%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL795-1 : 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 : n005.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 10:30:35 AM UTC 2026
% Result : Unsatisfiable 248.70s 50.10s
% Output : CNFRefutation 248.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 921
% Syntax : Number of formulae : 8269 (5090 unt; 0 typ; 0 def)
% Number of atoms : 45398 (16828 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 136013 (10955 ~;14103 |; 0 &;110955 @)
% ( 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 : 127 ( 124 usr; 19 con; 0-6 aty)
% Number of variables : 29578 ( 0 ^;29578 !; 0 ?;29578 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1,type,
c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1,type,
c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1: $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1,type,
c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1: $i > $i ).
thf(tp_c_Groebner__Basis_Ogb__semiring,type,
c_Groebner__Basis_Ogb__semiring: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
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 ).
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_Osubst,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(tp_c_List_Oappend,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(tp_c_List_Odrop,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(tp_c_List_Ofoldl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Ofoldr,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Olist_OCons,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_Olistsum,type,
c_List_Olistsum: $i > $i > $i ).
thf(tp_c_List_Oreplicate,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(tp_c_Nat_Onat_Onat__case,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(tp_c_Nat_Onat_Onat__rec,type,
c_Nat_Onat_Onat__rec: $i > $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_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(tp_c_Nitpick_Onat__gcd,type,
c_Nitpick_Onat__gcd: $i > $i > $i ).
thf(tp_c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tp_c_Orderings_Oord__class_Omax,type,
c_Orderings_Oord__class_Omax: $i > $i > $i > $i ).
thf(tp_c_Orderings_Oord__class_Omin,type,
c_Orderings_Oord__class_Omin: $i > $i > $i > $i ).
thf(tp_c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(tp_c_String_Ochