV773 @ tc_nat ) @ SV267 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV570 @ SV267 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV773 @ SV267 ) @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2327,plain,
! [SV776: $i,SV574: $i,SV272: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV272 @ SV574 ) @ ( c_Lambda_Olift @ SV776 @ SV574 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV272 @ SV776 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2328,plain,
! [SV575: $i,SV273: $i] :
( ( ( c_Lambda_Obeta @ SV273 @ SV575 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV273 ) @ ( c_Lambda_OdB_OAbs @ SV575 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2329,plain,
! [SV777: $i,SV576: $i,SV274: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV274 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV576 @ SV777 @ SV274 )
!= ( c_HOL_Ozero__class_Ozero @ SV274 ) )
| ( SV576 = SV777 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2072]) ).
thf(2330,plain,
! [SV882: $i,SV778: $i,SV577: $i,SV275: $i] :
( ( ! [SY1943: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV275 )
| ( ( c_HOL_Oplus__class_Oplus @ SV577 @ ( c_HOL_Oplus__class_Oplus @ SV778 @ SV882 @ SV275 ) @ SV275 )
!= ( c_HOL_Oplus__class_Oplus @ SV778 @ SY1943 @ SV275 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV577 @ SV882 @ SV275 )
= SY1943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2331,plain,
! [SV779: $i,SV578: $i,SV277: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV277 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV578 @ SV277 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV779 @ SV277 ) )
| ( SV578 = SV779 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2074]) ).
thf(2332,plain,
! [SV780: $i,SV579: $i,SV278: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV278 @ SV579 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV278 @ SV780 @ tc_nat ) )
= $true )
| ( ( SV579 = SV780 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2075]) ).
thf(2333,plain,
! [SV883: $i,SV781: $i,SV580: $i,SV280: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV280 )
| ( ( c_HOL_Oplus__class_Oplus @ SV580 @ SV781 @ SV280 )
!= ( c_HOL_Oplus__class_Oplus @ SV580 @ SV883 @ SV280 ) )
| ( SV781 = SV883 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2334,plain,
! [SV582: $i,SV283: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV283 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV582 @ SV582 @ SV283 )
!= ( c_HOL_Ozero__class_Ozero @ SV283 ) )
| ( SV582
= ( c_HOL_Ozero__class_Ozero @ SV283 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2335,plain,
! [SV782: $i,SV583: $i,SV284: $i] :
( ( ( c_Lambda_OdB_OApp @ SV284 @ SV583 )
= ( c_Lambda_OdB_OVar @ SV782 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2336,plain,
! [SV884: $i,SV783: $i,SV584: $i,SV285: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV285 )
| ( ( c_HOL_Ominus__class_Ominus @ SV584 @ SV783 @ SV285 )
!= ( c_HOL_Ominus__class_Ominus @ SV884 @ SV884 @ SV285 ) )
| ( SV584 = SV783 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2337,plain,
! [SV885: $i,SV784: $i,SV585: $i,SV286: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV286 @ SV585 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV784 @ SV885 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV784 @ SV585 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV286 @ SV885 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2338,plain,
! [SV886: $i,SV785: $i,SV586: $i,SV287: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV287 )
| ( ( c_HOL_Oplus__class_Oplus @ SV586 @ SV785 @ SV287 )
!= ( c_HOL_Oplus__class_Oplus @ SV886 @ SV785 @ SV287 ) )
| ( SV586 = SV886 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2339,plain,
! [SV587: $i,SV288: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV288 @ SV587 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV587
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2340,plain,
! [SV887: $i,SV786: $i,SV588: $i,SV290: $i] :
( ( ! [SY1944: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV290 )
| ~ ( class_Int_Onumber__ring @ SV290 )
| ( ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV887 @ SV290 ) @ SV290 )
!= ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SY1944 @ SV290 ) @ SV290 ) )
| ( SV887 = SY1944 )
| ( SV786
= ( c_HOL_Ozero__class_Ozero @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2341,plain,
! [SV888: $i,SV787: $i,SV589: $i,SV291: $i] :
( ( ! [SY1945: $i,SY1946: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV291 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV589 @ SV787 @ SV291 ) @ SV888 @ SV291 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1945 @ SV787 @ SV291 ) @ SY1946 @ SV291 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV589 @ SY1945 @ SV291 ) @ SV787 @ SV291 ) @ SV888 @ SV291 )
= SY1946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2342,plain,
! [SV590: $i,SV292: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV292 @ SV590 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV292
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV292
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2343,plain,
! [SV889: $i,SV788: $i,SV591: $i,SV293: $i] :
( ( ! [SY1947: $i,SY1948: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV293 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV591 @ SV788 @ SV293 ) @ SV889 @ SV293 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY1947 @ SV788 @ SV293 ) @ SY1948 @ SV293 ) )
| ( SV889
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY1947 @ SV591 @ SV293 ) @ SV788 @ SV293 ) @ SY1948 @ SV293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2344,plain,
! [SV789: $i,SV592: $i,SV294: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV294 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV592 @ SV789 @ SV294 )
!= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SV592
= ( c_HOL_Ozero__class_Ozero @ SV294 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2345,plain,
! [SV790: $i,SV593: $i,SV295: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV295 @ SV593 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV790 @ SV593 @ tc_nat ) )
= $true )
| ( ( SV295 = SV790 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2089]) ).
thf(2346,plain,
! [SV791: $i,SV594: $i,SV296: $i] :
( ( ( c_Lambda_OdB_OApp @ SV296 @ SV594 )
= ( c_Lambda_OdB_OAbs @ SV791 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2347,plain,
! [SV792: $i,SV595: $i,SV297: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV297 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV297 )
| ( ( c_HOL_Ominus__class_Ominus @ SV595 @ SV792 @ SV297 )
!= ( c_HOL_Ozero__class_Ozero @ SV297 ) )
| ( SV595 = SV792 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2348,plain,
! [SV793: $i,SV596: $i,SV299: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV299 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV596 @ SV793 @ SV299 )
!= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
| ( SV596
= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
| ( SV793
= ( c_HOL_Ozero__class_Ozero @ SV299 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2092]) ).
thf(2349,plain,
! [SV794: $i,SV597: $i,SV300: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV300 @ SV597 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV300 @ SV794 @ tc_nat ) )
= $true )
| ( ( SV597 = SV794 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2350,plain,
! [SV795: $i,SV598: $i,SV301: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV301 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV598 @ SV795 @ SV301 )
!= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
| ( SV795
= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
| ( SV598
= ( c_HOL_Ozero__class_Ozero @ SV301 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2094]) ).
thf(2351,plain,
! [SV599: $i,SV302: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV302 @ SV599 @ tc_nat ) )
= $false )
| ( ( ( SV302
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV302
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2095]) ).
thf(2352,plain,
! [SV796: $i,SV600: $i,SV304: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV304 )
= ( c_Lambda_OdB_OApp @ SV600 @ SV796 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2353,plain,
! [SV305: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV305 )
= ( c_HOL_Oone__class_Oone @ SV305 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV305 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2354,plain,
! [SV890: $i,SV797: $i,SV601: $i,SV306: $i] :
( ( ! [SY1949: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV306 )
| ~ ( class_Int_Onumber__ring @ SV306 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV797 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SY1949 @ SV306 ) @ SV306 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SY1949 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV797 @ SV306 ) @ SV306 ) )
| ( SV797 = SY1949 )
| ( SV601 = SV890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2355,plain,
! [SV891: $i,SV798: $i,SV602: $i,SV307: $i] :
( ( ! [SY1950: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV307 )
| ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV798 @ SV307 )
!= ( c_HOL_Ominus__class_Ominus @ SV891 @ SY1950 @ SV307 ) )
| ( c_HOL_Oord__class_Oless @ SV602 @ SV798 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SY1950 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2356,plain,
! [SV892: $i,SV799: $i,SV603: $i,SV308: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV308 @ SV603 )
!= ( c_Lambda_OdB_OApp @ SV799 @ SV892 ) )
| ( SV603 = SV892 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2357,plain,
! [SV800: $i,SV604: $i,SV309: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV309 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV604 @ SV604 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV800 @ SV800 @ SV309 ) @ SV309 )
!= ( c_HOL_Ozero__class_Ozero @ SV309 ) )
| ( SV800
= ( c_HOL_Ozero__class_Ozero @ SV309 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2358,plain,
! [SV605: $i,SV310: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV310 )
= ( c_Lambda_OdB_OAbs @ SV605 ) )
= $false )
| ( ( SV310 = SV605 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2359,plain,
! [SV606: $i,SV311: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV311 @ SV606 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV606
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV311
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2360,plain,
! [SV893: $i,SV801: $i,SV608: $i,SV313: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV313 )
| ~ ( class_Int_Onumber__ring @ SV313 )
| ( ( c_HOL_Oplus__class_Oplus @ SV608 @ SV801 @ SV313 )
!= ( c_HOL_Oplus__class_Oplus @ SV608 @ SV893 @ SV313 ) )
| ( SV801 = SV893 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2361,plain,
! [SV894: $i,SV802: $i,SV609: $i,SV314: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV314 )
| ( ( c_HOL_Ominus__class_Ominus @ SV609 @ SV609 @ SV314 )
!= ( c_HOL_Ominus__class_Ominus @ SV802 @ SV894 @ SV314 ) )
| ( SV802 = SV894 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2362,plain,
! [SV610: $i,SV315: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV315 @ SV610 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV315
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV610
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2363,plain,
! [SV803: $i,SV611: $i,SV316: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV316 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV316 )
| ( SV611
!= ( c_HOL_Oplus__class_Oplus @ SV611 @ SV803 @ SV316 ) )
| ( SV803
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2108]) ).
thf(2364,plain,
! [SV895: $i,SV804: $i,SV612: $i,SV317: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV317 )
| ( ( c_HOL_Oplus__class_Oplus @ SV612 @ SV804 @ SV317 )
!= ( c_HOL_Oplus__class_Oplus @ SV612 @ SV895 @ SV317 ) )
| ( SV804 = SV895 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2365,plain,
! [SV613: $i,SV318: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV318 @ SV613 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV613
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV613
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2366,plain,
! [SV614: $i,SV319: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV319 @ SV614 @ tc_nat ) )
= $false )
| ( ( ( SV614
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV614
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2367,plain,
! [SV805: $i,SV615: $i,SV320: $i] :
( ( ( c_Lambda_OdB_OVar @ SV320 )
= ( c_Lambda_OdB_OApp @ SV615 @ SV805 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2368,plain,
! [SV806: $i,SV616: $i,SV321: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV321 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV616 @ SV616 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SV806 @ SV806 @ SV321 ) @ SV321 )
!= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV616
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2113]) ).
thf(2369,plain,
! [SV617: $i,SV322: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV322 @ SV617 @ tc_nat )
= SV322 )
= $false )
| ( ( SV617
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2370,plain,
! [SV618: $i,SV323: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV323 @ SV618 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV618 @ SV323 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV618 = SV323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2371,plain,
! [SV619: $i,SV324: $i] :
( ( ( SV324
= ( c_HOL_Oplus__class_Oplus @ SV324 @ SV619 @ tc_nat ) )
= $false )
| ( ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2372,plain,
! [SV896: $i,SV807: $i,SV620: $i,SV325: $i] :
( ( ! [SY1951: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV807 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV896 @ SY1951 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SV896 @ SY1951 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV620 @ SV807 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2373,plain,
! [SV897: $i,SV808: $i,SV621: $i,SV326: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV326 @ SV621 )
!= ( c_Lambda_OdB_OApp @ SV808 @ SV897 ) )
| ( SV326 = SV808 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2374,plain,
! [SV622: $i,SV327: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV327 @ SV622 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV327
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2375,plain,
! [SV623: $i,SV328: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV328 @ SV623 @ tc_nat ) )
= $false )
| ( ( ( SV623
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV328
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2376,plain,
! [SV624: $i,SV329: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV329 @ SV624 @ tc_nat ) )
= $false )
| ( ( ( SV329
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV624
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2377,plain,
! [SV625: $i,SV330: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV330 )
= ( c_Lambda_OdB_OVar @ SV625 ) )
= $false )
| ( ( SV330 = SV625 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2378,plain,
! [SV809: $i,SV626: $i,SV331: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV331 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV626 @ SV809 @ SV331 )
!= ( c_HOL_Ozero__class_Ozero @ SV331 ) )
| ( SV626 = SV809 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2123]) ).
thf(2379,plain,
! [SV898: $i,SV810: $i,SV627: $i,SV332: $i] :
( ( ! [SY1952: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV332 )
| ~ ( class_Int_Onumber__ring @ SV332 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV810 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SY1952 @ SV332 ) @ SV332 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SY1952 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV810 @ SV332 ) @ SV332 ) )
| ( SV810 = SY1952 )
| ( SV627 = SV898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2380,plain,
! [SV333: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ SV333 )
= ( c_HOL_Ozero__class_Ozero @ SV333 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV333 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2381,plain,
! [SV628: $i,SV334: $i] :
( ( ( ( c_Suc @ SV334 )
= ( c_Suc @ SV628 ) )
= $false )
| ( ( SV334 = SV628 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2382,plain,
! [SV629: $i,SV335: $i] :
( ( ( ( c_Suc @ SV335 )
= ( c_Suc @ SV629 ) )
= $false )
| ( ( SV335 = SV629 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2383,plain,
! [SV899: $i,SV811: $i,SV630: $i,SV336: $i,SV2: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV630 @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SV811 @ SV899 @ SV2 ) @ SV2 )
= ( c_HOL_Otimes__class_Otimes @ SV811 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV630 @ SV2 ) @ SV899 @ SV2 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2384,plain,
! [SV900: $i,SV812: $i,SV631: $i,SV337: $i,SV3: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV3 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV337 @ SV631 @ SV3 ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV900 @ SV3 ) @ SV3 )
= ( c_HOL_Otimes__class_Otimes @ SV337 @ ( c_HOL_Otimes__class_Otimes @ SV631 @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV900 @ SV3 ) @ SV3 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2385,plain,
! [SV901: $i,SV813: $i,SV632: $i,SV338: $i,SV4: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV338 @ SV632 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV901 @ SV4 ) @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV338 @ SV813 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SV632 @ SV901 @ SV4 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2386,plain,
! [SV339: $i,SV5: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV5 @ ( c_Suc @ SV339 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV5 @ SV339 @ tc_nat )
= $true )
| ( ( SV5 = SV339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2387,plain,
! [SV6: $i,SV340: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV340 @ ( c_Suc @ SV6 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV340 @ SV6 @ tc_nat )
= $true )
| ( ( SV6 = SV340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2388,plain,
! [SV341: $i,SV7: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV7 @ ( c_Suc @ SV341 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV7 @ SV341 @ tc_nat )
= $true )
| ( ( SV7 = SV341 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2389,plain,
! [SV633: $i,SV343: $i,SV9: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV9 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV343 @ SV343 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV633 @ SV633 @ SV9 ) @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2390,plain,
! [SV344: $i,SV634: $i,SV11: $i] :
( ( ( SV11 = SV634 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV634 @ SV11 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV11 ) @ SV344 @ SV634 )
= ( c_Lambda_OdB_OVar @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2391,plain,
! [SV635: $i,SV345: $i,SV12: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV12 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SV345 @ SV635 @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SV635 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SV345 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2392,plain,
! [SV636: $i,SV346: $i,SV13: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV13 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SV346 @ SV636 @ SV13 ) @ SV13 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV636 @ SV13 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV346 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2393,plain,
! [SV637: $i,SV347: $i,SV14: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV14 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV347 @ SV14 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV637 @ SV14 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ ( c_HOL_Otimes__class_Otimes @ SV637 @ SV347 @ SV14 ) @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2394,plain,
! [SV638: $i,SV348: $i,SV15: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV15 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV348 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV638 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ ( c_HOL_Otimes__class_Otimes @ SV348 @ SV638 @ SV15 ) @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2395,plain,
! [SV16: $i,SV349: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV349 @ SV349 @ SV16 ) @ ( c_HOL_Ozero__class_Ozero @ SV16 ) @ SV16 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV349 @ ( c_HOL_Ozero__class_Ozero @ SV16 ) @ SV16 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2141]) ).
thf(2396,plain,
! [SV17: $i,SV350: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV350 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SV350 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2397,plain,
! [SV18: $i,SV351: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV351 @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV351 @ SV351 @ SV18 ) @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2143]) ).
thf(2398,plain,
! [SV19: $i,SV352: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV352 @ SV352 @ SV19 ) @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV352 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2399,plain,
! [SV902: $i,SV814: $i,SV639: $i,SV353: $i,SV20: $i] :
( ( ! [SY1953: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV20 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV353 @ SV639 @ SV20 ) @ SV814 @ SV20 ) @ SV902 @ SV20 ) @ SY1953 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV814 @ SV20 ) @ SV902 @ SV20 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV639 @ SV814 @ SV20 ) @ SY1953 @ SV20 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2400,plain,
! [SV903: $i,SV815: $i,SV640: $i,SV354: $i,SV21: $i] :
( ( ! [SY1954: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV21 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV354 @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV903 @ SV640 @ SV21 ) @ SY1954 @ SV21 ) @ SV21 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV354 @ SV903 @ SV21 ) @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ SY1954 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2401,plain,
! [SV904: $i,SV816: $i,SV641: $i,SV355: $i,SV22: $i] :
( ( ! [SY1955: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV22 )
| ( c_HOL_Oord__class_Oless @ SV355 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SV816 @ SV22 ) @ SV904 @ SV22 ) @ SY1955 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV904 @ SV22 ) @ SV355 @ SV22 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV641 @ SV904 @ SV22 ) @ SY1955 @ SV22 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2402,plain,
! [SV905: $i,SV817: $i,SV642: $i,SV356: $i,SV23: $i] :
( ( ! [SY1956: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV23 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV356 @ SV642 @ SV23 ) @ SV817 @ SV23 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV905 @ SV642 @ SV23 ) @ SY1956 @ SV23 ) @ SV23 )
| ~ ( c_HOL_Oord__class_Oless @ SV817 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV905 @ SV356 @ SV23 ) @ SV642 @ SV23 ) @ SY1956 @ SV23 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2403,plain,
! [SV358: $i,SV27: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV27 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV358 @ SV358 @ SV27 )
= ( c_HOL_Ozero__class_Ozero @ SV27 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2404,plain,
! [SV363: $i,SV32: $i,SV644: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV644 @ SV32 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV644 @ SV363 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV363 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV644 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2405,plain,
! [SV364: $i,SV645: $i,SV34: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV34 @ SV645 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV34 @ ( c_HOL_Oplus__class_Oplus @ SV364 @ SV645 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2406,plain,
! [SV646: $i,SV365: $i,SV35: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV35 @ SV365 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV35 @ ( c_HOL_Oplus__class_Oplus @ SV365 @ SV646 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2407,plain,
! [SV366: $i,SV647: $i,SV36: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV36 @ SV647 @ tc_nat ) @ SV366 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV36 @ SV366 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2408,plain,
! [SV367: $i,SV648: $i,SV37: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV37 @ SV648 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV37 @ ( c_HOL_Oplus__class_Oplus @ SV367 @ SV648 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2409,plain,
! [SV649: $i,SV368: $i,SV38: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV38 @ SV368 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV38 @ ( c_HOL_Oplus__class_Oplus @ SV368 @ SV649 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2410,plain,
! [SV906: $i,SV818: $i,SV650: $i,SV372: $i,SV42: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV42 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV372 @ SV650 @ SV42 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV818 @ SV372 @ SV42 ) @ SV650 @ SV42 ) @ SV906 @ SV42 ) @ SV42 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV818 @ SV650 @ SV42 ) @ SV906 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2411,plain,
! [SV907: $i,SV819: $i,SV651: $i,SV375: $i,SV45: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV45 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV375 @ SV651 @ SV45 ) @ SV819 @ SV45 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV907 @ SV651 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV375 @ SV907 @ SV45 ) @ SV651 @ SV45 ) @ SV819 @ SV45 ) @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2412,plain,
! [SV387: $i,SV652: $i,SV57: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV57 @ SV652 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV57 @ SV387 @ tc_nat ) @ SV652 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2413,plain,
! [SV60: $i,SV388: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV388 @ SV388 @ SV60 )
= $false )
| ( ( class_Orderings_Oorder @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2414,plain,
! [SV61: $i,SV389: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV389 @ SV389 @ SV61 )
= $false )
| ( ( class_Orderings_Olinorder @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2415,plain,
! [SV62: $i,SV390: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV390 @ SV390 @ SV62 )
= $false )
| ( ( class_Orderings_Opreorder @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2416,plain,
! [SV654: $i,SV392: $i,SV64: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV64 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ ( c_HOL_Oplus__class_Oplus @ SV392 @ SV654 @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV654 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV392 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2417,plain,
! [SV655: $i,SV393: $i,SV65: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV65 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV393 @ SV655 @ SV65 )
| ( c_HOL_Oord__class_Oless @ SV655 @ SV393 @ SV65 )
| ( SV655 = SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2178]) ).
thf(2418,plain,
! [SV656: $i,SV394: $i,SV66: $i] :
( ( ( class_Orderings_Olinorder @ SV66 )
= $false )
| ( ( ( SV394 = SV656 )
| ( c_HOL_Oord__class_Oless @ SV656 @ SV394 @ SV66 )
| ( c_HOL_Oord__class_Oless @ SV394 @ SV656 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2419,plain,
! [SV657: $i,SV397: $i,SV69: $i] :
( ( ( class_Orderings_Olinorder @ SV69 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV397 @ SV657 @ SV69 )
| ( c_HOL_Oord__class_Oless @ SV657 @ SV397 @ SV69 )
| ( SV657 = SV397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2420,plain,
! [SV658: $i,SV398: $i,SV70: $i] :
( ( ( class_Orderings_Olinorder @ SV70 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV398 @ SV658 @ SV70 )
| ( SV658 = SV398 )
| ( c_HOL_Oord__class_Oless @ SV658 @ SV398 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2183]) ).
thf(2421,plain,
! [SV659: $i,SV399: $i,SV71: $i] :
( ( ( class_Orderings_Olinorder @ SV71 )
= $false )
| ( ( ( SV399 = SV659 )
| ( c_HOL_Oord__class_Oless @ SV399 @ SV659 @ SV71 )
| ( c_HOL_Oord__class_Oless @ SV659 @ SV399 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2422,plain,
! [SV908: $i,SV820: $i,SV660: $i,SV400: $i,SV74: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV74 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV400 @ SV660 @ SV74 ) @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV908 @ SV74 ) @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV660 @ SV908 @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV400 @ SV820 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2423,plain,
! [SV821: $i,SV661: $i,SV401: $i,SV75: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV75 @ SV401 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV661 @ SV821 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV401 @ SV821 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV75 @ SV661 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2186]) ).
thf(2424,plain,
! [SV662: $i,SV402: $i,SV76: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV76 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV402 @ SV662 @ SV76 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV402 @ SV662 @ SV76 ) @ ( c_HOL_Ozero__class_Ozero @ SV76 ) @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2425,plain,
! [SV663: $i,SV403: $i,SV77: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV77 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SV663 @ SV77 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SV403 @ SV663 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2426,plain,
! [SV664: $i,SV404: $i,SV78: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV78 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV404 @ SV78 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV664 @ SV78 ) @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV404 @ SV664 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2189]) ).
thf(2427,plain,
! [SV665: $i,SV405: $i,SV79: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV79 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV405 @ SV665 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV405 @ SV79 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV665 @ SV79 ) @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2428,plain,
! [SV82: $i,SV406: $i,SV666: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV666 @ SV406 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV82 @ SV666 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV82 ) @ SV406 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2191]) ).
thf(2429,plain,
! [SV667: $i,SV407: $i,SV84: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV84 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV407 @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SV667 @ SV84 ) @ SV84 )
= ( c_HOL_Otimes__class_Otimes @ SV407 @ SV667 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2430,plain,
! [SV408: $i,SV85: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV408 @ SV85 ) @ SV85 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV408 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2431,plain,
! [SV86: $i,SV409: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV409 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV409 @ SV86 ) @ SV86 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2194]) ).
thf(2432,plain,
! [SV668: $i,SV411: $i,SV89: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV89 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SV668 @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV668 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2433,plain,
! [SV669: $i,SV412: $i,SV90: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV90 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV412 @ SV669 @ SV90 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV412 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2196]) ).
thf(2434,plain,
! [SV670: $i,SV413: $i,SV91: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV91 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV413 @ SV670 @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV670 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV413 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2435,plain,
! [SV822: $i,SV671: $i,SV415: $i,SV93: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV93 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV415 @ ( c_HOL_Oplus__class_Oplus @ SV671 @ SV822 @ SV93 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV415 @ SV822 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV671 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2436,plain,
! [SV418: $i,SV672: $i,SV96: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV96 @ ( c_HOL_Ominus__class_Ominus @ SV672 @ SV418 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV96 @ SV418 @ tc_nat ) @ SV672 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2437,plain,
! [SV419: $i,SV673: $i,SV97: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV97 @ SV673 @ tc_nat ) @ SV419 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV97 @ ( c_HOL_Ominus__class_Ominus @ SV419 @ SV673 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2438,plain,
! [SV823: $i,SV674: $i,SV420: $i,SV98: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV98 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV420 @ SV674 @ SV98 ) @ ( c_HOL_Oplus__class_Oplus @ SV823 @ SV674 @ SV98 ) @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV420 @ SV823 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2439,plain,
! [SV824: $i,SV675: $i,SV421: $i,SV99: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV99 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV421 @ SV675 @ SV99 ) @ ( c_HOL_Oplus__class_Oplus @ SV824 @ SV675 @ SV99 ) @ SV99 )
| ~ ( c_HOL_Oord__class_Oless @ SV421 @ SV824 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2440,plain,
! [SV825: $i,SV676: $i,SV422: $i,SV100: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV100 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV422 @ SV676 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV422 @ SV825 @ SV100 ) @ ( c_HOL_Oplus__class_Oplus @ SV676 @ SV825 @ SV100 ) @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2441,plain,
! [SV826: $i,SV677: $i,SV423: $i,SV101: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV101 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SV677 @ SV101 ) @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SV826 @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV826 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2442,plain,
! [SV827: $i,SV678: $i,SV424: $i,SV102: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV102 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SV678 @ SV102 ) @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SV827 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SV678 @ SV827 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2205]) ).
thf(2443,plain,
! [SV828: $i,SV679: $i,SV425: $i,SV103: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV103 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV425 @ SV679 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV828 @ SV425 @ SV103 ) @ ( c_HOL_Oplus__class_Oplus @ SV828 @ SV679 @ SV103 ) @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2444,plain,
! [SV426: $i,SV680: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV104 @ SV680 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV104 @ SV426 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV680 @ SV426 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2445,plain,
! [SV427: $i,SV105: $i,SV681: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV681 @ SV105 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV681 @ SV427 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV105 @ SV427 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2446,plain,
! [SV106: $i,SV682: $i,SV428: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV428 @ SV682 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV106 @ SV428 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV106 @ SV682 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2447,plain,
! [SV829: $i,SV683: $i,SV434: $i,SV113: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV113 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV434 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
| ( c_HOL_Oord__class_Oless @ SV683 @ SV829 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV683 @ SV434 @ SV113 ) @ ( c_HOL_Otimes__class_Otimes @ SV829 @ SV434 @ SV113 ) @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2215]) ).
thf(2448,plain,
! [SV830: $i,SV684: $i,SV435: $i,SV114: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV114 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV435 @ SV684 @ SV114 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV830 @ SV114 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV684 @ SV830 @ SV114 ) @ ( c_HOL_Otimes__class_Otimes @ SV435 @ SV830 @ SV114 ) @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2216]) ).
thf(2449,plain,
! [SV831: $i,SV685: $i,SV436: $i,SV115: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV115 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV436 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
| ( c_HOL_Oord__class_Oless @ SV685 @ SV831 @ SV115 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV685 @ SV115 ) @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV831 @ SV115 ) @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2217]) ).
thf(2450,plain,
! [SV832: $i,SV686: $i,SV437: $i,SV116: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV116 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV437 @ SV686 @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV832 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV832 @ SV686 @ SV116 ) @ ( c_HOL_Otimes__class_Otimes @ SV832 @ SV437 @ SV116 ) @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2218]) ).
thf(2451,plain,
! [SV438: $i,SV118: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV118 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV438 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV118 @ SV438 @ tc_nat ) @ SV118 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2452,plain,
! [SV833: $i,SV687: $i,SV441: $i,SV121: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV121 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV441 @ SV687 @ SV121 ) @ SV833 @ SV121 )
= ( c_HOL_Otimes__class_Otimes @ SV441 @ ( c_HOL_Otimes__class_Otimes @ SV687 @ SV833 @ SV121 ) @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2453,plain,
! [SV834: $i,SV688: $i,SV442: $i,SV122: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV122 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV442 @ SV688 @ SV122 ) @ SV834 @ SV122 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV442 @ SV834 @ SV122 ) @ SV688 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2454,plain,
! [SV835: $i,SV689: $i,SV443: $i,SV123: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV123 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV443 @ SV689 @ SV123 ) @ SV835 @ SV123 )
= ( c_HOL_Otimes__class_Otimes @ SV443 @ ( c_HOL_Otimes__class_Otimes @ SV689 @ SV835 @ SV123 ) @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2455,plain,
! [SV836: $i,SV690: $i,SV444: $i,SV124: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV124 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV444 @ ( c_HOL_Otimes__class_Otimes @ SV690 @ SV836 @ SV124 ) @ SV124 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV444 @ SV690 @ SV124 ) @ SV836 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2224]) ).
thf(2456,plain,
! [SV837: $i,SV691: $i,SV445: $i,SV125: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV445 @ ( c_HOL_Otimes__class_Otimes @ SV691 @ SV837 @ SV125 ) @ SV125 )
= ( c_HOL_Otimes__class_Otimes @ SV691 @ ( c_HOL_Otimes__class_Otimes @ SV445 @ SV837 @ SV125 ) @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2225]) ).
thf(2457,plain,
! [SV838: $i,SV692: $i,SV446: $i,SV126: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV126 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV446 @ ( c_HOL_Otimes__class_Otimes @ SV692 @ SV838 @ SV126 ) @ SV126 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV446 @ SV692 @ SV126 ) @ SV838 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2458,plain,
! [SV839: $i,SV693: $i,SV447: $i,SV127: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV447 @ SV693 @ SV127 ) @ SV839 @ SV127 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV447 @ SV839 @ SV127 ) @ ( c_HOL_Otimes__class_Otimes @ SV693 @ SV839 @ SV127 ) @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2459,plain,
! [SV840: $i,SV694: $i,SV448: $i,SV128: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV128 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV448 @ SV694 @ SV128 ) @ SV840 @ SV128 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV448 @ SV840 @ SV128 ) @ ( c_HOL_Otimes__class_Otimes @ SV694 @ SV840 @ SV128 ) @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2228]) ).
thf(2460,plain,
! [SV841: $i,SV695: $i,SV449: $i,SV129: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV129 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV449 @ ( c_HOL_Oplus__class_Oplus @ SV695 @ SV841 @ SV129 ) @ SV129 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV449 @ SV695 @ SV129 ) @ ( c_HOL_Otimes__class_Otimes @ SV449 @ SV841 @ SV129 ) @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2229]) ).
thf(2461,plain,
! [SV696: $i,SV450: $i,SV130: $i] :
( ( ( class_Orderings_Oorder @ SV130 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV450 @ SV696 @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV696 @ SV450 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2462,plain,
! [SV697: $i,SV451: $i,SV131: $i] :
( ( ( class_Orderings_Olinorder @ SV131 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV451 @ SV697 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ SV697 @ SV451 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2231]) ).
thf(2463,plain,
! [SV698: $i,SV452: $i,SV132: $i] :
( ( ( class_Orderings_Opreorder @ SV132 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV452 @ SV698 @ SV132 )
| ~ ( c_HOL_Oord__class_Oless @ SV698 @ SV452 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2464,plain,
! [SV699: $i,SV453: $i,SV133: $i] :
( ( ( class_Orderings_Opreorder @ SV133 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV453 @ SV699 @ SV133 )
| ~ ( c_HOL_Oord__class_Oless @ SV699 @ SV453 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2465,plain,
! [SV842: $i,SV700: $i,SV457: $i,SV137: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV137 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV137 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV700 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV842 @ SV137 ) @ SV137 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV842 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV700 @ SV137 ) @ SV137 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2466,plain,
! [SV843: $i,SV701: $i,SV458: $i,SV138: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV138 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV138 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV701 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV843 @ SV138 ) @ SV138 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV843 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV701 @ SV138 ) @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2467,plain,
! [SV702: $i,SV459: $i,SV140: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV140 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV459 @ SV702 @ SV140 ) @ SV702 @ SV140 )
= SV459 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2468,plain,
! [SV704: $i,SV461: $i,SV142: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV142 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV461 @ SV704 @ SV142 )
= ( c_HOL_Otimes__class_Otimes @ SV704 @ SV461 @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2240]) ).
thf(2469,plain,
! [SV705: $i,SV462: $i,SV144: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV462 @ SV705 @ SV144 )
= ( c_HOL_Otimes__class_Otimes @ SV705 @ SV462 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2470,plain,
! [SV844: $i,SV706: $i,SV464: $i,SV146: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV146 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV464 @ SV706 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SV844 @ SV706 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SV464 @ SV844 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2471,plain,
! [SV845: $i,SV707: $i,SV465: $i,SV147: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV147 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV465 @ SV707 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SV465 @ SV845 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SV845 @ SV707 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2243]) ).
thf(2472,plain,
! [SV148: $i,SV466: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV466 @ SV148 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV466 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV148 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2473,plain,
! [SV909: $i,SV846: $i,SV711: $i,SV473: $i,SV160: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring @ SV160 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV473 @ SV711 @ SV160 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV846 @ SV711 @ SV160 ) @ SV909 @ SV160 ) @ SV160 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV473 @ SV846 @ SV160 ) @ SV711 @ SV160 ) @ SV909 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2474,plain,
! [SV712: $i,SV474: $i,SV162: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV162 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SV712 @ SV162 ) @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV712 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV474 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2475,plain,
! [SV164: $i,SV476: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SV476 @ SV164 ) @ ( c_HOL_Ozero__class_Ozero @ SV164 ) @ SV164 )
= $false )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2476,plain,
! [SV477: $i,SV165: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV165 @ SV477 @ tc_nat )
= $false )
| ( ( ( c_Suc @ SV165 )
= SV477 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV165 ) @ SV477 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2477,plain,
! [SV715: $i,SV480: $i,SV168: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV168 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV480 @ SV480 @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SV715 @ SV715 @ SV168 ) @ SV168 ) @ SV168 )
| ( SV480
= ( c_HOL_Ozero__class_Ozero @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2478,plain,
! [SV716: $i,SV481: $i,SV169: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV169 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV481 @ SV481 @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SV716 @ SV716 @ SV169 ) @ SV169 ) @ SV169 )
| ( SV716
= ( c_HOL_Ozero__class_Ozero @ SV169 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2479,plain,
! [SV170: $i,SV482: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV482 @ SV170 ) @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2480,plain,
! [SV483: $i,SV171: $i,SV717: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV717 @ SV171 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV171 ) @ SV483 @ SV717 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV171 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2481,plain,
! [SV172: $i,SV718: $i,SV484: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV484 @ SV718 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Oliftn @ SV172 @ ( c_Lambda_OdB_OVar @ SV484 ) @ SV718 )
= ( c_Lambda_OdB_OVar @ SV484 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2482,plain,
! [SV848: $i,SV720: $i,SV486: $i,SV174: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV174 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV486 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV486 @ SV174 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV720 @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV848 @ SV174 ) @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2483,plain,
! [SV849: $i,SV721: $i,SV487: $i,SV175: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV175 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV487 @ SV721 @ SV175 )
| ( c_HOL_Oord__class_Oless @ SV721 @ SV487 @ SV175 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV849 @ SV721 @ SV175 ) @ ( c_HOL_Otimes__class_Otimes @ SV849 @ SV487 @ SV175 ) @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2484,plain,
! [SV850: $i,SV722: $i,SV488: $i,SV176: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV176 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV488 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV488 @ SV176 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV722 @ SV488 @ SV176 ) @ ( c_HOL_Otimes__class_Otimes @ SV850 @ SV488 @ SV176 ) @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2258]) ).
thf(2485,plain,
! [SV851: $i,SV723: $i,SV489: $i,SV177: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV177 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV489 @ SV723 @ SV177 )
| ( c_HOL_Oord__class_Oless @ SV723 @ SV489 @ SV177 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV723 @ SV851 @ SV177 ) @ ( c_HOL_Otimes__class_Otimes @ SV489 @ SV851 @ SV177 ) @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2486,plain,
! [SV180: $i,SV491: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV491 @ ( c_Suc @ SV180 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV180 @ SV491 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2487,plain,
! [SV852: $i,SV724: $i,SV493: $i,SV182: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV182 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV493 @ SV724 @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV724 @ SV182 ) @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV493 @ SV182 ) @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2488,plain,
! [SV853: $i,SV725: $i,SV494: $i,SV183: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV183 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV725 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV853 @ SV183 ) @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SV853 @ SV725 @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2262]) ).
thf(2489,plain,
! [SV854: $i,SV726: $i,SV495: $i,SV184: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV184 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV495 @ SV726 @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV495 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV726 @ SV184 ) @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV184 ) @ SV854 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2490,plain,
! [SV855: $i,SV727: $i,SV496: $i,SV185: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV185 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV727 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV855 @ SV185 ) @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SV727 @ SV855 @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV185 ) @ SV496 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2491,plain,
! [SV856: $i,SV728: $i,SV497: $i,SV186: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV186 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV728 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV856 @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SV497 @ ( c_HOL_Ozero__class_Ozero @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SV856 @ SV728 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2492,plain,
! [SV857: $i,SV729: $i,SV498: $i,SV187: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV187 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV729 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV857 @ SV187 ) @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SV498 @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ SV729 @ SV857 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2266]) ).
thf(2493,plain,
! [SV858: $i,SV730: $i,SV499: $i,SV188: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV188 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV730 @ SV188 ) @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV858 @ SV188 ) @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ SV730 @ SV858 @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV188 ) @ SV499 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2267]) ).
thf(2494,plain,
! [SV859: $i,SV731: $i,SV500: $i,SV189: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV189 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV731 @ SV189 ) @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV859 @ SV189 ) @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SV859 @ SV731 @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SV500 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2495,plain,
! [SV860: $i,SV732: $i,SV501: $i,SV190: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV190 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV501 @ SV732 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SV860 @ SV732 @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SV732 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SV860 @ SV501 @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2496,plain,
! [SV861: $i,SV733: $i,SV502: $i,SV191: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV191 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SV733 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SV861 @ SV733 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV733 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV502 @ SV861 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2497,plain,
! [SV862: $i,SV734: $i,SV503: $i,SV192: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV192 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV503 @ SV734 @ SV192 ) @ ( c_HOL_Otimes__class_Otimes @ SV862 @ SV734 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SV503 @ SV862 @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV734 @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2498,plain,
! [SV863: $i,SV735: $i,SV504: $i,SV193: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV193 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV504 @ SV735 @ SV193 ) @ ( c_HOL_Otimes__class_Otimes @ SV863 @ SV735 @ SV193 ) @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV504 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SV735 @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2272]) ).
thf(2499,plain,
! [SV864: $i,SV736: $i,SV505: $i,SV194: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV194 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV736 @ SV194 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV864 @ SV194 ) @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV505 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ SV736 @ SV864 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2500,plain,
! [SV865: $i,SV737: $i,SV506: $i,SV196: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV196 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV737 @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SV865 @ SV737 @ SV196 ) @ SV196 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV506 @ SV865 @ SV196 ) @ SV737 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2501,plain,
! [SV509: $i,SV202: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV202 ) )
= $true )
| ( ( SV509
= ( c_HOL_Oplus__class_Oplus @ SV509 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2502,plain,
! [SV739: $i,SV518: $i,SV212: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV212 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV518 @ SV739 @ SV212 ) @ SV739 @ SV212 )
= SV518 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2503,plain,
! [SV740: $i,SV519: $i,SV213: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV213 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV519 @ SV740 @ SV213 ) @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV740 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV519 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2504,plain,
! [SV525: $i,SV219: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV525 @ SV219 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ ( c_HOL_Oplus__class_Oplus @ SV525 @ SV525 @ SV219 ) @ SV219 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2292]) ).
thf(2505,plain,
! [SV526: $i,SV220: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ ( c_HOL_Oplus__class_Oplus @ SV526 @ SV526 @ SV220 ) @ SV220 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV526 @ SV220 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2293]) ).
thf(2506,plain,
! [SV222: $i,SV741: $i,SV528: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV528 @ ( c_HOL_Oplus__class_Oplus @ SV741 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV222 @ SV528 ) @ ( c_Suc @ SV741 ) )
= ( c_Lambda_Olift @ ( c_Lambda_Olift @ SV222 @ SV741 ) @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2507,plain,
! [SV867: $i,SV742: $i,SV529: $i,SV223: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ SV223 @ SV529 @ SV742 ) @ SV867 )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV223 @ ( c_HOL_Oplus__class_Oplus @ SV867 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ SV529 @ SV867 ) @ SV742 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV742 @ ( c_HOL_Oplus__class_Oplus @ SV867 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2296]) ).
thf(2508,plain,
! [SV531: $i,SV743: $i,SV225: $i] :
( ( ( c_Lambda_Obeta @ SV225 @ SV743 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV225 @ SV531 ) @ ( c_Lambda_OdB_OApp @ SV743 @ SV531 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2509,plain,
! [SV226: $i,SV744: $i,SV532: $i] :
( ( ( c_Lambda_Obeta @ SV532 @ SV744 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV226 @ SV532 ) @ ( c_Lambda_OdB_OApp @ SV226 @ SV744 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2510,plain,
! [SV910: $i,SV868: $i,SV745: $i,SV533: $i,SV227: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV745 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV868 @ SV910 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV868 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV745 @ SV910 @ SV227 ) @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2511,plain,
! [SV911: $i,SV869: $i,SV746: $i,SV534: $i,SV228: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ ( c_Lambda_Olift @ SV534 @ SV746 ) @ ( c_Suc @ SV869 ) ) @ ( c_Lambda_Osubst @ SV911 @ SV534 @ SV869 ) @ SV746 )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ SV911 @ SV746 ) @ SV534 @ SV869 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV746 @ ( c_HOL_Oplus__class_Oplus @ SV869 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2512,plain,
! [SV870: $i,SV748: $i,SV536: $i,SV230: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ SV230 @ SV536 @ SV748 ) @ SV870 )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV230 @ SV870 ) @ ( c_Lambda_Olift @ SV536 @ SV870 ) @ ( c_HOL_Oplus__class_Oplus @ SV748 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV870 @ ( c_HOL_Oplus__class_Oplus @ SV748 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2513,plain,
! [SV871: $i,SV749: $i,SV539: $i,SV234: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV234 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV539 @ SV749 @ SV234 ) @ SV871 @ SV234 )
= ( c_HOL_Oplus__class_Oplus @ SV539 @ ( c_HOL_Oplus__class_Oplus @ SV749 @ SV871 @ SV234 ) @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2303]) ).
thf(2514,plain,
! [SV872: $i,SV750: $i,SV540: $i,SV235: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV235 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV540 @ ( c_HOL_Oplus__class_Oplus @ SV750 @ SV872 @ SV235 ) @ SV235 )
= ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Oplus__class_Oplus @ SV540 @ SV872 @ SV235 ) @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2304]) ).
thf(2515,plain,
! [SV873: $i,SV751: $i,SV541: $i,SV236: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV236 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV541 @ SV751 @ SV236 ) @ SV873 @ SV236 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV541 @ SV873 @ SV236 ) @ SV751 @ SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2305]) ).
thf(2516,plain,
! [SV874: $i,SV752: $i,SV542: $i,SV237: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV542 @ ( c_HOL_Oplus__class_Oplus @ SV752 @ SV874 @ SV237 ) @ SV237 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV542 @ SV752 @ SV237 ) @ SV874 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2517,plain,
! [SV875: $i,SV753: $i,SV543: $i,SV238: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV238 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV543 @ SV753 @ SV238 ) @ SV875 @ SV238 )
= ( c_HOL_Oplus__class_Oplus @ SV543 @ ( c_HOL_Oplus__class_Oplus @ SV753 @ SV875 @ SV238 ) @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2307]) ).
thf(2518,plain,
! [SV876: $i,SV754: $i,SV544: $i,SV239: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV239 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV544 @ ( c_HOL_Oplus__class_Oplus @ SV754 @ SV876 @ SV239 ) @ SV239 )
= ( c_HOL_Oplus__class_Oplus @ SV754 @ ( c_HOL_Oplus__class_Oplus @ SV544 @ SV876 @ SV239 ) @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2308]) ).
thf(2519,plain,
! [SV877: $i,SV755: $i,SV545: $i,SV240: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV240 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV545 @ SV755 @ SV240 ) @ SV877 @ SV240 )
= ( c_HOL_Oplus__class_Oplus @ SV545 @ ( c_HOL_Oplus__class_Oplus @ SV755 @ SV877 @ SV240 ) @ SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2309]) ).
thf(2520,plain,
! [SV878: $i,SV758: $i,SV548: $i,SV243: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV243 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV548 @ ( c_HOL_Oplus__class_Oplus @ SV758 @ SV878 @ SV243 ) @ SV243 )
= ( c_HOL_Oplus__class_Oplus @ SV758 @ ( c_HOL_Oplus__class_Oplus @ SV548 @ SV878 @ SV243 ) @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2521,plain,
! [SV879: $i,SV759: $i,SV549: $i,SV244: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV244 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV549 @ ( c_HOL_Oplus__class_Oplus @ SV759 @ SV879 @ SV244 ) @ SV244 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV549 @ SV759 @ SV244 ) @ SV879 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2522,plain,
! [SV550: $i,SV760: $i,SV245: $i] :
( ( ( SV245 = SV760 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV760 @ SV245 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV245 ) @ SV550 @ SV760 )
= ( c_Lambda_OdB_OVar @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2312]) ).
thf(2523,plain,
! [SV880: $i,SV761: $i,SV551: $i,SV246: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV246 @ SV551 @ SV761 ) @ ( c_Lambda_Osubst @ SV880 @ SV551 @ SV761 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV246 @ SV880 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2313]) ).
thf(2524,plain,
! [SV763: $i,SV553: $i,SV250: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV250 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV553 @ SV763 @ SV250 )
= ( c_HOL_Oplus__class_Oplus @ SV763 @ SV553 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2525,plain,
! [SV764: $i,SV554: $i,SV251: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV251 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV554 @ SV764 @ SV251 )
= ( c_HOL_Oplus__class_Oplus @ SV764 @ SV554 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2315]) ).
thf(2526,plain,
! [SV765: $i,SV556: $i,SV253: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV253 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV556 @ SV765 @ SV253 )
= ( c_HOL_Oplus__class_Oplus @ SV765 @ SV556 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2527,plain,
! [SV766: $i,SV558: $i,SV255: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV255 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV558 @ SV766 @ SV255 ) @ SV766 @ SV255 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV558 @ ( c_HOL_Oone__class_Oone @ SV255 ) @ SV255 ) @ SV766 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2528,plain,
! [SV767: $i,SV559: $i,SV256: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV256 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV559 @ ( c_HOL_Otimes__class_Otimes @ SV767 @ SV559 @ SV256 ) @ SV256 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV767 @ ( c_HOL_Oone__class_Oone @ SV256 ) @ SV256 ) @ SV559 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2529,plain,
! [SV565: $i,SV262: $i,SV769: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV769 @ SV262 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV262 ) @ SV565 @ SV769 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV262 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2530,plain,
! [SV566: $i,SV263: $i,SV770: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV770 @ SV263 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV263 ) @ SV566 @ SV770 )
= ( c_Lambda_OdB_OVar @ ( c_HOL_Ominus__class_Ominus @ SV263 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2531,plain,
! [SV567: $i,SV771: $i,SV264: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV264 @ SV771 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV264 ) @ SV567 @ SV771 )
= ( c_Lambda_OdB_OVar @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2532,plain,
! [SV773: $i,SV570: $i,SV267: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV267 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SV570 @ SV773 @ tc_nat ) @ SV267 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV570 @ SV267 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV773 @ SV267 ) @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2533,plain,
! [SV574: $i,SV776: $i,SV272: $i] :
( ( ( c_Lambda_Obeta @ SV272 @ SV776 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV272 @ SV574 ) @ ( c_Lambda_Olift @ SV776 @ SV574 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2534,plain,
! [SV777: $i,SV576: $i,SV274: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV274 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV576 @ SV777 @ SV274 )
!= ( c_HOL_Ozero__class_Ozero @ SV274 ) )
| ( SV576 = SV777 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2535,plain,
! [SV912: $i,SV882: $i,SV778: $i,SV577: $i,SV275: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV275 )
| ( ( c_HOL_Oplus__class_Oplus @ SV577 @ ( c_HOL_Oplus__class_Oplus @ SV778 @ SV882 @ SV275 ) @ SV275 )
!= ( c_HOL_Oplus__class_Oplus @ SV778 @ SV912 @ SV275 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV577 @ SV882 @ SV275 )
= SV912 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2536,plain,
! [SV779: $i,SV578: $i,SV277: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV277 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV578 @ SV277 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV779 @ SV277 ) )
| ( SV578 = SV779 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2537,plain,
! [SV780: $i,SV579: $i,SV278: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV278 @ SV579 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV278 @ SV780 @ tc_nat ) )
= $false )
| ( ( SV579 = SV780 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2538,plain,
! [SV883: $i,SV781: $i,SV580: $i,SV280: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV280 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV580 @ SV781 @ SV280 )
!= ( c_HOL_Oplus__class_Oplus @ SV580 @ SV883 @ SV280 ) )
| ( SV781 = SV883 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2539,plain,
! [SV283: $i,SV582: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV582 @ SV582 @ SV283 )
!= ( c_HOL_Ozero__class_Ozero @ SV283 ) )
= $true )
| ( ( SV582
= ( c_HOL_Ozero__class_Ozero @ SV283 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2540,plain,
! [SV884: $i,SV783: $i,SV584: $i,SV285: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV285 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV584 @ SV783 @ SV285 )
!= ( c_HOL_Ominus__class_Ominus @ SV884 @ SV884 @ SV285 ) )
| ( SV584 = SV783 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2336]) ).
thf(2541,plain,
! [SV885: $i,SV784: $i,SV585: $i,SV286: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV286 @ SV585 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV784 @ SV885 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV784 @ SV585 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV286 @ SV885 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2542,plain,
! [SV886: $i,SV785: $i,SV586: $i,SV287: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV287 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV586 @ SV785 @ SV287 )
!= ( c_HOL_Oplus__class_Oplus @ SV886 @ SV785 @ SV287 ) )
| ( SV586 = SV886 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2543,plain,
! [SV913: $i,SV887: $i,SV786: $i,SV588: $i,SV290: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV290 )
| ~ ( class_Int_Onumber__ring @ SV290 )
| ( ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV887 @ SV290 ) @ SV290 )
!= ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV913 @ SV290 ) @ SV290 ) )
| ( SV887 = SV913 )
| ( SV786
= ( c_HOL_Ozero__class_Ozero @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2544,plain,
! [SV914: $i,SV888: $i,SV787: $i,SV589: $i,SV291: $i] :
( ( ! [SY1957: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV291 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV589 @ SV787 @ SV291 ) @ SV888 @ SV291 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV787 @ SV291 ) @ SY1957 @ SV291 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV589 @ SV914 @ SV291 ) @ SV787 @ SV291 ) @ SV888 @ SV291 )
= SY1957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2545,plain,
! [SV590: $i,SV292: $i] :
( ( ( SV292
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV292
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV292 @ SV590 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2342]) ).
thf(2546,plain,
! [SV915: $i,SV889: $i,SV788: $i,SV591: $i,SV293: $i] :
( ( ! [SY1958: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV293 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV591 @ SV788 @ SV293 ) @ SV889 @ SV293 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV788 @ SV293 ) @ SY1958 @ SV293 ) )
| ( SV889
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV915 @ SV591 @ SV293 ) @ SV788 @ SV293 ) @ SY1958 @ SV293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2547,plain,
! [SV789: $i,SV592: $i,SV294: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV294 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV592 @ SV789 @ SV294 )
!= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SV592
= ( c_HOL_Ozero__class_Ozero @ SV294 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2548,plain,
! [SV790: $i,SV593: $i,SV295: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV295 @ SV593 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV790 @ SV593 @ tc_nat ) )
= $false )
| ( ( SV295 = SV790 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2549,plain,
! [SV792: $i,SV595: $i,SV297: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV297 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV297 )
| ( ( c_HOL_Ominus__class_Ominus @ SV595 @ SV792 @ SV297 )
!= ( c_HOL_Ozero__class_Ozero @ SV297 ) )
| ( SV595 = SV792 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2550,plain,
! [SV793: $i,SV596: $i,SV299: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV299 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV596 @ SV793 @ SV299 )
!= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
| ( SV596
= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
| ( SV793
= ( c_HOL_Ozero__class_Ozero @ SV299 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2551,plain,
! [SV794: $i,SV597: $i,SV300: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV300 @ SV597 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV300 @ SV794 @ tc_nat ) )
= $false )
| ( ( SV597 = SV794 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2552,plain,
! [SV795: $i,SV598: $i,SV301: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV301 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV598 @ SV795 @ SV301 )
!= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
| ( SV795
= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
| ( SV598
= ( c_HOL_Ozero__class_Ozero @ SV301 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2553,plain,
! [SV599: $i,SV302: $i] :
( ( ( SV302
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV302
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV302 @ SV599 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2351]) ).
thf(2554,plain,
! [SV916: $i,SV890: $i,SV797: $i,SV601: $i,SV306: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV306 )
| ~ ( class_Int_Onumber__ring @ SV306 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV797 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV916 @ SV306 ) @ SV306 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV916 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV797 @ SV306 ) @ SV306 ) )
| ( SV797 = SV916 )
| ( SV601 = SV890 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(2555,plain,
! [SV917: $i,SV891: $i,SV798: $i,SV602: $i,SV307: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV307 )
| ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV798 @ SV307 )
!= ( c_HOL_Ominus__class_Ominus @ SV891 @ SV917 @ SV307 ) )
| ( c_HOL_Oord__class_Oless @ SV602 @ SV798 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV917 @ SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2556,plain,
! [SV892: $i,SV799: $i,SV603: $i,SV308: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV308 @ SV603 )
!= ( c_Lambda_OdB_OApp @ SV799 @ SV892 ) )
= $true )
| ( ( SV603 = SV892 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2356]) ).
thf(2557,plain,
! [SV800: $i,SV604: $i,SV309: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV604 @ SV604 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV800 @ SV800 @ SV309 ) @ SV309 )
!= ( c_HOL_Ozero__class_Ozero @ SV309 ) )
| ( SV800
= ( c_HOL_Ozero__class_Ozero @ SV309 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2558,plain,
! [SV311: $i,SV606: $i] :
( ( ( SV606
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV311
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV311 @ SV606 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2359]) ).
thf(2559,plain,
! [SV893: $i,SV801: $i,SV608: $i,SV313: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV313 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV313 )
| ( ( c_HOL_Oplus__class_Oplus @ SV608 @ SV801 @ SV313 )
!= ( c_HOL_Oplus__class_Oplus @ SV608 @ SV893 @ SV313 ) )
| ( SV801 = SV893 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(2560,plain,
! [SV894: $i,SV802: $i,SV609: $i,SV314: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV314 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV609 @ SV609 @ SV314 )
!= ( c_HOL_Ominus__class_Ominus @ SV802 @ SV894 @ SV314 ) )
| ( SV802 = SV894 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2561,plain,
! [SV610: $i,SV315: $i] :
( ( ( SV315
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV610
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV315 @ SV610 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2562,plain,
! [SV803: $i,SV611: $i,SV316: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV316 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV316 )
| ( SV611
!= ( c_HOL_Oplus__class_Oplus @ SV611 @ SV803 @ SV316 ) )
| ( SV803
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2563,plain,
! [SV895: $i,SV804: $i,SV612: $i,SV317: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV317 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV612 @ SV804 @ SV317 )
!= ( c_HOL_Oplus__class_Oplus @ SV612 @ SV895 @ SV317 ) )
| ( SV804 = SV895 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2564,plain,
! [SV318: $i,SV613: $i] :
( ( ( SV613
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV613
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV318 @ SV613 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2565,plain,
! [SV319: $i,SV614: $i] :
( ( ( SV614
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV614
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV319 @ SV614 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2566,plain,
! [SV806: $i,SV616: $i,SV321: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV321 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV616 @ SV616 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SV806 @ SV806 @ SV321 ) @ SV321 )
!= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV616
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2567,plain,
! [SV323: $i,SV618: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV618 @ SV323 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV618 = SV323 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV323 @ SV618 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2568,plain,
! [SV918: $i,SV896: $i,SV807: $i,SV620: $i,SV325: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV807 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV896 @ SV918 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SV896 @ SV918 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV620 @ SV807 @ SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2569,plain,
! [SV897: $i,SV808: $i,SV621: $i,SV326: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV326 @ SV621 )
!= ( c_Lambda_OdB_OApp @ SV808 @ SV897 ) )
= $true )
| ( ( SV326 = SV808 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2373]) ).
thf(2570,plain,
! [SV328: $i,SV623: $i] :
( ( ( SV623
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV328
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV328 @ SV623 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2375]) ).
thf(2571,plain,
! [SV624: $i,SV329: $i] :
( ( ( SV329
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV624
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV329 @ SV624 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2376]) ).
thf(2572,plain,
! [SV809: $i,SV626: $i,SV331: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV331 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV626 @ SV809 @ SV331 )
!= ( c_HOL_Ozero__class_Ozero @ SV331 ) )
| ( SV626 = SV809 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2573,plain,
! [SV919: $i,SV898: $i,SV810: $i,SV627: $i,SV332: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV332 )
| ~ ( class_Int_Onumber__ring @ SV332 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV810 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV919 @ SV332 ) @ SV332 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV919 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV810 @ SV332 ) @ SV332 ) )
| ( SV810 = SV919 )
| ( SV627 = SV898 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2379]) ).
thf(2574,plain,
! [SV899: $i,SV811: $i,SV630: $i,SV336: $i,SV2: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV630 @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SV811 @ SV899 @ SV2 ) @ SV2 )
= ( c_HOL_Otimes__class_Otimes @ SV811 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV630 @ SV2 ) @ SV899 @ SV2 ) @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2575,plain,
! [SV900: $i,SV812: $i,SV631: $i,SV337: $i,SV3: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV3 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV337 @ SV631 @ SV3 ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV900 @ SV3 ) @ SV3 )
= ( c_HOL_Otimes__class_Otimes @ SV337 @ ( c_HOL_Otimes__class_Otimes @ SV631 @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV900 @ SV3 ) @ SV3 ) @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2384]) ).
thf(2576,plain,
! [SV901: $i,SV813: $i,SV632: $i,SV338: $i,SV4: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV338 @ SV632 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV901 @ SV4 ) @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV338 @ SV813 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SV632 @ SV901 @ SV4 ) @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2385]) ).
thf(2577,plain,
! [SV633: $i,SV9: $i,SV343: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV343 @ SV343 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV633 @ SV633 @ SV9 ) @ SV9 ) @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV9 )
= $false )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2578,plain,
! [SV635: $i,SV345: $i,SV12: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SV345 @ SV635 @ SV12 ) @ SV12 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV635 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SV345 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2391]) ).
thf(2579,plain,
! [SV636: $i,SV346: $i,SV13: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SV346 @ SV636 @ SV13 ) @ SV13 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV636 @ SV13 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV346 @ SV13 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2392]) ).
thf(2580,plain,
! [SV637: $i,SV347: $i,SV14: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV347 @ SV14 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV637 @ SV14 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ ( c_HOL_Otimes__class_Otimes @ SV637 @ SV347 @ SV14 ) @ SV14 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2393]) ).
thf(2581,plain,
! [SV638: $i,SV348: $i,SV15: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV348 @ SV15 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV638 @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ ( c_HOL_Otimes__class_Otimes @ SV348 @ SV638 @ SV15 ) @ SV15 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2582,plain,
! [SV16: $i,SV349: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV349 @ ( c_HOL_Ozero__class_Ozero @ SV16 ) @ SV16 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV349 @ SV349 @ SV16 ) @ ( c_HOL_Ozero__class_Ozero @ SV16 ) @ SV16 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2583,plain,
! [SV17: $i,SV350: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SV350 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV350 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2396]) ).
thf(2584,plain,
! [SV18: $i,SV351: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV351 @ SV351 @ SV18 ) @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV351 @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2585,plain,
! [SV19: $i,SV352: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV352 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV352 @ SV352 @ SV19 ) @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2398]) ).
thf(2586,plain,
! [SV920: $i,SV902: $i,SV814: $i,SV639: $i,SV353: $i,SV20: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV20 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV353 @ SV639 @ SV20 ) @ SV814 @ SV20 ) @ SV902 @ SV20 ) @ SV920 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV814 @ SV20 ) @ SV902 @ SV20 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV639 @ SV814 @ SV20 ) @ SV920 @ SV20 ) @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(2587,plain,
! [SV921: $i,SV903: $i,SV815: $i,SV640: $i,SV354: $i,SV21: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV21 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV354 @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV903 @ SV640 @ SV21 ) @ SV921 @ SV21 ) @ SV21 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV354 @ SV903 @ SV21 ) @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ SV921 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(2588,plain,
! [SV922: $i,SV904: $i,SV816: $i,SV641: $i,SV355: $i,SV22: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV22 )
| ( c_HOL_Oord__class_Oless @ SV355 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SV816 @ SV22 ) @ SV904 @ SV22 ) @ SV922 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV904 @ SV22 ) @ SV355 @ SV22 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV641 @ SV904 @ SV22 ) @ SV922 @ SV22 ) @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2589,plain,
! [SV923: $i,SV905: $i,SV817: $i,SV642: $i,SV356: $i,SV23: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV23 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV356 @ SV642 @ SV23 ) @ SV817 @ SV23 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV905 @ SV642 @ SV23 ) @ SV923 @ SV23 ) @ SV23 )
| ~ ( c_HOL_Oord__class_Oless @ SV817 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV905 @ SV356 @ SV23 ) @ SV642 @ SV23 ) @ SV923 @ SV23 ) @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2590,plain,
! [SV358: $i,SV27: $i] :
( ( ( class_Int_Onumber__ring @ SV27 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV358 @ SV358 @ SV27 )
= ( c_HOL_Ozero__class_Ozero @ SV27 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2591,plain,
! [SV363: $i,SV32: $i,SV644: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV644 @ SV32 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV644 @ SV363 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV363 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV644 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2404]) ).
thf(2592,plain,
! [SV906: $i,SV818: $i,SV650: $i,SV372: $i,SV42: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV42 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV372 @ SV650 @ SV42 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV818 @ SV372 @ SV42 ) @ SV650 @ SV42 ) @ SV906 @ SV42 ) @ SV42 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV818 @ SV650 @ SV42 ) @ SV906 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2410]) ).
thf(2593,plain,
! [SV907: $i,SV819: $i,SV651: $i,SV375: $i,SV45: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV45 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV375 @ SV651 @ SV45 ) @ SV819 @ SV45 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV907 @ SV651 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV375 @ SV907 @ SV45 ) @ SV651 @ SV45 ) @ SV819 @ SV45 ) @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2594,plain,
! [SV654: $i,SV392: $i,SV64: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ ( c_HOL_Oplus__class_Oplus @ SV392 @ SV654 @ SV64 ) @ SV64 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV654 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV392 @ SV64 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2595,plain,
! [SV65: $i,SV655: $i,SV393: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV393 @ SV655 @ SV65 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV655 @ SV393 @ SV65 )
| ( SV655 = SV393 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2596,plain,
! [SV66: $i,SV656: $i,SV394: $i] :
( ( ( SV394 = SV656 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV656 @ SV394 @ SV66 )
| ( c_HOL_Oord__class_Oless @ SV394 @ SV656 @ SV66 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2418]) ).
thf(2597,plain,
! [SV69: $i,SV657: $i,SV397: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV397 @ SV657 @ SV69 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV657 @ SV397 @ SV69 )
| ( SV657 = SV397 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2419]) ).
thf(2598,plain,
! [SV70: $i,SV658: $i,SV398: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV398 @ SV658 @ SV70 )
= $true )
| ( ( ( SV658 = SV398 )
| ( c_HOL_Oord__class_Oless @ SV658 @ SV398 @ SV70 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2599,plain,
! [SV71: $i,SV659: $i,SV399: $i] :
( ( ( SV399 = SV659 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV399 @ SV659 @ SV71 )
| ( c_HOL_Oord__class_Oless @ SV659 @ SV399 @ SV71 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2600,plain,
! [SV908: $i,SV820: $i,SV660: $i,SV400: $i,SV74: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV74 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV400 @ SV660 @ SV74 ) @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV908 @ SV74 ) @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV660 @ SV908 @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV400 @ SV820 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2422]) ).
thf(2601,plain,
! [SV661: $i,SV75: $i,SV821: $i,SV401: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV401 @ SV821 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV75 @ SV661 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV75 @ SV401 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV661 @ SV821 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2423]) ).
thf(2602,plain,
! [SV76: $i,SV662: $i,SV402: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV402 @ SV662 @ SV76 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV402 @ SV662 @ SV76 ) @ ( c_HOL_Ozero__class_Ozero @ SV76 ) @ SV76 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2603,plain,
! [SV77: $i,SV663: $i,SV403: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SV663 @ SV77 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV403 @ SV663 @ SV77 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2604,plain,
! [SV664: $i,SV78: $i,SV404: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV404 @ SV78 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV664 @ SV78 ) @ SV78 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV404 @ SV664 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2426]) ).
thf(2605,plain,
! [SV79: $i,SV665: $i,SV405: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV405 @ SV665 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV405 @ SV79 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV665 @ SV79 ) @ SV79 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2427]) ).
thf(2606,plain,
! [SV82: $i,SV406: $i,SV666: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV666 @ SV406 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV82 @ SV666 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV82 ) @ SV406 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2607,plain,
! [SV85: $i,SV408: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV408 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV85 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV408 @ SV85 ) @ SV85 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2608,plain,
! [SV409: $i,SV86: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV409 @ SV86 ) @ SV86 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV409 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2609,plain,
! [SV89: $i,SV668: $i,SV411: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SV668 @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV411 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV668 @ SV89 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2610,plain,
! [SV90: $i,SV669: $i,SV412: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV412 @ SV669 @ SV90 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV412 @ SV90 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2433]) ).
thf(2611,plain,
! [SV91: $i,SV670: $i,SV413: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV413 @ SV670 @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV670 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV413 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2612,plain,
! [SV822: $i,SV671: $i,SV415: $i,SV93: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV93 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV415 @ ( c_HOL_Oplus__class_Oplus @ SV671 @ SV822 @ SV93 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV415 @ SV822 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV671 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2613,plain,
! [SV823: $i,SV674: $i,SV420: $i,SV98: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV98 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV420 @ SV674 @ SV98 ) @ ( c_HOL_Oplus__class_Oplus @ SV823 @ SV674 @ SV98 ) @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ SV420 @ SV823 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2614,plain,
! [SV824: $i,SV675: $i,SV421: $i,SV99: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV99 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV421 @ SV675 @ SV99 ) @ ( c_HOL_Oplus__class_Oplus @ SV824 @ SV675 @ SV99 ) @ SV99 )
| ~ ( c_HOL_Oord__class_Oless @ SV421 @ SV824 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2615,plain,
! [SV825: $i,SV676: $i,SV422: $i,SV100: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV100 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV422 @ SV676 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV422 @ SV825 @ SV100 ) @ ( c_HOL_Oplus__class_Oplus @ SV676 @ SV825 @ SV100 ) @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2616,plain,
! [SV826: $i,SV677: $i,SV423: $i,SV101: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV101 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SV677 @ SV101 ) @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SV826 @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV826 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2617,plain,
! [SV827: $i,SV678: $i,SV424: $i,SV102: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV102 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SV678 @ SV102 ) @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SV827 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SV678 @ SV827 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2618,plain,
! [SV828: $i,SV679: $i,SV425: $i,SV103: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV103 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV425 @ SV679 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV828 @ SV425 @ SV103 ) @ ( c_HOL_Oplus__class_Oplus @ SV828 @ SV679 @ SV103 ) @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2443]) ).
thf(2619,plain,
! [SV829: $i,SV683: $i,SV434: $i,SV113: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV113 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV434 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
| ( c_HOL_Oord__class_Oless @ SV683 @ SV829 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV683 @ SV434 @ SV113 ) @ ( c_HOL_Otimes__class_Otimes @ SV829 @ SV434 @ SV113 ) @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2620,plain,
! [SV830: $i,SV684: $i,SV435: $i,SV114: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV114 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV435 @ SV684 @ SV114 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV830 @ SV114 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV684 @ SV830 @ SV114 ) @ ( c_HOL_Otimes__class_Otimes @ SV435 @ SV830 @ SV114 ) @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2621,plain,
! [SV831: $i,SV685: $i,SV436: $i,SV115: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV115 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV436 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
| ( c_HOL_Oord__class_Oless @ SV685 @ SV831 @ SV115 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV685 @ SV115 ) @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV831 @ SV115 ) @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(2622,plain,
! [SV832: $i,SV686: $i,SV437: $i,SV116: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV116 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV437 @ SV686 @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV832 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV832 @ SV686 @ SV116 ) @ ( c_HOL_Otimes__class_Otimes @ SV832 @ SV437 @ SV116 ) @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2623,plain,
! [SV118: $i,SV438: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV438 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV118 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV118 @ SV438 @ tc_nat ) @ SV118 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2624,plain,
! [SV833: $i,SV687: $i,SV441: $i,SV121: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__mult @ SV121 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV441 @ SV687 @ SV121 ) @ SV833 @ SV121 )
= ( c_HOL_Otimes__class_Otimes @ SV441 @ ( c_HOL_Otimes__class_Otimes @ SV687 @ SV833 @ SV121 ) @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2625,plain,
! [SV834: $i,SV688: $i,SV442: $i,SV122: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV122 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV442 @ SV688 @ SV122 ) @ SV834 @ SV122 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV442 @ SV834 @ SV122 ) @ SV688 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2626,plain,
! [SV835: $i,SV689: $i,SV443: $i,SV123: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV123 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV443 @ SV689 @ SV123 ) @ SV835 @ SV123 )
= ( c_HOL_Otimes__class_Otimes @ SV443 @ ( c_HOL_Otimes__class_Otimes @ SV689 @ SV835 @ SV123 ) @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2627,plain,
! [SV836: $i,SV690: $i,SV444: $i,SV124: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV124 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV444 @ ( c_HOL_Otimes__class_Otimes @ SV690 @ SV836 @ SV124 ) @ SV124 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV444 @ SV690 @ SV124 ) @ SV836 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2628,plain,
! [SV837: $i,SV691: $i,SV445: $i,SV125: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV445 @ ( c_HOL_Otimes__class_Otimes @ SV691 @ SV837 @ SV125 ) @ SV125 )
= ( c_HOL_Otimes__class_Otimes @ SV691 @ ( c_HOL_Otimes__class_Otimes @ SV445 @ SV837 @ SV125 ) @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2629,plain,
! [SV838: $i,SV692: $i,SV446: $i,SV126: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV126 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV446 @ ( c_HOL_Otimes__class_Otimes @ SV692 @ SV838 @ SV126 ) @ SV126 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV446 @ SV692 @ SV126 ) @ SV838 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2457]) ).
thf(2630,plain,
! [SV839: $i,SV693: $i,SV447: $i,SV127: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV127 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV447 @ SV693 @ SV127 ) @ SV839 @ SV127 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV447 @ SV839 @ SV127 ) @ ( c_HOL_Otimes__class_Otimes @ SV693 @ SV839 @ SV127 ) @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2631,plain,
! [SV840: $i,SV694: $i,SV448: $i,SV128: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ SV128 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV448 @ SV694 @ SV128 ) @ SV840 @ SV128 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV448 @ SV840 @ SV128 ) @ ( c_HOL_Otimes__class_Otimes @ SV694 @ SV840 @ SV128 ) @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2632,plain,
! [SV841: $i,SV695: $i,SV449: $i,SV129: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV129 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV449 @ ( c_HOL_Oplus__class_Oplus @ SV695 @ SV841 @ SV129 ) @ SV129 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV449 @ SV695 @ SV129 ) @ ( c_HOL_Otimes__class_Otimes @ SV449 @ SV841 @ SV129 ) @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2633,plain,
! [SV130: $i,SV696: $i,SV450: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV450 @ SV696 @ SV130 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV696 @ SV450 @ SV130 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2634,plain,
! [SV131: $i,SV697: $i,SV451: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV451 @ SV697 @ SV131 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV697 @ SV451 @ SV131 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2635,plain,
! [SV132: $i,SV698: $i,SV452: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV452 @ SV698 @ SV132 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV698 @ SV452 @ SV132 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2463]) ).
thf(2636,plain,
! [SV133: $i,SV699: $i,SV453: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV453 @ SV699 @ SV133 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV699 @ SV453 @ SV133 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2464]) ).
thf(2637,plain,
! [SV842: $i,SV700: $i,SV457: $i,SV137: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV137 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV137 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV700 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV842 @ SV137 ) @ SV137 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV842 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV700 @ SV137 ) @ SV137 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(2638,plain,
! [SV843: $i,SV701: $i,SV458: $i,SV138: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV138 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV138 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV701 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV843 @ SV138 ) @ SV138 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV843 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV701 @ SV138 ) @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2639,plain,
! [SV844: $i,SV706: $i,SV464: $i,SV146: $i] :
( ( ( class_Orderings_Opreorder @ SV146 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV464 @ SV706 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SV844 @ SV706 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SV464 @ SV844 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2470]) ).
thf(2640,plain,
! [SV845: $i,SV707: $i,SV465: $i,SV147: $i] :
( ( ( class_Orderings_Oorder @ SV147 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV465 @ SV707 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SV465 @ SV845 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SV845 @ SV707 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2641,plain,
! [SV909: $i,SV846: $i,SV711: $i,SV473: $i,SV160: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV160 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV473 @ SV711 @ SV160 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV846 @ SV711 @ SV160 ) @ SV909 @ SV160 ) @ SV160 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV473 @ SV846 @ SV160 ) @ SV711 @ SV160 ) @ SV909 @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2642,plain,
! [SV162: $i,SV712: $i,SV474: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SV712 @ SV162 ) @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV712 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV474 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2474]) ).
thf(2643,plain,
! [SV715: $i,SV480: $i,SV168: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV480 @ SV480 @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SV715 @ SV715 @ SV168 ) @ SV168 ) @ SV168 )
= $true )
| ( ( SV480
= ( c_HOL_Ozero__class_Ozero @ SV168 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2644,plain,
! [SV716: $i,SV481: $i,SV169: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV481 @ SV481 @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SV716 @ SV716 @ SV169 ) @ SV169 ) @ SV169 )
= $true )
| ( ( SV716
= ( c_HOL_Ozero__class_Ozero @ SV169 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2645,plain,
! [SV848: $i,SV720: $i,SV486: $i,SV174: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV174 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV486 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV486 @ SV174 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV720 @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV848 @ SV174 ) @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2646,plain,
! [SV849: $i,SV721: $i,SV487: $i,SV175: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV175 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV487 @ SV721 @ SV175 )
| ( c_HOL_Oord__class_Oless @ SV721 @ SV487 @ SV175 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV849 @ SV721 @ SV175 ) @ ( c_HOL_Otimes__class_Otimes @ SV849 @ SV487 @ SV175 ) @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2647,plain,
! [SV850: $i,SV722: $i,SV488: $i,SV176: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV176 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV488 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV488 @ SV176 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV722 @ SV488 @ SV176 ) @ ( c_HOL_Otimes__class_Otimes @ SV850 @ SV488 @ SV176 ) @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2648,plain,
! [SV851: $i,SV723: $i,SV489: $i,SV177: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV177 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV489 @ SV723 @ SV177 )
| ( c_HOL_Oord__class_Oless @ SV723 @ SV489 @ SV177 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV723 @ SV851 @ SV177 ) @ ( c_HOL_Otimes__class_Otimes @ SV489 @ SV851 @ SV177 ) @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2485]) ).
thf(2649,plain,
! [SV852: $i,SV724: $i,SV493: $i,SV182: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV182 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV493 @ SV724 @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV724 @ SV182 ) @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV493 @ SV182 ) @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2650,plain,
! [SV853: $i,SV725: $i,SV494: $i,SV183: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV183 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV725 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV853 @ SV183 ) @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SV853 @ SV725 @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2651,plain,
! [SV854: $i,SV726: $i,SV495: $i,SV184: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV184 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV495 @ SV726 @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV495 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV726 @ SV184 ) @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV184 ) @ SV854 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2652,plain,
! [SV855: $i,SV727: $i,SV496: $i,SV185: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV185 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV727 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV855 @ SV185 ) @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SV727 @ SV855 @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV185 ) @ SV496 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(2653,plain,
! [SV856: $i,SV728: $i,SV497: $i,SV186: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV186 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV728 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV856 @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SV497 @ ( c_HOL_Ozero__class_Ozero @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SV856 @ SV728 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2654,plain,
! [SV857: $i,SV729: $i,SV498: $i,SV187: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV187 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV729 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV857 @ SV187 ) @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SV498 @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ SV729 @ SV857 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2655,plain,
! [SV858: $i,SV730: $i,SV499: $i,SV188: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV188 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV730 @ SV188 ) @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV858 @ SV188 ) @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ SV730 @ SV858 @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV188 ) @ SV499 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2656,plain,
! [SV859: $i,SV731: $i,SV500: $i,SV189: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV189 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV731 @ SV189 ) @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV859 @ SV189 ) @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SV859 @ SV731 @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SV500 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2657,plain,
! [SV860: $i,SV732: $i,SV501: $i,SV190: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV190 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV501 @ SV732 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SV860 @ SV732 @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SV732 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SV860 @ SV501 @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2495]) ).
thf(2658,plain,
! [SV861: $i,SV733: $i,SV502: $i,SV191: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV191 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SV733 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SV861 @ SV733 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV733 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV502 @ SV861 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2659,plain,
! [SV862: $i,SV734: $i,SV503: $i,SV192: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV192 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV503 @ SV734 @ SV192 ) @ ( c_HOL_Otimes__class_Otimes @ SV862 @ SV734 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SV503 @ SV862 @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV734 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2660,plain,
! [SV863: $i,SV735: $i,SV504: $i,SV193: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV193 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV504 @ SV735 @ SV193 ) @ ( c_HOL_Otimes__class_Otimes @ SV863 @ SV735 @ SV193 ) @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV504 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SV735 @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2661,plain,
! [SV864: $i,SV736: $i,SV505: $i,SV194: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV194 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV736 @ SV194 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV864 @ SV194 ) @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV505 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ SV736 @ SV864 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2662,plain,
! [SV865: $i,SV737: $i,SV506: $i,SV196: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV196 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV737 @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SV865 @ SV737 @ SV196 ) @ SV196 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV506 @ SV865 @ SV196 ) @ SV737 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2663,plain,
! [SV509: $i,SV202: $i] :
( ( ( class_Int_Onumber__ring @ SV202 )
= $false )
| ( ( SV509
= ( c_HOL_Oplus__class_Oplus @ SV509 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2664,plain,
! [SV740: $i,SV519: $i,SV213: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV519 @ SV740 @ SV213 ) @ SV213 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV740 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV519 @ SV213 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2665,plain,
! [SV525: $i,SV219: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ ( c_HOL_Oplus__class_Oplus @ SV525 @ SV525 @ SV219 ) @ SV219 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV525 @ SV219 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2666,plain,
! [SV526: $i,SV220: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV526 @ SV220 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ ( c_HOL_Oplus__class_Oplus @ SV526 @ SV526 @ SV220 ) @ SV220 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(2667,plain,
! [SV529: $i,SV223: $i,SV867: $i,SV742: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV742 @ ( c_HOL_Oplus__class_Oplus @ SV867 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ SV223 @ SV529 @ SV742 ) @ SV867 )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV223 @ ( c_HOL_Oplus__class_Oplus @ SV867 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) @ ( c_Lambda_Olift @ SV529 @ SV867 ) @ SV742 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2507]) ).
thf(2668,plain,
! [SV910: $i,SV868: $i,SV745: $i,SV533: $i,SV227: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV745 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV868 @ SV910 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV868 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV745 @ SV910 @ SV227 ) @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2510]) ).
thf(2669,plain,
! [SV911: $i,SV869: $i,SV746: $i,SV534: $i,SV228: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ ( c_Lambda_Olift @ SV534 @ SV746 ) @ ( c_Suc @ SV869 ) ) @ ( c_Lambda_Osubst @ SV911 @ SV534 @ SV869 ) @ SV746 )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ SV911 @ SV746 ) @ SV534 @ SV869 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV746 @ ( c_HOL_Oplus__class_Oplus @ SV869 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2670,plain,
! [SV536: $i,SV230: $i,SV748: $i,SV870: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV870 @ ( c_HOL_Oplus__class_Oplus @ SV748 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( c_Lambda_Osubst @ SV230 @ SV536 @ SV748 ) @ SV870 )
= ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV230 @ SV870 ) @ ( c_Lambda_Olift @ SV536 @ SV870 ) @ ( c_HOL_Oplus__class_Oplus @ SV748 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2512]) ).
thf(2671,plain,
! [SV871: $i,SV749: $i,SV539: $i,SV234: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV234 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV539 @ SV749 @ SV234 ) @ SV871 @ SV234 )
= ( c_HOL_Oplus__class_Oplus @ SV539 @ ( c_HOL_Oplus__class_Oplus @ SV749 @ SV871 @ SV234 ) @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2672,plain,
! [SV872: $i,SV750: $i,SV540: $i,SV235: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV235 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV540 @ ( c_HOL_Oplus__class_Oplus @ SV750 @ SV872 @ SV235 ) @ SV235 )
= ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Oplus__class_Oplus @ SV540 @ SV872 @ SV235 ) @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2673,plain,
! [SV873: $i,SV751: $i,SV541: $i,SV236: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV236 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV541 @ SV751 @ SV236 ) @ SV873 @ SV236 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV541 @ SV873 @ SV236 ) @ SV751 @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2515]) ).
thf(2674,plain,
! [SV874: $i,SV752: $i,SV542: $i,SV237: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV542 @ ( c_HOL_Oplus__class_Oplus @ SV752 @ SV874 @ SV237 ) @ SV237 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV542 @ SV752 @ SV237 ) @ SV874 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2516]) ).
thf(2675,plain,
! [SV875: $i,SV753: $i,SV543: $i,SV238: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV238 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV543 @ SV753 @ SV238 ) @ SV875 @ SV238 )
= ( c_HOL_Oplus__class_Oplus @ SV543 @ ( c_HOL_Oplus__class_Oplus @ SV753 @ SV875 @ SV238 ) @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2676,plain,
! [SV876: $i,SV754: $i,SV544: $i,SV239: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV239 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV544 @ ( c_HOL_Oplus__class_Oplus @ SV754 @ SV876 @ SV239 ) @ SV239 )
= ( c_HOL_Oplus__class_Oplus @ SV754 @ ( c_HOL_Oplus__class_Oplus @ SV544 @ SV876 @ SV239 ) @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2677,plain,
! [SV877: $i,SV755: $i,SV545: $i,SV240: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV240 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV545 @ SV755 @ SV240 ) @ SV877 @ SV240 )
= ( c_HOL_Oplus__class_Oplus @ SV545 @ ( c_HOL_Oplus__class_Oplus @ SV755 @ SV877 @ SV240 ) @ SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2678,plain,
! [SV878: $i,SV758: $i,SV548: $i,SV243: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV243 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV548 @ ( c_HOL_Oplus__class_Oplus @ SV758 @ SV878 @ SV243 ) @ SV243 )
= ( c_HOL_Oplus__class_Oplus @ SV758 @ ( c_HOL_Oplus__class_Oplus @ SV548 @ SV878 @ SV243 ) @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2679,plain,
! [SV879: $i,SV759: $i,SV549: $i,SV244: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV244 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV549 @ ( c_HOL_Oplus__class_Oplus @ SV759 @ SV879 @ SV244 ) @ SV244 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV549 @ SV759 @ SV244 ) @ SV879 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2680,plain,
! [SV761: $i,SV551: $i,SV880: $i,SV246: $i] :
( ( ( c_Lambda_Obeta @ SV246 @ SV880 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV246 @ SV551 @ SV761 ) @ ( c_Lambda_Osubst @ SV880 @ SV551 @ SV761 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2681,plain,
! [SV274: $i,SV777: $i,SV576: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV576 @ SV777 @ SV274 )
!= ( c_HOL_Ozero__class_Ozero @ SV274 ) )
= $true )
| ( ( SV576 = SV777 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2534]) ).
thf(2682,plain,
! [SV912: $i,SV882: $i,SV778: $i,SV577: $i,SV275: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV275 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV577 @ ( c_HOL_Oplus__class_Oplus @ SV778 @ SV882 @ SV275 ) @ SV275 )
!= ( c_HOL_Oplus__class_Oplus @ SV778 @ SV912 @ SV275 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV577 @ SV882 @ SV275 )
= SV912 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2683,plain,
! [SV779: $i,SV277: $i,SV578: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV578 @ SV277 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV779 @ SV277 ) )
= $true )
| ( ( SV578 = SV779 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2536]) ).
thf(2684,plain,
! [SV883: $i,SV781: $i,SV580: $i,SV280: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV280 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV580 @ SV781 @ SV280 )
!= ( c_HOL_Oplus__class_Oplus @ SV580 @ SV883 @ SV280 ) )
| ( SV781 = SV883 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(2685,plain,
! [SV283: $i,SV582: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV582 @ SV582 @ SV283 )
= ( c_HOL_Ozero__class_Ozero @ SV283 ) )
= $false )
| ( ( SV582
= ( c_HOL_Ozero__class_Ozero @ SV283 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2539]) ).
thf(2686,plain,
! [SV884: $i,SV783: $i,SV584: $i,SV285: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV285 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV584 @ SV783 @ SV285 )
!= ( c_HOL_Ominus__class_Ominus @ SV884 @ SV884 @ SV285 ) )
| ( SV584 = SV783 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2687,plain,
! [SV885: $i,SV784: $i,SV585: $i,SV286: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV286 @ SV585 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV784 @ SV885 @ tc_nat ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV784 @ SV585 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV286 @ SV885 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2688,plain,
! [SV886: $i,SV785: $i,SV586: $i,SV287: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV287 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV586 @ SV785 @ SV287 )
!= ( c_HOL_Oplus__class_Oplus @ SV886 @ SV785 @ SV287 ) )
| ( SV586 = SV886 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2689,plain,
! [SV913: $i,SV887: $i,SV786: $i,SV588: $i,SV290: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV290 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV290 )
| ( ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV887 @ SV290 ) @ SV290 )
!= ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV913 @ SV290 ) @ SV290 ) )
| ( SV887 = SV913 )
| ( SV786
= ( c_HOL_Ozero__class_Ozero @ SV290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2543]) ).
thf(2690,plain,
! [SV924: $i,SV914: $i,SV888: $i,SV787: $i,SV589: $i,SV291: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV291 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV589 @ SV787 @ SV291 ) @ SV888 @ SV291 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV787 @ SV291 ) @ SV924 @ SV291 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV589 @ SV914 @ SV291 ) @ SV787 @ SV291 ) @ SV888 @ SV291 )
= SV924 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(2691,plain,
! [SV925: $i,SV915: $i,SV889: $i,SV788: $i,SV591: $i,SV293: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV293 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV591 @ SV788 @ SV293 ) @ SV889 @ SV293 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV788 @ SV293 ) @ SV925 @ SV293 ) )
| ( SV889
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV915 @ SV591 @ SV293 ) @ SV788 @ SV293 ) @ SV925 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(2692,plain,
! [SV294: $i,SV789: $i,SV592: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV592 @ SV789 @ SV294 )
!= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
= $true )
| ( ( ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SV592
= ( c_HOL_Ozero__class_Ozero @ SV294 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2547]) ).
thf(2693,plain,
! [SV792: $i,SV595: $i,SV297: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV297 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV595 @ SV792 @ SV297 )
!= ( c_HOL_Ozero__class_Ozero @ SV297 ) )
| ( SV595 = SV792 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2549]) ).
thf(2694,plain,
! [SV299: $i,SV793: $i,SV596: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV596 @ SV793 @ SV299 )
!= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
= $true )
| ( ( ( SV596
= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
| ( SV793
= ( c_HOL_Ozero__class_Ozero @ SV299 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV299 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2695,plain,
! [SV301: $i,SV795: $i,SV598: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV598 @ SV795 @ SV301 )
!= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
= $true )
| ( ( ( SV795
= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
| ( SV598
= ( c_HOL_Ozero__class_Ozero @ SV301 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV301 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2552]) ).
thf(2696,plain,
! [SV916: $i,SV890: $i,SV797: $i,SV601: $i,SV306: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV306 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV306 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV797 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV916 @ SV306 ) @ SV306 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV916 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV797 @ SV306 ) @ SV306 ) )
| ( SV797 = SV916 )
| ( SV601 = SV890 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(2697,plain,
! [SV917: $i,SV891: $i,SV798: $i,SV602: $i,SV307: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV307 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV798 @ SV307 )
!= ( c_HOL_Ominus__class_Ominus @ SV891 @ SV917 @ SV307 ) )
| ( c_HOL_Oord__class_Oless @ SV602 @ SV798 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV917 @ SV307 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2555]) ).
thf(2698,plain,
! [SV892: $i,SV799: $i,SV603: $i,SV308: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV308 @ SV603 )
= ( c_Lambda_OdB_OApp @ SV799 @ SV892 ) )
= $false )
| ( ( SV603 = SV892 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2556]) ).
thf(2699,plain,
! [SV800: $i,SV309: $i,SV604: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV604 @ SV604 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV800 @ SV800 @ SV309 ) @ SV309 )
!= ( c_HOL_Ozero__class_Ozero @ SV309 ) )
= $true )
| ( ( SV800
= ( c_HOL_Ozero__class_Ozero @ SV309 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2700,plain,
! [SV893: $i,SV801: $i,SV608: $i,SV313: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV313 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV313 )
| ( ( c_HOL_Oplus__class_Oplus @ SV608 @ SV801 @ SV313 )
!= ( c_HOL_Oplus__class_Oplus @ SV608 @ SV893 @ SV313 ) )
| ( SV801 = SV893 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2701,plain,
! [SV894: $i,SV802: $i,SV609: $i,SV314: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV314 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV609 @ SV609 @ SV314 )
!= ( c_HOL_Ominus__class_Ominus @ SV802 @ SV894 @ SV314 ) )
| ( SV802 = SV894 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2702,plain,
! [SV803: $i,SV611: $i,SV316: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV316 ) )
= $true )
| ( ( ( SV611
!= ( c_HOL_Oplus__class_Oplus @ SV611 @ SV803 @ SV316 ) )
| ( SV803
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(2703,plain,
! [SV895: $i,SV804: $i,SV612: $i,SV317: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV317 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV612 @ SV804 @ SV317 )
!= ( c_HOL_Oplus__class_Oplus @ SV612 @ SV895 @ SV317 ) )
| ( SV804 = SV895 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2563]) ).
thf(2704,plain,
! [SV806: $i,SV321: $i,SV616: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV616 @ SV616 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SV806 @ SV806 @ SV321 ) @ SV321 )
!= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $true )
| ( ( SV616
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2566]) ).
thf(2705,plain,
! [SV323: $i,SV618: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV618 @ SV323 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV618 = SV323 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV323 @ SV618 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2567]) ).
thf(2706,plain,
! [SV918: $i,SV896: $i,SV807: $i,SV620: $i,SV325: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV807 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV896 @ SV918 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SV896 @ SV918 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV620 @ SV807 @ SV325 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2707,plain,
! [SV897: $i,SV808: $i,SV621: $i,SV326: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV326 @ SV621 )
= ( c_Lambda_OdB_OApp @ SV808 @ SV897 ) )
= $false )
| ( ( SV326 = SV808 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(2708,plain,
! [SV331: $i,SV809: $i,SV626: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV626 @ SV809 @ SV331 )
!= ( c_HOL_Ozero__class_Ozero @ SV331 ) )
= $true )
| ( ( SV626 = SV809 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV331 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2572]) ).
thf(2709,plain,
! [SV919: $i,SV898: $i,SV810: $i,SV627: $i,SV332: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV332 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV332 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV810 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV919 @ SV332 ) @ SV332 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV919 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV810 @ SV332 ) @ SV332 ) )
| ( SV810 = SV919 )
| ( SV627 = SV898 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2573]) ).
thf(2710,plain,
! [SV899: $i,SV811: $i,SV630: $i,SV336: $i,SV2: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV630 @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SV811 @ SV899 @ SV2 ) @ SV2 )
= ( c_HOL_Otimes__class_Otimes @ SV811 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV630 @ SV2 ) @ SV899 @ SV2 ) @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2711,plain,
! [SV900: $i,SV812: $i,SV631: $i,SV337: $i,SV3: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV3 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV337 @ SV631 @ SV3 ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV900 @ SV3 ) @ SV3 )
= ( c_HOL_Otimes__class_Otimes @ SV337 @ ( c_HOL_Otimes__class_Otimes @ SV631 @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV900 @ SV3 ) @ SV3 ) @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2712,plain,
! [SV901: $i,SV813: $i,SV632: $i,SV338: $i,SV4: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV4 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV338 @ SV632 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV901 @ SV4 ) @ SV4 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV338 @ SV813 @ SV4 ) @ ( c_HOL_Otimes__class_Otimes @ SV632 @ SV901 @ SV4 ) @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2713,plain,
! [SV345: $i,SV12: $i,SV635: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV635 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV345 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SV345 @ SV635 @ SV12 ) @ SV12 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2578]) ).
thf(2714,plain,
! [SV346: $i,SV636: $i,SV13: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV636 @ SV13 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV346 @ SV13 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SV346 @ SV636 @ SV13 ) @ SV13 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2579]) ).
thf(2715,plain,
! [SV347: $i,SV637: $i,SV14: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV637 @ SV14 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ ( c_HOL_Otimes__class_Otimes @ SV637 @ SV347 @ SV14 ) @ SV14 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV347 @ SV14 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(2716,plain,
! [SV348: $i,SV638: $i,SV15: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV638 @ SV15 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ ( c_HOL_Otimes__class_Otimes @ SV348 @ SV638 @ SV15 ) @ SV15 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV348 @ SV15 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2581]) ).
thf(2717,plain,
! [SV920: $i,SV902: $i,SV814: $i,SV639: $i,SV353: $i,SV20: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV20 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV353 @ SV639 @ SV20 ) @ SV814 @ SV20 ) @ SV902 @ SV20 ) @ SV920 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV814 @ SV20 ) @ SV902 @ SV20 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV639 @ SV814 @ SV20 ) @ SV920 @ SV20 ) @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2586]) ).
thf(2718,plain,
! [SV921: $i,SV903: $i,SV815: $i,SV640: $i,SV354: $i,SV21: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV21 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV354 @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV903 @ SV640 @ SV21 ) @ SV921 @ SV21 ) @ SV21 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV354 @ SV903 @ SV21 ) @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ SV921 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2719,plain,
! [SV922: $i,SV904: $i,SV816: $i,SV641: $i,SV355: $i,SV22: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV22 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV355 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SV816 @ SV22 ) @ SV904 @ SV22 ) @ SV922 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV904 @ SV22 ) @ SV355 @ SV22 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV641 @ SV904 @ SV22 ) @ SV922 @ SV22 ) @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2588]) ).
thf(2720,plain,
! [SV923: $i,SV905: $i,SV817: $i,SV642: $i,SV356: $i,SV23: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV23 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV356 @ SV642 @ SV23 ) @ SV817 @ SV23 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV905 @ SV642 @ SV23 ) @ SV923 @ SV23 ) @ SV23 )
| ~ ( c_HOL_Oord__class_Oless @ SV817 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV905 @ SV356 @ SV23 ) @ SV642 @ SV23 ) @ SV923 @ SV23 ) @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2721,plain,
! [SV32: $i,SV363: $i,SV644: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV644 @ SV363 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV644 @ SV32 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV363 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV644 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2722,plain,
! [SV906: $i,SV818: $i,SV650: $i,SV372: $i,SV42: $i] :
( ( ( class_Ring__and__Field_Oring @ SV42 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV372 @ SV650 @ SV42 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV818 @ SV372 @ SV42 ) @ SV650 @ SV42 ) @ SV906 @ SV42 ) @ SV42 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV818 @ SV650 @ SV42 ) @ SV906 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2723,plain,
! [SV907: $i,SV819: $i,SV651: $i,SV375: $i,SV45: $i] :
( ( ( class_Ring__and__Field_Oring @ SV45 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV375 @ SV651 @ SV45 ) @ SV819 @ SV45 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV907 @ SV651 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV375 @ SV907 @ SV45 ) @ SV651 @ SV45 ) @ SV819 @ SV45 ) @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2593]) ).
thf(2724,plain,
! [SV392: $i,SV654: $i,SV64: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV654 @ SV64 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV392 @ SV64 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ ( c_HOL_Oplus__class_Oplus @ SV392 @ SV654 @ SV64 ) @ SV64 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2594]) ).
thf(2725,plain,
! [SV65: $i,SV393: $i,SV655: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV655 @ SV393 @ SV65 )
= $true )
| ( ( SV655 = SV393 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV393 @ SV655 @ SV65 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2595]) ).
thf(2726,plain,
! [SV66: $i,SV394: $i,SV656: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV656 @ SV394 @ SV66 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV394 @ SV656 @ SV66 )
= $true )
| ( ( SV394 = SV656 )
= $true )
| ( ( class_Orderings_Olinorder @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2596]) ).
thf(2727,plain,
! [SV69: $i,SV397: $i,SV657: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV657 @ SV397 @ SV69 )
= $true )
| ( ( SV657 = SV397 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV397 @ SV657 @ SV69 )
= $true )
| ( ( class_Orderings_Olinorder @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2597]) ).
thf(2728,plain,
! [SV70: $i,SV398: $i,SV658: $i] :
( ( ( SV658 = SV398 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV658 @ SV398 @ SV70 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV398 @ SV658 @ SV70 )
= $true )
| ( ( class_Orderings_Olinorder @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(2729,plain,
! [SV71: $i,SV659: $i,SV399: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV399 @ SV659 @ SV71 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV659 @ SV399 @ SV71 )
= $true )
| ( ( SV399 = SV659 )
= $true )
| ( ( class_Orderings_Olinorder @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2599]) ).
thf(2730,plain,
! [SV908: $i,SV820: $i,SV660: $i,SV400: $i,SV74: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV74 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV400 @ SV660 @ SV74 ) @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV908 @ SV74 ) @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV660 @ SV908 @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV400 @ SV820 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2731,plain,
! [SV661: $i,SV75: $i,SV821: $i,SV401: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV401 @ SV821 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV75 @ SV661 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV75 @ SV401 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV661 @ SV821 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2732,plain,
! [SV76: $i,SV662: $i,SV402: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV402 @ SV662 @ SV76 ) @ ( c_HOL_Ozero__class_Ozero @ SV76 ) @ SV76 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV402 @ SV662 @ SV76 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2733,plain,
! [SV77: $i,SV663: $i,SV403: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV403 @ SV663 @ SV77 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV403 @ SV663 @ SV77 ) @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV77 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2603]) ).
thf(2734,plain,
! [SV78: $i,SV664: $i,SV404: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV404 @ SV664 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV404 @ SV78 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV664 @ SV78 ) @ SV78 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2735,plain,
! [SV665: $i,SV79: $i,SV405: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV405 @ SV79 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV665 @ SV79 ) @ SV79 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV405 @ SV665 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2736,plain,
! [SV406: $i,SV666: $i,SV82: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV82 @ SV666 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV666 @ SV406 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV82 ) @ SV406 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2737,plain,
! [SV668: $i,SV89: $i,SV411: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV411 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV668 @ SV89 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SV668 @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2609]) ).
thf(2738,plain,
! [SV412: $i,SV90: $i,SV669: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV412 @ SV90 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV412 @ SV669 @ SV90 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2610]) ).
thf(2739,plain,
! [SV413: $i,SV670: $i,SV91: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV670 @ SV91 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV413 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV413 @ SV670 @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2611]) ).
thf(2740,plain,
! [SV93: $i,SV822: $i,SV671: $i,SV415: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV415 @ ( c_HOL_Oplus__class_Oplus @ SV671 @ SV822 @ SV93 ) @ SV93 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV415 @ SV822 @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV671 @ SV93 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2741,plain,
! [SV823: $i,SV98: $i,SV674: $i,SV420: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV420 @ SV674 @ SV98 ) @ ( c_HOL_Oplus__class_Oplus @ SV823 @ SV674 @ SV98 ) @ SV98 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV420 @ SV823 @ SV98 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2613]) ).
thf(2742,plain,
! [SV824: $i,SV99: $i,SV675: $i,SV421: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV421 @ SV675 @ SV99 ) @ ( c_HOL_Oplus__class_Oplus @ SV824 @ SV675 @ SV99 ) @ SV99 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV421 @ SV824 @ SV99 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2614]) ).
thf(2743,plain,
! [SV825: $i,SV100: $i,SV676: $i,SV422: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV422 @ SV676 @ SV100 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV422 @ SV825 @ SV100 ) @ ( c_HOL_Oplus__class_Oplus @ SV676 @ SV825 @ SV100 ) @ SV100 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2615]) ).
thf(2744,plain,
! [SV826: $i,SV101: $i,SV677: $i,SV423: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SV677 @ SV101 ) @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SV826 @ SV101 ) @ SV101 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV826 @ SV101 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2616]) ).
thf(2745,plain,
! [SV827: $i,SV102: $i,SV678: $i,SV424: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SV678 @ SV102 ) @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SV827 @ SV102 ) @ SV102 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV678 @ SV827 @ SV102 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2617]) ).
thf(2746,plain,
! [SV828: $i,SV103: $i,SV679: $i,SV425: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV425 @ SV679 @ SV103 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV828 @ SV425 @ SV103 ) @ ( c_HOL_Oplus__class_Oplus @ SV828 @ SV679 @ SV103 ) @ SV103 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2618]) ).
thf(2747,plain,
! [SV829: $i,SV683: $i,SV113: $i,SV434: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV434 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV683 @ SV829 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV683 @ SV434 @ SV113 ) @ ( c_HOL_Otimes__class_Otimes @ SV829 @ SV434 @ SV113 ) @ SV113 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2619]) ).
thf(2748,plain,
! [SV830: $i,SV114: $i,SV684: $i,SV435: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV435 @ SV684 @ SV114 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV830 @ SV114 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV684 @ SV830 @ SV114 ) @ ( c_HOL_Otimes__class_Otimes @ SV435 @ SV830 @ SV114 ) @ SV114 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2620]) ).
thf(2749,plain,
! [SV831: $i,SV685: $i,SV115: $i,SV436: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV436 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV685 @ SV831 @ SV115 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV685 @ SV115 ) @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV831 @ SV115 ) @ SV115 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2621]) ).
thf(2750,plain,
! [SV832: $i,SV116: $i,SV686: $i,SV437: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV437 @ SV686 @ SV116 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV832 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV832 @ SV686 @ SV116 ) @ ( c_HOL_Otimes__class_Otimes @ SV832 @ SV437 @ SV116 ) @ SV116 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2622]) ).
thf(2751,plain,
! [SV130: $i,SV696: $i,SV450: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV450 @ SV696 @ SV130 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV696 @ SV450 @ SV130 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2752,plain,
! [SV131: $i,SV697: $i,SV451: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV451 @ SV697 @ SV131 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV697 @ SV451 @ SV131 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2753,plain,
! [SV132: $i,SV698: $i,SV452: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV452 @ SV698 @ SV132 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV698 @ SV452 @ SV132 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(2754,plain,
! [SV133: $i,SV699: $i,SV453: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV453 @ SV699 @ SV133 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV699 @ SV453 @ SV133 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2755,plain,
! [SV842: $i,SV700: $i,SV457: $i,SV137: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV137 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV700 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV842 @ SV137 ) @ SV137 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV842 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV700 @ SV137 ) @ SV137 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2637]) ).
thf(2756,plain,
! [SV843: $i,SV701: $i,SV458: $i,SV138: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV138 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV701 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV843 @ SV138 ) @ SV138 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV843 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV701 @ SV138 ) @ SV138 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2638]) ).
thf(2757,plain,
! [SV844: $i,SV146: $i,SV706: $i,SV464: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV464 @ SV706 @ SV146 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV844 @ SV706 @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SV464 @ SV844 @ SV146 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2758,plain,
! [SV845: $i,SV147: $i,SV707: $i,SV465: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV465 @ SV707 @ SV147 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV465 @ SV845 @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ SV845 @ SV707 @ SV147 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2640]) ).
thf(2759,plain,
! [SV909: $i,SV846: $i,SV711: $i,SV473: $i,SV160: $i] :
( ( ( class_Ring__and__Field_Osemiring @ SV160 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV473 @ SV711 @ SV160 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV846 @ SV711 @ SV160 ) @ SV909 @ SV160 ) @ SV160 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV473 @ SV846 @ SV160 ) @ SV711 @ SV160 ) @ SV909 @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2760,plain,
! [SV474: $i,SV162: $i,SV712: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV712 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV474 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SV712 @ SV162 ) @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(2761,plain,
! [SV848: $i,SV720: $i,SV174: $i,SV486: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV486 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV486 @ SV174 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV720 @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV848 @ SV174 ) @ SV174 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2762,plain,
! [SV849: $i,SV175: $i,SV721: $i,SV487: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV487 @ SV721 @ SV175 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV721 @ SV487 @ SV175 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV849 @ SV721 @ SV175 ) @ ( c_HOL_Otimes__class_Otimes @ SV849 @ SV487 @ SV175 ) @ SV175 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2646]) ).
thf(2763,plain,
! [SV850: $i,SV722: $i,SV176: $i,SV488: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV488 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV488 @ SV176 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV722 @ SV488 @ SV176 ) @ ( c_HOL_Otimes__class_Otimes @ SV850 @ SV488 @ SV176 ) @ SV176 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2647]) ).
thf(2764,plain,
! [SV851: $i,SV177: $i,SV723: $i,SV489: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV489 @ SV723 @ SV177 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV723 @ SV489 @ SV177 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV723 @ SV851 @ SV177 ) @ ( c_HOL_Otimes__class_Otimes @ SV489 @ SV851 @ SV177 ) @ SV177 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2648]) ).
thf(2765,plain,
! [SV852: $i,SV182: $i,SV724: $i,SV493: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV493 @ SV724 @ SV182 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV724 @ SV182 ) @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV493 @ SV182 ) @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2649]) ).
thf(2766,plain,
! [SV853: $i,SV183: $i,SV725: $i,SV494: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV725 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV853 @ SV183 ) @ SV183 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV853 @ SV725 @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV183 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2650]) ).
thf(2767,plain,
! [SV854: $i,SV184: $i,SV726: $i,SV495: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV495 @ SV726 @ SV184 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV495 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV726 @ SV184 ) @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV184 ) @ SV854 @ SV184 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(2768,plain,
! [SV855: $i,SV185: $i,SV727: $i,SV496: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV727 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV855 @ SV185 ) @ SV185 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV727 @ SV855 @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV185 ) @ SV496 @ SV185 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2652]) ).
thf(2769,plain,
! [SV856: $i,SV186: $i,SV728: $i,SV497: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV728 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV856 @ SV186 ) @ SV186 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV497 @ ( c_HOL_Ozero__class_Ozero @ SV186 ) @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SV856 @ SV728 @ SV186 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(2770,plain,
! [SV857: $i,SV187: $i,SV729: $i,SV498: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV729 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV857 @ SV187 ) @ SV187 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SV498 @ SV187 )
| ~ ( c_HOL_Oord__class_Oless @ SV729 @ SV857 @ SV187 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(2771,plain,
! [SV858: $i,SV188: $i,SV730: $i,SV499: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV730 @ SV188 ) @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV858 @ SV188 ) @ SV188 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV730 @ SV858 @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV188 ) @ SV499 @ SV188 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(2772,plain,
! [SV859: $i,SV189: $i,SV731: $i,SV500: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV731 @ SV189 ) @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV859 @ SV189 ) @ SV189 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV859 @ SV731 @ SV189 )
| ~ ( c_HOL_Oord__class_Oless @ SV500 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV189 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2656]) ).
thf(2773,plain,
! [SV860: $i,SV190: $i,SV732: $i,SV501: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV501 @ SV732 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SV860 @ SV732 @ SV190 ) @ SV190 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV732 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_HOL_Oord__class_Oless @ SV860 @ SV501 @ SV190 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2657]) ).
thf(2774,plain,
! [SV861: $i,SV191: $i,SV733: $i,SV502: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SV733 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SV861 @ SV733 @ SV191 ) @ SV191 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV733 @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ SV502 @ SV861 @ SV191 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2658]) ).
thf(2775,plain,
! [SV862: $i,SV192: $i,SV734: $i,SV503: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV503 @ SV734 @ SV192 ) @ ( c_HOL_Otimes__class_Otimes @ SV862 @ SV734 @ SV192 ) @ SV192 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV503 @ SV862 @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV734 @ SV192 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2659]) ).
thf(2776,plain,
! [SV863: $i,SV193: $i,SV735: $i,SV504: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV504 @ SV735 @ SV193 ) @ ( c_HOL_Otimes__class_Otimes @ SV863 @ SV735 @ SV193 ) @ SV193 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV504 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ SV735 @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV193 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(2777,plain,
! [SV864: $i,SV194: $i,SV736: $i,SV505: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV736 @ SV194 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV864 @ SV194 ) @ SV194 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV505 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ SV736 @ SV864 @ SV194 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2661]) ).
thf(2778,plain,
! [SV519: $i,SV740: $i,SV213: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV740 @ SV213 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV519 @ SV213 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV519 @ SV740 @ SV213 ) @ SV213 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2664]) ).
thf(2779,plain,
! [SV910: $i,SV868: $i,SV745: $i,SV533: $i,SV227: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV745 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV868 @ SV910 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV868 @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV745 @ SV910 @ SV227 ) @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2780,plain,
! [SV911: $i,SV534: $i,SV228: $i,SV869: $i,SV746: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV746 @ ( c_HOL_Oplus__class_Oplus @ SV869 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ ( c_Lambda_Olift @ SV534 @ SV746 ) @ ( c_Suc @ SV869 ) ) @ ( c_Lambda_Osubst @ SV911 @ SV534 @ SV869 ) @ SV746 )
= ( c_Lambda_Osubst @ ( c_Lambda_Osubst @ SV228 @ SV911 @ SV746 ) @ SV534 @ SV869 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(2781,plain,
! [SV274: $i,SV777: $i,SV576: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV576 @ SV777 @ SV274 )
= ( c_HOL_Ozero__class_Ozero @ SV274 ) )
= $false )
| ( ( SV576 = SV777 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2782,plain,
! [SV912: $i,SV882: $i,SV778: $i,SV577: $i,SV275: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV275 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV577 @ ( c_HOL_Oplus__class_Oplus @ SV778 @ SV882 @ SV275 ) @ SV275 )
!= ( c_HOL_Oplus__class_Oplus @ SV778 @ SV912 @ SV275 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV577 @ SV882 @ SV275 )
= SV912 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2783,plain,
! [SV779: $i,SV277: $i,SV578: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV578 @ SV277 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV779 @ SV277 ) )
= $false )
| ( ( SV578 = SV779 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2784,plain,
! [SV883: $i,SV280: $i,SV781: $i,SV580: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV580 @ SV781 @ SV280 )
!= ( c_HOL_Oplus__class_Oplus @ SV580 @ SV883 @ SV280 ) )
= $true )
| ( ( SV781 = SV883 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2684]) ).
thf(2785,plain,
! [SV884: $i,SV285: $i,SV783: $i,SV584: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV584 @ SV783 @ SV285 )
!= ( c_HOL_Ominus__class_Ominus @ SV884 @ SV884 @ SV285 ) )
= $true )
| ( ( SV584 = SV783 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2686]) ).
thf(2786,plain,
! [SV885: $i,SV286: $i,SV585: $i,SV784: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV784 @ SV585 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV286 @ SV885 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV286 @ SV585 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV784 @ SV885 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2687]) ).
thf(2787,plain,
! [SV886: $i,SV287: $i,SV785: $i,SV586: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV586 @ SV785 @ SV287 )
!= ( c_HOL_Oplus__class_Oplus @ SV886 @ SV785 @ SV287 ) )
= $true )
| ( ( SV586 = SV886 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2688]) ).
thf(2788,plain,
! [SV913: $i,SV887: $i,SV786: $i,SV588: $i,SV290: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV290 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV290 )
| ( ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV887 @ SV290 ) @ SV290 )
!= ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV913 @ SV290 ) @ SV290 ) )
| ( SV887 = SV913 )
| ( SV786
= ( c_HOL_Ozero__class_Ozero @ SV290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2789,plain,
! [SV924: $i,SV914: $i,SV888: $i,SV787: $i,SV589: $i,SV291: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV291 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV589 @ SV787 @ SV291 ) @ SV888 @ SV291 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV787 @ SV291 ) @ SV924 @ SV291 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV589 @ SV914 @ SV291 ) @ SV787 @ SV291 ) @ SV888 @ SV291 )
= SV924 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2690]) ).
thf(2790,plain,
! [SV925: $i,SV915: $i,SV889: $i,SV788: $i,SV591: $i,SV293: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV293 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV591 @ SV788 @ SV293 ) @ SV889 @ SV293 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV788 @ SV293 ) @ SV925 @ SV293 ) )
| ( SV889
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV915 @ SV591 @ SV293 ) @ SV788 @ SV293 ) @ SV925 @ SV293 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2691]) ).
thf(2791,plain,
! [SV294: $i,SV789: $i,SV592: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV592 @ SV789 @ SV294 )
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
= $false )
| ( ( ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SV592
= ( c_HOL_Ozero__class_Ozero @ SV294 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2792,plain,
! [SV792: $i,SV595: $i,SV297: $i] :
( ( ( class_Int_Onumber__ring @ SV297 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV595 @ SV792 @ SV297 )
!= ( c_HOL_Ozero__class_Ozero @ SV297 ) )
| ( SV595 = SV792 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2793,plain,
! [SV299: $i,SV793: $i,SV596: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV596 @ SV793 @ SV299 )
= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
= $false )
| ( ( ( SV596
= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
| ( SV793
= ( c_HOL_Ozero__class_Ozero @ SV299 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV299 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2794,plain,
! [SV301: $i,SV795: $i,SV598: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV598 @ SV795 @ SV301 )
= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
= $false )
| ( ( ( SV795
= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
| ( SV598
= ( c_HOL_Ozero__class_Ozero @ SV301 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV301 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(2795,plain,
! [SV916: $i,SV890: $i,SV797: $i,SV601: $i,SV306: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV306 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV306 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV797 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV916 @ SV306 ) @ SV306 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV916 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV797 @ SV306 ) @ SV306 ) )
| ( SV797 = SV916 )
| ( SV601 = SV890 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(2796,plain,
! [SV917: $i,SV891: $i,SV798: $i,SV602: $i,SV307: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV307 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV798 @ SV307 )
!= ( c_HOL_Ominus__class_Ominus @ SV891 @ SV917 @ SV307 ) )
| ( c_HOL_Oord__class_Oless @ SV602 @ SV798 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV917 @ SV307 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2797,plain,
! [SV800: $i,SV309: $i,SV604: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV604 @ SV604 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV800 @ SV800 @ SV309 ) @ SV309 )
= ( c_HOL_Ozero__class_Ozero @ SV309 ) )
= $false )
| ( ( SV800
= ( c_HOL_Ozero__class_Ozero @ SV309 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2798,plain,
! [SV893: $i,SV801: $i,SV608: $i,SV313: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV313 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV608 @ SV801 @ SV313 )
!= ( c_HOL_Oplus__class_Oplus @ SV608 @ SV893 @ SV313 ) )
| ( SV801 = SV893 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2700]) ).
thf(2799,plain,
! [SV894: $i,SV802: $i,SV314: $i,SV609: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV609 @ SV609 @ SV314 )
!= ( c_HOL_Ominus__class_Ominus @ SV802 @ SV894 @ SV314 ) )
= $true )
| ( ( SV802 = SV894 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV314 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2701]) ).
thf(2800,plain,
! [SV803: $i,SV611: $i,SV316: $i] :
( ( ( class_Int_Onumber__ring @ SV316 )
= $false )
| ( ( ( SV611
!= ( c_HOL_Oplus__class_Oplus @ SV611 @ SV803 @ SV316 ) )
| ( SV803
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(2801,plain,
! [SV895: $i,SV317: $i,SV804: $i,SV612: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV612 @ SV804 @ SV317 )
!= ( c_HOL_Oplus__class_Oplus @ SV612 @ SV895 @ SV317 ) )
= $true )
| ( ( SV804 = SV895 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2703]) ).
thf(2802,plain,
! [SV806: $i,SV321: $i,SV616: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV616 @ SV616 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SV806 @ SV806 @ SV321 ) @ SV321 )
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $false )
| ( ( SV616
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2803,plain,
! [SV918: $i,SV896: $i,SV807: $i,SV620: $i,SV325: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV807 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV896 @ SV918 @ SV325 ) )
| ( c_HOL_Oord__class_Oless @ SV896 @ SV918 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV620 @ SV807 @ SV325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2804,plain,
! [SV331: $i,SV809: $i,SV626: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV626 @ SV809 @ SV331 )
= ( c_HOL_Ozero__class_Ozero @ SV331 ) )
= $false )
| ( ( SV626 = SV809 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2805,plain,
! [SV919: $i,SV898: $i,SV810: $i,SV627: $i,SV332: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV332 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV332 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV810 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV919 @ SV332 ) @ SV332 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV919 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV810 @ SV332 ) @ SV332 ) )
| ( SV810 = SV919 )
| ( SV627 = SV898 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2806,plain,
! [SV345: $i,SV12: $i,SV635: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV635 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV345 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SV345 @ SV635 @ SV12 ) @ SV12 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(2807,plain,
! [SV346: $i,SV636: $i,SV13: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV636 @ SV13 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV346 @ SV13 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SV346 @ SV636 @ SV13 ) @ SV13 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(2808,plain,
! [SV347: $i,SV637: $i,SV14: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV637 @ SV14 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ ( c_HOL_Otimes__class_Otimes @ SV637 @ SV347 @ SV14 ) @ SV14 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV347 @ SV14 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2809,plain,
! [SV348: $i,SV638: $i,SV15: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV638 @ SV15 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ ( c_HOL_Otimes__class_Otimes @ SV348 @ SV638 @ SV15 ) @ SV15 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV348 @ SV15 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2716]) ).
thf(2810,plain,
! [SV920: $i,SV902: $i,SV814: $i,SV639: $i,SV353: $i,SV20: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV20 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV353 @ SV639 @ SV20 ) @ SV814 @ SV20 ) @ SV902 @ SV20 ) @ SV920 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV814 @ SV20 ) @ SV902 @ SV20 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV639 @ SV814 @ SV20 ) @ SV920 @ SV20 ) @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2811,plain,
! [SV921: $i,SV903: $i,SV815: $i,SV640: $i,SV354: $i,SV21: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV21 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV354 @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV903 @ SV640 @ SV21 ) @ SV921 @ SV21 ) @ SV21 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV354 @ SV903 @ SV21 ) @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ SV921 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(2812,plain,
! [SV922: $i,SV904: $i,SV816: $i,SV641: $i,SV355: $i,SV22: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV22 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV355 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SV816 @ SV22 ) @ SV904 @ SV22 ) @ SV922 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV904 @ SV22 ) @ SV355 @ SV22 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV641 @ SV904 @ SV22 ) @ SV922 @ SV22 ) @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(2813,plain,
! [SV923: $i,SV905: $i,SV817: $i,SV642: $i,SV356: $i,SV23: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV23 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV356 @ SV642 @ SV23 ) @ SV817 @ SV23 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV905 @ SV642 @ SV23 ) @ SV923 @ SV23 ) @ SV23 )
| ~ ( c_HOL_Oord__class_Oless @ SV817 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV905 @ SV356 @ SV23 ) @ SV642 @ SV23 ) @ SV923 @ SV23 ) @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2814,plain,
! [SV392: $i,SV654: $i,SV64: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV654 @ SV64 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV392 @ SV64 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ ( c_HOL_Oplus__class_Oplus @ SV392 @ SV654 @ SV64 ) @ SV64 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2724]) ).
thf(2815,plain,
! [SV908: $i,SV820: $i,SV74: $i,SV660: $i,SV400: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV400 @ SV660 @ SV74 ) @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV908 @ SV74 ) @ SV74 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV660 @ SV908 @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV400 @ SV820 @ SV74 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(2816,plain,
! [SV821: $i,SV401: $i,SV661: $i,SV75: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV75 @ SV661 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV401 @ SV821 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV75 @ SV401 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV661 @ SV821 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(2817,plain,
! [SV668: $i,SV89: $i,SV411: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV411 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV668 @ SV89 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SV668 @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(2818,plain,
! [SV412: $i,SV90: $i,SV669: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV412 @ SV90 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV412 @ SV669 @ SV90 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2738]) ).
thf(2819,plain,
! [SV413: $i,SV670: $i,SV91: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV670 @ SV91 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV413 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV413 @ SV670 @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2739]) ).
thf(2820,plain,
! [SV671: $i,SV93: $i,SV822: $i,SV415: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV415 @ SV822 @ SV93 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV671 @ SV93 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV415 @ ( c_HOL_Oplus__class_Oplus @ SV671 @ SV822 @ SV93 ) @ SV93 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(2821,plain,
! [SV674: $i,SV98: $i,SV823: $i,SV420: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV420 @ SV823 @ SV98 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV420 @ SV674 @ SV98 ) @ ( c_HOL_Oplus__class_Oplus @ SV823 @ SV674 @ SV98 ) @ SV98 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(2822,plain,
! [SV675: $i,SV99: $i,SV824: $i,SV421: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV421 @ SV824 @ SV99 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV421 @ SV675 @ SV99 ) @ ( c_HOL_Oplus__class_Oplus @ SV824 @ SV675 @ SV99 ) @ SV99 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2742]) ).
thf(2823,plain,
! [SV676: $i,SV100: $i,SV825: $i,SV422: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV422 @ SV825 @ SV100 ) @ ( c_HOL_Oplus__class_Oplus @ SV676 @ SV825 @ SV100 ) @ SV100 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV422 @ SV676 @ SV100 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2824,plain,
! [SV423: $i,SV101: $i,SV826: $i,SV677: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV677 @ SV826 @ SV101 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SV677 @ SV101 ) @ ( c_HOL_Oplus__class_Oplus @ SV423 @ SV826 @ SV101 ) @ SV101 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(2825,plain,
! [SV424: $i,SV102: $i,SV827: $i,SV678: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV678 @ SV827 @ SV102 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SV678 @ SV102 ) @ ( c_HOL_Oplus__class_Oplus @ SV424 @ SV827 @ SV102 ) @ SV102 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2745]) ).
thf(2826,plain,
! [SV679: $i,SV103: $i,SV425: $i,SV828: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV828 @ SV425 @ SV103 ) @ ( c_HOL_Oplus__class_Oplus @ SV828 @ SV679 @ SV103 ) @ SV103 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV425 @ SV679 @ SV103 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(2827,plain,
! [SV434: $i,SV113: $i,SV829: $i,SV683: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV683 @ SV829 @ SV113 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV683 @ SV434 @ SV113 ) @ ( c_HOL_Otimes__class_Otimes @ SV829 @ SV434 @ SV113 ) @ SV113 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV434 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2747]) ).
thf(2828,plain,
! [SV435: $i,SV684: $i,SV830: $i,SV114: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV830 @ SV114 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV684 @ SV830 @ SV114 ) @ ( c_HOL_Otimes__class_Otimes @ SV435 @ SV830 @ SV114 ) @ SV114 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV435 @ SV684 @ SV114 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2748]) ).
thf(2829,plain,
! [SV436: $i,SV115: $i,SV831: $i,SV685: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV685 @ SV831 @ SV115 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV685 @ SV115 ) @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV831 @ SV115 ) @ SV115 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV436 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2749]) ).
thf(2830,plain,
! [SV437: $i,SV686: $i,SV832: $i,SV116: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV832 @ SV116 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV832 @ SV686 @ SV116 ) @ ( c_HOL_Otimes__class_Otimes @ SV832 @ SV437 @ SV116 ) @ SV116 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV437 @ SV686 @ SV116 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2750]) ).
thf(2831,plain,
! [SV130: $i,SV450: $i,SV696: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV696 @ SV450 @ SV130 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV450 @ SV696 @ SV130 )
= $false )
| ( ( class_Orderings_Oorder @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2832,plain,
! [SV131: $i,SV451: $i,SV697: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV697 @ SV451 @ SV131 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV451 @ SV697 @ SV131 )
= $false )
| ( ( class_Orderings_Olinorder @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(2833,plain,
! [SV132: $i,SV452: $i,SV698: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV698 @ SV452 @ SV132 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV452 @ SV698 @ SV132 )
= $false )
| ( ( class_Orderings_Opreorder @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2834,plain,
! [SV133: $i,SV453: $i,SV699: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV699 @ SV453 @ SV133 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV453 @ SV699 @ SV133 )
= $false )
| ( ( class_Orderings_Opreorder @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(2835,plain,
! [SV842: $i,SV700: $i,SV457: $i,SV137: $i] :
( ( ( class_Int_Onumber__ring @ SV137 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV700 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV842 @ SV137 ) @ SV137 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV842 @ SV137 ) @ ( c_HOL_Otimes__class_Otimes @ SV457 @ SV700 @ SV137 ) @ SV137 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(2836,plain,
! [SV843: $i,SV701: $i,SV458: $i,SV138: $i] :
( ( ( class_Int_Onumber__ring @ SV138 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV701 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV843 @ SV138 ) @ SV138 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV843 @ SV138 ) @ ( c_HOL_Otimes__class_Otimes @ SV458 @ SV701 @ SV138 ) @ SV138 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2837,plain,
! [SV464: $i,SV146: $i,SV706: $i,SV844: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV844 @ SV706 @ SV146 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV464 @ SV844 @ SV146 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV464 @ SV706 @ SV146 )
= $true )
| ( ( class_Orderings_Opreorder @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2757]) ).
thf(2838,plain,
! [SV707: $i,SV147: $i,SV845: $i,SV465: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV465 @ SV845 @ SV147 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV845 @ SV707 @ SV147 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV465 @ SV707 @ SV147 )
= $true )
| ( ( class_Orderings_Oorder @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2758]) ).
thf(2839,plain,
! [SV474: $i,SV162: $i,SV712: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV712 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV474 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SV712 @ SV162 ) @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(2840,plain,
! [SV848: $i,SV720: $i,SV486: $i,SV174: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV486 @ SV174 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV720 @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV848 @ SV174 ) @ SV174 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV486 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2761]) ).
thf(2841,plain,
! [SV849: $i,SV175: $i,SV487: $i,SV721: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV721 @ SV487 @ SV175 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV849 @ SV721 @ SV175 ) @ ( c_HOL_Otimes__class_Otimes @ SV849 @ SV487 @ SV175 ) @ SV175 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV487 @ SV721 @ SV175 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2762]) ).
thf(2842,plain,
! [SV850: $i,SV722: $i,SV488: $i,SV176: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV488 @ SV176 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV722 @ SV488 @ SV176 ) @ ( c_HOL_Otimes__class_Otimes @ SV850 @ SV488 @ SV176 ) @ SV176 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV488 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2763]) ).
thf(2843,plain,
! [SV851: $i,SV177: $i,SV489: $i,SV723: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV723 @ SV489 @ SV177 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV723 @ SV851 @ SV177 ) @ ( c_HOL_Otimes__class_Otimes @ SV489 @ SV851 @ SV177 ) @ SV177 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV489 @ SV723 @ SV177 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2764]) ).
thf(2844,plain,
! [SV493: $i,SV182: $i,SV724: $i,SV852: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV724 @ SV182 ) @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV493 @ SV182 ) @ SV182 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV493 @ SV724 @ SV182 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2765]) ).
thf(2845,plain,
! [SV494: $i,SV183: $i,SV725: $i,SV853: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV853 @ SV725 @ SV183 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV183 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV725 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV853 @ SV183 ) @ SV183 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2766]) ).
thf(2846,plain,
! [SV726: $i,SV184: $i,SV495: $i,SV854: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV495 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV726 @ SV184 ) @ SV184 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV184 ) @ SV854 @ SV184 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV495 @ SV726 @ SV184 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2767]) ).
thf(2847,plain,
! [SV496: $i,SV185: $i,SV855: $i,SV727: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV727 @ SV855 @ SV185 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV185 ) @ SV496 @ SV185 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV727 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV855 @ SV185 ) @ SV185 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2768]) ).
thf(2848,plain,
! [SV728: $i,SV856: $i,SV186: $i,SV497: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV497 @ ( c_HOL_Ozero__class_Ozero @ SV186 ) @ SV186 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV856 @ SV728 @ SV186 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV728 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV856 @ SV186 ) @ SV186 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2769]) ).
thf(2849,plain,
! [SV857: $i,SV729: $i,SV498: $i,SV187: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SV498 @ SV187 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV729 @ SV857 @ SV187 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV729 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV857 @ SV187 ) @ SV187 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2770]) ).
thf(2850,plain,
! [SV499: $i,SV188: $i,SV858: $i,SV730: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV730 @ SV858 @ SV188 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV188 ) @ SV499 @ SV188 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV730 @ SV188 ) @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV858 @ SV188 ) @ SV188 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2771]) ).
thf(2851,plain,
! [SV500: $i,SV189: $i,SV731: $i,SV859: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV859 @ SV731 @ SV189 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV500 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV731 @ SV189 ) @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV859 @ SV189 ) @ SV189 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV189 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(2852,plain,
! [SV501: $i,SV860: $i,SV190: $i,SV732: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV732 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV860 @ SV501 @ SV190 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV501 @ SV732 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SV860 @ SV732 @ SV190 ) @ SV190 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(2853,plain,
! [SV861: $i,SV502: $i,SV733: $i,SV191: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV733 @ SV191 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV502 @ SV861 @ SV191 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SV733 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SV861 @ SV733 @ SV191 ) @ SV191 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2774]) ).
thf(2854,plain,
! [SV734: $i,SV192: $i,SV862: $i,SV503: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV503 @ SV862 @ SV192 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV734 @ SV192 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV503 @ SV734 @ SV192 ) @ ( c_HOL_Otimes__class_Otimes @ SV862 @ SV734 @ SV192 ) @ SV192 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2775]) ).
thf(2855,plain,
! [SV735: $i,SV193: $i,SV504: $i,SV863: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV504 @ SV193 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV735 @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV193 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV504 @ SV735 @ SV193 ) @ ( c_HOL_Otimes__class_Otimes @ SV863 @ SV735 @ SV193 ) @ SV193 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2776]) ).
thf(2856,plain,
! [SV864: $i,SV736: $i,SV505: $i,SV194: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV505 @ SV194 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV736 @ SV864 @ SV194 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV736 @ SV194 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV864 @ SV194 ) @ SV194 )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(2857,plain,
! [SV519: $i,SV740: $i,SV213: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV740 @ SV213 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV519 @ SV213 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV519 @ SV740 @ SV213 ) @ SV213 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(2858,plain,
! [SV912: $i,SV275: $i,SV882: $i,SV778: $i,SV577: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV577 @ ( c_HOL_Oplus__class_Oplus @ SV778 @ SV882 @ SV275 ) @ SV275 )
!= ( c_HOL_Oplus__class_Oplus @ SV778 @ SV912 @ SV275 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV577 @ SV882 @ SV275 )
= SV912 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV275 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(2859,plain,
! [SV883: $i,SV280: $i,SV781: $i,SV580: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV580 @ SV781 @ SV280 )
= ( c_HOL_Oplus__class_Oplus @ SV580 @ SV883 @ SV280 ) )
= $false )
| ( ( SV781 = SV883 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(2860,plain,
! [SV884: $i,SV285: $i,SV783: $i,SV584: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV584 @ SV783 @ SV285 )
= ( c_HOL_Ominus__class_Ominus @ SV884 @ SV884 @ SV285 ) )
= $false )
| ( ( SV584 = SV783 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2785]) ).
thf(2861,plain,
! [SV885: $i,SV286: $i,SV585: $i,SV784: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV784 @ SV585 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV286 @ SV885 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV286 @ SV585 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV784 @ SV885 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(2862,plain,
! [SV886: $i,SV287: $i,SV785: $i,SV586: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV586 @ SV785 @ SV287 )
= ( c_HOL_Oplus__class_Oplus @ SV886 @ SV785 @ SV287 ) )
= $false )
| ( ( SV586 = SV886 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(2863,plain,
! [SV913: $i,SV887: $i,SV786: $i,SV588: $i,SV290: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV290 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV887 @ SV290 ) @ SV290 )
!= ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV913 @ SV290 ) @ SV290 ) )
| ( SV887 = SV913 )
| ( SV786
= ( c_HOL_Ozero__class_Ozero @ SV290 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2788]) ).
thf(2864,plain,
! [SV924: $i,SV914: $i,SV888: $i,SV787: $i,SV589: $i,SV291: $i] :
( ( ( class_Ring__and__Field_Oring @ SV291 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV589 @ SV787 @ SV291 ) @ SV888 @ SV291 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV787 @ SV291 ) @ SV924 @ SV291 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV589 @ SV914 @ SV291 ) @ SV787 @ SV291 ) @ SV888 @ SV291 )
= SV924 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(2865,plain,
! [SV925: $i,SV915: $i,SV889: $i,SV788: $i,SV591: $i,SV293: $i] :
( ( ( class_Ring__and__Field_Oring @ SV293 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV591 @ SV788 @ SV293 ) @ SV889 @ SV293 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV788 @ SV293 ) @ SV925 @ SV293 ) )
| ( SV889
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV915 @ SV591 @ SV293 ) @ SV788 @ SV293 ) @ SV925 @ SV293 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(2866,plain,
! [SV592: $i,SV294: $i,SV789: $i] :
( ( ( SV789
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
= $true )
| ( ( SV592
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV592 @ SV789 @ SV294 )
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2791]) ).
thf(2867,plain,
! [SV297: $i,SV792: $i,SV595: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV595 @ SV792 @ SV297 )
!= ( c_HOL_Ozero__class_Ozero @ SV297 ) )
= $true )
| ( ( SV595 = SV792 )
= $true )
| ( ( class_Int_Onumber__ring @ SV297 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2792]) ).
thf(2868,plain,
! [SV793: $i,SV299: $i,SV596: $i] :
( ( ( SV596
= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
= $true )
| ( ( SV793
= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV596 @ SV793 @ SV299 )
= ( c_HOL_Ozero__class_Ozero @ SV299 ) )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV299 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2793]) ).
thf(2869,plain,
! [SV598: $i,SV301: $i,SV795: $i] :
( ( ( SV795
= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
= $true )
| ( ( SV598
= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV598 @ SV795 @ SV301 )
= ( c_HOL_Ozero__class_Ozero @ SV301 ) )
= $false )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV301 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2794]) ).
thf(2870,plain,
! [SV916: $i,SV890: $i,SV797: $i,SV601: $i,SV306: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV306 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV797 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV916 @ SV306 ) @ SV306 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV916 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV797 @ SV306 ) @ SV306 ) )
| ( SV797 = SV916 )
| ( SV601 = SV890 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(2871,plain,
! [SV917: $i,SV891: $i,SV307: $i,SV798: $i,SV602: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV798 @ SV307 )
!= ( c_HOL_Ominus__class_Ominus @ SV891 @ SV917 @ SV307 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV602 @ SV798 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV917 @ SV307 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2796]) ).
thf(2872,plain,
! [SV893: $i,SV801: $i,SV608: $i,SV313: $i] :
( ( ( class_Int_Onumber__ring @ SV313 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV608 @ SV801 @ SV313 )
!= ( c_HOL_Oplus__class_Oplus @ SV608 @ SV893 @ SV313 ) )
| ( SV801 = SV893 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(2873,plain,
! [SV894: $i,SV802: $i,SV314: $i,SV609: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV609 @ SV609 @ SV314 )
= ( c_HOL_Ominus__class_Ominus @ SV802 @ SV894 @ SV314 ) )
= $false )
| ( ( SV802 = SV894 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2799]) ).
thf(2874,plain,
! [SV316: $i,SV803: $i,SV611: $i] :
( ( ( SV611
!= ( c_HOL_Oplus__class_Oplus @ SV611 @ SV803 @ SV316 ) )
= $true )
| ( ( SV803
= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV316 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2800]) ).
thf(2875,plain,
! [SV895: $i,SV317: $i,SV804: $i,SV612: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV612 @ SV804 @ SV317 )
= ( c_HOL_Oplus__class_Oplus @ SV612 @ SV895 @ SV317 ) )
= $false )
| ( ( SV804 = SV895 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2876,plain,
! [SV918: $i,SV896: $i,SV325: $i,SV807: $i,SV620: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV807 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV896 @ SV918 @ SV325 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV896 @ SV918 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV620 @ SV807 @ SV325 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2803]) ).
thf(2877,plain,
! [SV919: $i,SV898: $i,SV810: $i,SV627: $i,SV332: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV332 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV810 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV919 @ SV332 ) @ SV332 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV919 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV810 @ SV332 ) @ SV332 ) )
| ( SV810 = SV919 )
| ( SV627 = SV898 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2805]) ).
thf(2878,plain,
! [SV635: $i,SV12: $i,SV345: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV345 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV635 @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ SV12 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SV345 @ SV635 @ SV12 ) @ SV12 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2806]) ).
thf(2879,plain,
! [SV636: $i,SV346: $i,SV13: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV346 @ SV13 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ SV636 @ SV13 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SV346 @ SV636 @ SV13 ) @ SV13 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2880,plain,
! [SV347: $i,SV637: $i,SV14: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ ( c_HOL_Otimes__class_Otimes @ SV637 @ SV347 @ SV14 ) @ SV14 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV637 @ SV14 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV347 @ SV14 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(2881,plain,
! [SV638: $i,SV348: $i,SV15: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ ( c_HOL_Otimes__class_Otimes @ SV348 @ SV638 @ SV15 ) @ SV15 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV638 @ SV15 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV348 @ SV15 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(2882,plain,
! [SV920: $i,SV902: $i,SV814: $i,SV20: $i,SV639: $i,SV353: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV353 @ SV639 @ SV20 ) @ SV814 @ SV20 ) @ SV902 @ SV20 ) @ SV920 @ SV20 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV814 @ SV20 ) @ SV902 @ SV20 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV639 @ SV814 @ SV20 ) @ SV920 @ SV20 ) @ SV20 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2810]) ).
thf(2883,plain,
! [SV921: $i,SV903: $i,SV815: $i,SV21: $i,SV640: $i,SV354: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV354 @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV903 @ SV640 @ SV21 ) @ SV921 @ SV21 ) @ SV21 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV354 @ SV903 @ SV21 ) @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ SV921 @ SV21 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2811]) ).
thf(2884,plain,
! [SV922: $i,SV904: $i,SV22: $i,SV816: $i,SV641: $i,SV355: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV355 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SV816 @ SV22 ) @ SV904 @ SV22 ) @ SV922 @ SV22 ) @ SV22 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV904 @ SV22 ) @ SV355 @ SV22 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV641 @ SV904 @ SV22 ) @ SV922 @ SV22 ) @ SV22 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2812]) ).
thf(2885,plain,
! [SV923: $i,SV905: $i,SV817: $i,SV23: $i,SV642: $i,SV356: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV356 @ SV642 @ SV23 ) @ SV817 @ SV23 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV905 @ SV642 @ SV23 ) @ SV923 @ SV23 ) @ SV23 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV817 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV905 @ SV356 @ SV23 ) @ SV642 @ SV23 ) @ SV923 @ SV23 ) @ SV23 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2813]) ).
thf(2886,plain,
! [SV654: $i,SV392: $i,SV64: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV392 @ SV64 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV654 @ SV64 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ ( c_HOL_Oplus__class_Oplus @ SV392 @ SV654 @ SV64 ) @ SV64 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(2887,plain,
! [SV820: $i,SV400: $i,SV74: $i,SV908: $i,SV660: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV660 @ SV908 @ SV74 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV400 @ SV820 @ SV74 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV400 @ SV660 @ SV74 ) @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV908 @ SV74 ) @ SV74 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2815]) ).
thf(2888,plain,
! [SV411: $i,SV668: $i,SV89: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV668 @ SV89 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV411 @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV411 @ SV668 @ SV89 ) @ ( c_HOL_Ozero__class_Ozero @ SV89 ) @ SV89 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2817]) ).
thf(2889,plain,
! [SV669: $i,SV412: $i,SV90: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV412 @ SV90 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV412 @ SV669 @ SV90 ) @ ( c_HOL_Ozero__class_Ozero @ SV90 ) @ SV90 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2818]) ).
thf(2890,plain,
! [SV670: $i,SV91: $i,SV413: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV413 @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV670 @ SV91 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV413 @ SV670 @ SV91 ) @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV91 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(2891,plain,
! [SV671: $i,SV93: $i,SV822: $i,SV415: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV415 @ SV822 @ SV93 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV671 @ SV93 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV415 @ ( c_HOL_Oplus__class_Oplus @ SV671 @ SV822 @ SV93 ) @ SV93 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(2892,plain,
! [SV829: $i,SV113: $i,SV434: $i,SV683: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV683 @ SV434 @ SV113 ) @ ( c_HOL_Otimes__class_Otimes @ SV829 @ SV434 @ SV113 ) @ SV113 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV683 @ SV829 @ SV113 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV434 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2827]) ).
thf(2893,plain,
! [SV435: $i,SV114: $i,SV830: $i,SV684: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV684 @ SV830 @ SV114 ) @ ( c_HOL_Otimes__class_Otimes @ SV435 @ SV830 @ SV114 ) @ SV114 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV830 @ SV114 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV435 @ SV684 @ SV114 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(2894,plain,
! [SV831: $i,SV115: $i,SV685: $i,SV436: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV685 @ SV115 ) @ ( c_HOL_Otimes__class_Otimes @ SV436 @ SV831 @ SV115 ) @ SV115 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV685 @ SV831 @ SV115 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV436 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2895,plain,
! [SV437: $i,SV116: $i,SV686: $i,SV832: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV832 @ SV686 @ SV116 ) @ ( c_HOL_Otimes__class_Otimes @ SV832 @ SV437 @ SV116 ) @ SV116 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV832 @ SV116 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV437 @ SV686 @ SV116 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(2896,plain,
! [SV464: $i,SV146: $i,SV706: $i,SV844: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV844 @ SV706 @ SV146 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV464 @ SV844 @ SV146 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV464 @ SV706 @ SV146 )
= $true )
| ( ( class_Orderings_Opreorder @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(2897,plain,
! [SV707: $i,SV147: $i,SV845: $i,SV465: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV465 @ SV845 @ SV147 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV845 @ SV707 @ SV147 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV465 @ SV707 @ SV147 )
= $true )
| ( ( class_Orderings_Oorder @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(2898,plain,
! [SV712: $i,SV162: $i,SV474: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV474 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV712 @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV474 @ SV712 @ SV162 ) @ ( c_HOL_Ozero__class_Ozero @ SV162 ) @ SV162 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2899,plain,
! [SV848: $i,SV174: $i,SV720: $i,SV486: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV720 @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV486 @ SV848 @ SV174 ) @ SV174 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV486 @ SV174 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV486 @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV174 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(2900,plain,
! [SV487: $i,SV175: $i,SV721: $i,SV849: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV849 @ SV721 @ SV175 ) @ ( c_HOL_Otimes__class_Otimes @ SV849 @ SV487 @ SV175 ) @ SV175 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV721 @ SV487 @ SV175 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV487 @ SV721 @ SV175 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2841]) ).
thf(2901,plain,
! [SV850: $i,SV176: $i,SV488: $i,SV722: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV722 @ SV488 @ SV176 ) @ ( c_HOL_Otimes__class_Otimes @ SV850 @ SV488 @ SV176 ) @ SV176 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV488 @ SV176 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV488 @ ( c_HOL_Ozero__class_Ozero @ SV176 ) @ SV176 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2842]) ).
thf(2902,plain,
! [SV489: $i,SV177: $i,SV851: $i,SV723: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV723 @ SV851 @ SV177 ) @ ( c_HOL_Otimes__class_Otimes @ SV489 @ SV851 @ SV177 ) @ SV177 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV723 @ SV489 @ SV177 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV489 @ SV723 @ SV177 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(2903,plain,
! [SV493: $i,SV182: $i,SV724: $i,SV852: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV724 @ SV182 ) @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV493 @ SV182 ) @ SV182 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV493 @ SV724 @ SV182 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2844]) ).
thf(2904,plain,
! [SV494: $i,SV183: $i,SV725: $i,SV853: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV853 @ SV725 @ SV183 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV183 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV725 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV853 @ SV183 ) @ SV183 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2845]) ).
thf(2905,plain,
! [SV726: $i,SV184: $i,SV495: $i,SV854: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV495 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV726 @ SV184 ) @ SV184 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV184 ) @ SV854 @ SV184 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV495 @ SV726 @ SV184 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2846]) ).
thf(2906,plain,
! [SV496: $i,SV185: $i,SV855: $i,SV727: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV727 @ SV855 @ SV185 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV185 ) @ SV496 @ SV185 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV727 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV855 @ SV185 ) @ SV185 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2847]) ).
thf(2907,plain,
! [SV728: $i,SV856: $i,SV186: $i,SV497: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV497 @ ( c_HOL_Ozero__class_Ozero @ SV186 ) @ SV186 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV856 @ SV728 @ SV186 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV728 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV856 @ SV186 ) @ SV186 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2848]) ).
thf(2908,plain,
! [SV857: $i,SV729: $i,SV498: $i,SV187: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SV498 @ SV187 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV729 @ SV857 @ SV187 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV729 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV857 @ SV187 ) @ SV187 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2849]) ).
thf(2909,plain,
! [SV499: $i,SV188: $i,SV858: $i,SV730: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV730 @ SV858 @ SV188 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV188 ) @ SV499 @ SV188 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV730 @ SV188 ) @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV858 @ SV188 ) @ SV188 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(2910,plain,
! [SV500: $i,SV189: $i,SV731: $i,SV859: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV859 @ SV731 @ SV189 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV500 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV731 @ SV189 ) @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV859 @ SV189 ) @ SV189 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(2911,plain,
! [SV501: $i,SV860: $i,SV190: $i,SV732: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV732 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV860 @ SV501 @ SV190 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV501 @ SV732 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SV860 @ SV732 @ SV190 ) @ SV190 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2852]) ).
thf(2912,plain,
! [SV861: $i,SV502: $i,SV733: $i,SV191: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV733 @ SV191 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV502 @ SV861 @ SV191 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SV733 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SV861 @ SV733 @ SV191 ) @ SV191 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2853]) ).
thf(2913,plain,
! [SV734: $i,SV192: $i,SV862: $i,SV503: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV503 @ SV862 @ SV192 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV734 @ SV192 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV503 @ SV734 @ SV192 ) @ ( c_HOL_Otimes__class_Otimes @ SV862 @ SV734 @ SV192 ) @ SV192 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2854]) ).
thf(2914,plain,
! [SV735: $i,SV193: $i,SV504: $i,SV863: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV863 @ SV504 @ SV193 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV735 @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV193 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV504 @ SV735 @ SV193 ) @ ( c_HOL_Otimes__class_Otimes @ SV863 @ SV735 @ SV193 ) @ SV193 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(2915,plain,
! [SV864: $i,SV736: $i,SV505: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV505 @ SV194 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV736 @ SV864 @ SV194 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV736 @ SV194 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV864 @ SV194 ) @ SV194 )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(2916,plain,
! [SV740: $i,SV519: $i,SV213: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV519 @ SV213 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ SV740 @ SV213 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV519 @ SV740 @ SV213 ) @ SV213 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(2917,plain,
! [SV912: $i,SV275: $i,SV882: $i,SV778: $i,SV577: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV577 @ ( c_HOL_Oplus__class_Oplus @ SV778 @ SV882 @ SV275 ) @ SV275 )
= ( c_HOL_Oplus__class_Oplus @ SV778 @ SV912 @ SV275 ) )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV577 @ SV882 @ SV275 )
= SV912 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV275 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(2918,plain,
! [SV913: $i,SV887: $i,SV786: $i,SV588: $i,SV290: $i] :
( ( ( class_Int_Onumber__ring @ SV290 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV887 @ SV290 ) @ SV290 )
!= ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV913 @ SV290 ) @ SV290 ) )
| ( SV887 = SV913 )
| ( SV786
= ( c_HOL_Ozero__class_Ozero @ SV290 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(2919,plain,
! [SV924: $i,SV914: $i,SV888: $i,SV291: $i,SV787: $i,SV589: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV589 @ SV787 @ SV291 ) @ SV888 @ SV291 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV787 @ SV291 ) @ SV924 @ SV291 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV589 @ SV914 @ SV291 ) @ SV787 @ SV291 ) @ SV888 @ SV291 )
= SV924 )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2864]) ).
thf(2920,plain,
! [SV925: $i,SV915: $i,SV889: $i,SV293: $i,SV788: $i,SV591: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV591 @ SV788 @ SV293 ) @ SV889 @ SV293 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV788 @ SV293 ) @ SV925 @ SV293 ) )
= $true )
| ( ( SV889
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV915 @ SV591 @ SV293 ) @ SV788 @ SV293 ) @ SV925 @ SV293 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2865]) ).
thf(2921,plain,
! [SV297: $i,SV792: $i,SV595: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV595 @ SV792 @ SV297 )
= ( c_HOL_Ozero__class_Ozero @ SV297 ) )
= $false )
| ( ( SV595 = SV792 )
= $true )
| ( ( class_Int_Onumber__ring @ SV297 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2867]) ).
thf(2922,plain,
! [SV916: $i,SV890: $i,SV797: $i,SV601: $i,SV306: $i] :
( ( ( class_Int_Onumber__ring @ SV306 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV797 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV916 @ SV306 ) @ SV306 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV916 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV797 @ SV306 ) @ SV306 ) )
| ( SV797 = SV916 )
| ( SV601 = SV890 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(2923,plain,
! [SV917: $i,SV891: $i,SV307: $i,SV798: $i,SV602: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV798 @ SV307 )
= ( c_HOL_Ominus__class_Ominus @ SV891 @ SV917 @ SV307 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV602 @ SV798 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV917 @ SV307 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(2924,plain,
! [SV893: $i,SV313: $i,SV801: $i,SV608: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV608 @ SV801 @ SV313 )
!= ( c_HOL_Oplus__class_Oplus @ SV608 @ SV893 @ SV313 ) )
= $true )
| ( ( SV801 = SV893 )
= $true )
| ( ( class_Int_Onumber__ring @ SV313 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2872]) ).
thf(2925,plain,
! [SV316: $i,SV803: $i,SV611: $i] :
( ( ( SV611
= ( c_HOL_Oplus__class_Oplus @ SV611 @ SV803 @ SV316 ) )
= $false )
| ( ( SV803
= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV316 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(2926,plain,
! [SV918: $i,SV896: $i,SV325: $i,SV807: $i,SV620: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV807 @ SV325 )
= ( c_HOL_Ominus__class_Ominus @ SV896 @ SV918 @ SV325 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV896 @ SV918 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV620 @ SV807 @ SV325 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(2927,plain,
! [SV919: $i,SV898: $i,SV810: $i,SV627: $i,SV332: $i] :
( ( ( class_Int_Onumber__ring @ SV332 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV810 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV919 @ SV332 ) @ SV332 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV919 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV810 @ SV332 ) @ SV332 ) )
| ( SV810 = SV919 )
| ( SV627 = SV898 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(2928,plain,
! [SV920: $i,SV639: $i,SV902: $i,SV20: $i,SV814: $i,SV353: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV814 @ SV20 ) @ SV902 @ SV20 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV639 @ SV814 @ SV20 ) @ SV920 @ SV20 ) @ SV20 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV353 @ SV639 @ SV20 ) @ SV814 @ SV20 ) @ SV902 @ SV20 ) @ SV920 @ SV20 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(2929,plain,
! [SV921: $i,SV815: $i,SV640: $i,SV21: $i,SV903: $i,SV354: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV354 @ SV903 @ SV21 ) @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ SV921 @ SV21 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV354 @ SV640 @ SV21 ) @ SV815 @ SV21 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV903 @ SV640 @ SV21 ) @ SV921 @ SV21 ) @ SV21 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2883]) ).
thf(2930,plain,
! [SV922: $i,SV641: $i,SV355: $i,SV22: $i,SV904: $i,SV816: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV904 @ SV22 ) @ SV355 @ SV22 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV641 @ SV904 @ SV22 ) @ SV922 @ SV22 ) @ SV22 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV355 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SV816 @ SV22 ) @ SV904 @ SV22 ) @ SV922 @ SV22 ) @ SV22 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(2931,plain,
! [SV923: $i,SV642: $i,SV23: $i,SV356: $i,SV905: $i,SV817: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV817 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV905 @ SV356 @ SV23 ) @ SV642 @ SV23 ) @ SV923 @ SV23 ) @ SV23 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV356 @ SV642 @ SV23 ) @ SV817 @ SV23 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV905 @ SV642 @ SV23 ) @ SV923 @ SV23 ) @ SV23 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2885]) ).
thf(2932,plain,
! [SV820: $i,SV400: $i,SV74: $i,SV908: $i,SV660: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV660 @ SV908 @ SV74 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV400 @ SV820 @ SV74 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV400 @ SV660 @ SV74 ) @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV908 @ SV74 ) @ SV74 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2887]) ).
thf(2933,plain,
! [SV822: $i,SV415: $i,SV671: $i,SV93: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV671 @ SV93 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV415 @ SV822 @ SV93 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV415 @ ( c_HOL_Oplus__class_Oplus @ SV671 @ SV822 @ SV93 ) @ SV93 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2891]) ).
thf(2934,plain,
! [SV706: $i,SV146: $i,SV844: $i,SV464: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV464 @ SV844 @ SV146 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV844 @ SV706 @ SV146 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV464 @ SV706 @ SV146 )
= $true )
| ( ( class_Orderings_Opreorder @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(2935,plain,
! [SV465: $i,SV147: $i,SV707: $i,SV845: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV845 @ SV707 @ SV147 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV465 @ SV845 @ SV147 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV465 @ SV707 @ SV147 )
= $true )
| ( ( class_Orderings_Oorder @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2897]) ).
thf(2936,plain,
! [SV493: $i,SV724: $i,SV182: $i,SV852: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV182 ) @ SV182 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV724 @ SV182 ) @ ( c_HOL_Otimes__class_Otimes @ SV852 @ SV493 @ SV182 ) @ SV182 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV493 @ SV724 @ SV182 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(2937,plain,
! [SV725: $i,SV853: $i,SV183: $i,SV494: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV494 @ ( c_HOL_Ozero__class_Ozero @ SV183 ) @ SV183 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV853 @ SV725 @ SV183 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV725 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV494 @ SV853 @ SV183 ) @ SV183 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2904]) ).
thf(2938,plain,
! [SV726: $i,SV495: $i,SV854: $i,SV184: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV184 ) @ SV854 @ SV184 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV495 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV726 @ SV184 ) @ SV184 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV495 @ SV726 @ SV184 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(2939,plain,
! [SV855: $i,SV727: $i,SV496: $i,SV185: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV185 ) @ SV496 @ SV185 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV727 @ SV855 @ SV185 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV727 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV496 @ SV855 @ SV185 ) @ SV185 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2906]) ).
thf(2940,plain,
! [SV497: $i,SV186: $i,SV728: $i,SV856: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV856 @ SV728 @ SV186 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV497 @ ( c_HOL_Ozero__class_Ozero @ SV186 ) @ SV186 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV728 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV497 @ SV856 @ SV186 ) @ SV186 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(2941,plain,
! [SV498: $i,SV187: $i,SV857: $i,SV729: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV729 @ SV857 @ SV187 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV187 ) @ SV498 @ SV187 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV729 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV498 @ SV857 @ SV187 ) @ SV187 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(2942,plain,
! [SV858: $i,SV730: $i,SV499: $i,SV188: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV188 ) @ SV499 @ SV188 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV730 @ SV858 @ SV188 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV730 @ SV188 ) @ ( c_HOL_Otimes__class_Otimes @ SV499 @ SV858 @ SV188 ) @ SV188 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(2943,plain,
! [SV731: $i,SV859: $i,SV189: $i,SV500: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV500 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV859 @ SV731 @ SV189 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV731 @ SV189 ) @ ( c_HOL_Otimes__class_Otimes @ SV500 @ SV859 @ SV189 ) @ SV189 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2910]) ).
thf(2944,plain,
! [SV732: $i,SV190: $i,SV501: $i,SV860: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV860 @ SV501 @ SV190 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV732 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV501 @ SV732 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SV860 @ SV732 @ SV190 ) @ SV190 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2911]) ).
thf(2945,plain,
! [SV733: $i,SV191: $i,SV861: $i,SV502: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV502 @ SV861 @ SV191 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV733 @ SV191 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV502 @ SV733 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SV861 @ SV733 @ SV191 ) @ SV191 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2912]) ).
thf(2946,plain,
! [SV862: $i,SV503: $i,SV734: $i,SV192: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV734 @ SV192 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV503 @ SV862 @ SV192 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV503 @ SV734 @ SV192 ) @ ( c_HOL_Otimes__class_Otimes @ SV862 @ SV734 @ SV192 ) @ SV192 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2913]) ).
thf(2947,plain,
! [SV504: $i,SV863: $i,SV193: $i,SV735: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV735 @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV193 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV863 @ SV504 @ SV193 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV504 @ SV735 @ SV193 ) @ ( c_HOL_Otimes__class_Otimes @ SV863 @ SV735 @ SV193 ) @ SV193 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2914]) ).
thf(2948,plain,
! [SV505: $i,SV194: $i,SV864: $i,SV736: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV736 @ SV864 @ SV194 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV505 @ SV194 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV736 @ SV194 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV864 @ SV194 ) @ SV194 )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2915]) ).
thf(2949,plain,
! [SV913: $i,SV290: $i,SV887: $i,SV786: $i,SV588: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV887 @ SV290 ) @ SV290 )
!= ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV913 @ SV290 ) @ SV290 ) )
= $true )
| ( ( ( SV887 = SV913 )
| ( SV786
= ( c_HOL_Ozero__class_Ozero @ SV290 ) ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV290 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2918]) ).
thf(2950,plain,
! [SV924: $i,SV914: $i,SV888: $i,SV291: $i,SV787: $i,SV589: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV589 @ SV787 @ SV291 ) @ SV888 @ SV291 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV787 @ SV291 ) @ SV924 @ SV291 ) )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV589 @ SV914 @ SV291 ) @ SV787 @ SV291 ) @ SV888 @ SV291 )
= SV924 )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(2951,plain,
! [SV925: $i,SV915: $i,SV889: $i,SV293: $i,SV788: $i,SV591: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV591 @ SV788 @ SV293 ) @ SV889 @ SV293 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV788 @ SV293 ) @ SV925 @ SV293 ) )
= $false )
| ( ( SV889
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV915 @ SV591 @ SV293 ) @ SV788 @ SV293 ) @ SV925 @ SV293 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2920]) ).
thf(2952,plain,
! [SV916: $i,SV890: $i,SV306: $i,SV797: $i,SV601: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV797 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV916 @ SV306 ) @ SV306 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV916 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV797 @ SV306 ) @ SV306 ) )
= $true )
| ( ( ( SV797 = SV916 )
| ( SV601 = SV890 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV306 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(2953,plain,
! [SV917: $i,SV891: $i,SV307: $i,SV798: $i,SV602: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV602 @ SV798 @ SV307 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV917 @ SV307 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV798 @ SV307 )
= ( c_HOL_Ominus__class_Ominus @ SV891 @ SV917 @ SV307 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2923]) ).
thf(2954,plain,
! [SV893: $i,SV313: $i,SV801: $i,SV608: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV608 @ SV801 @ SV313 )
= ( c_HOL_Oplus__class_Oplus @ SV608 @ SV893 @ SV313 ) )
= $false )
| ( ( SV801 = SV893 )
= $true )
| ( ( class_Int_Onumber__ring @ SV313 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(2955,plain,
! [SV807: $i,SV620: $i,SV325: $i,SV918: $i,SV896: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV896 @ SV918 @ SV325 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV620 @ SV807 @ SV325 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV807 @ SV325 )
= ( c_HOL_Ominus__class_Ominus @ SV896 @ SV918 @ SV325 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2926]) ).
thf(2956,plain,
! [SV919: $i,SV898: $i,SV332: $i,SV810: $i,SV627: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV810 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV919 @ SV332 ) @ SV332 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV919 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV810 @ SV332 ) @ SV332 ) )
= $true )
| ( ( ( SV810 = SV919 )
| ( SV627 = SV898 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2927]) ).
thf(2957,plain,
! [SV908: $i,SV660: $i,SV74: $i,SV820: $i,SV400: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV400 @ SV820 @ SV74 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV660 @ SV908 @ SV74 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV400 @ SV660 @ SV74 ) @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV908 @ SV74 ) @ SV74 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2932]) ).
thf(2958,plain,
! [SV913: $i,SV290: $i,SV887: $i,SV786: $i,SV588: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV887 @ SV290 ) @ SV290 )
= ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV913 @ SV290 ) @ SV290 ) )
= $false )
| ( ( ( SV887 = SV913 )
| ( SV786
= ( c_HOL_Ozero__class_Ozero @ SV290 ) ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV290 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(2959,plain,
! [SV916: $i,SV890: $i,SV306: $i,SV797: $i,SV601: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV797 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV916 @ SV306 ) @ SV306 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV916 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV797 @ SV306 ) @ SV306 ) )
= $false )
| ( ( ( SV797 = SV916 )
| ( SV601 = SV890 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV306 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2952]) ).
thf(2960,plain,
! [SV798: $i,SV602: $i,SV307: $i,SV917: $i,SV891: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV891 @ SV917 @ SV307 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV602 @ SV798 @ SV307 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV602 @ SV798 @ SV307 )
= ( c_HOL_Ominus__class_Ominus @ SV891 @ SV917 @ SV307 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2953]) ).
thf(2961,plain,
! [SV918: $i,SV896: $i,SV325: $i,SV807: $i,SV620: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV620 @ SV807 @ SV325 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV896 @ SV918 @ SV325 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV620 @ SV807 @ SV325 )
= ( c_HOL_Ominus__class_Ominus @ SV896 @ SV918 @ SV325 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(2962,plain,
! [SV919: $i,SV898: $i,SV332: $i,SV810: $i,SV627: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV810 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV919 @ SV332 ) @ SV332 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV919 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV810 @ SV332 ) @ SV332 ) )
= $false )
| ( ( ( SV810 = SV919 )
| ( SV627 = SV898 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2956]) ).
thf(2963,plain,
! [SV588: $i,SV290: $i,SV786: $i,SV913: $i,SV887: $i] :
( ( ( SV887 = SV913 )
= $true )
| ( ( SV786
= ( c_HOL_Ozero__class_Ozero @ SV290 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV887 @ SV290 ) @ SV290 )
= ( c_HOL_Oplus__class_Oplus @ SV588 @ ( c_HOL_Otimes__class_Otimes @ SV786 @ SV913 @ SV290 ) @ SV290 ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV290 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2958]) ).
thf(2964,plain,
! [SV306: $i,SV890: $i,SV601: $i,SV916: $i,SV797: $i] :
( ( ( SV797 = SV916 )
= $true )
| ( ( SV601 = SV890 )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV797 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV916 @ SV306 ) @ SV306 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV601 @ SV916 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV890 @ SV797 @ SV306 ) @ SV306 ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV306 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(2965,plain,
! [SV332: $i,SV898: $i,SV627: $i,SV919: $i,SV810: $i] :
( ( ( SV810 = SV919 )
= $true )
| ( ( SV627 = SV898 )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV810 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV919 @ SV332 ) @ SV332 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV627 @ SV919 @ SV332 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV810 @ SV332 ) @ SV332 ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2962]) ).
thf(2966,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[745,2965,2964,2963,2961,2960,2957,2954,2951,2950,2948,2947,2946,2945,2944,2943,2942,2941,2940,2939,2938,2937,2936,2935,2934,2933,2931,2930,2929,2928,2925,2921,2917,2916,2902,2901,2900,2899,2898,2895,2894,2893,2892,2890,2889,2888,2886,2881,2880,2879,2878,2875,2873,2869,2868,2866,2862,2861,2860,2859,2836,2835,2834,2833,2832,2831,2826,2825,2824,2823,2822,2821,2816,2804,2802,2797,2783,2781,2780,2779,2759,2736,2735,2734,2733,2732,2729,2728,2727,2726,2725,2723,2722,2721,2712,2711,2710,2707,2705,2698,2685,2680,2679,2678,2677,2676,2675,2674,2673,2672,2671,2670,2667,2666,2665,2663,2662,2644,2643,2632,2631,2630,2629,2628,2627,2626,2625,2624,2623,2608,2607,2590,2585,2584,2583,2582,2577,2571,2570,2565,2564,2561,2558,2553,2551,2548,2545,2537,2533,2532,2531,2530,2529,2528,2527,2526,2525,2524,2522,2509,2508,2506,2502,2486,2481,2480,2479,2476,2475,2472,2469,2468,2467,2446,2445,2444,2437,2436,2429,2415,2414,2413,2412,2409,2408,2407,2406,2405,2390,2388,2387,2386,2382,2381,2380,2377,2374,2371,2369,2367,2358,2353,2352,2346,2339,2335,2328,2325,2321,2320,2317,2297,2294,2291,2290,2289,2288,2287,2284,2283,2282,2281,2280,2279,2278,2276,2275,2255,2245,2236,2235,2234,2220,2214,2213,2212,2211,2210,2181,2180,2176,2171,2170,2169,2168,2167,2166,2165,2164,2163,2162,2153,2152,2151,2150,2135,2104,2077,2069,2068,2067,2059,2058,2051,2046,2045,2037,2036,2035,2033,2004,1990,1988,1977,1974,1972,1970,1969,1967,1962,1960,1958,1938,1936,1931,1914,1913,1905,1897,1896,1882,1858,1804,1799,1790,1783,1780,1777,1769,1766,1758,1753,1714,1713,1685,1673,1663,1660,1659,1658,1654,1601,1597,1596,1570,1569,1555,1554,1552,1551,1550,1522,1453,1427,1426,1380,1379,1378,1338,1337,1334,1267,1259,1258,1211,1204,1203,1179,1178,1114,1113,1112,1111,1110,1109,1108,1107,1106,1105,1104,1103,1102,1101,1100,1099,1098,1097,1096,1095,1094,1093,1092,1091,1090,938,930,922,887,828,779,771]) ).
thf(2967,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2966]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL748-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n001.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 12:39:24 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 159.88/27.20 ..
% 159.88/27.20
% 159.88/27.20 No.of.Axioms: 370
% 159.88/27.20
% 159.88/27.20 Length.of.Defs: 0
% 159.88/27.20
% 159.88/27.20 Contains.Choice.Funs: false
% 159.88/27.20 ...........................................................................................
% 159.88/27.20
% 159.88/27.20 ********************************
% 159.88/27.20 * All subproblems solved! *
% 159.88/27.20 ********************************
% 159.88/27.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:370,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2966,loop_count:0,foatp_calls:1,translation:fof_full)
% 159.88/27.20
% 159.88/27.20 %**** Beginning of derivation protocol ****
% 159.88/27.20 % SZS output start CNFRefutation
% See solution above
% 26.54/27.22
% 26.54/27.22 %**** End of derivation protocol ****
% 26.54/27.22 %**** no. of clauses in derivation: 2967 ****
% 26.54/27.22 %**** clause counter: 2966 ****
% 26.54/27.22
% 26.54/27.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:370,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2966,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------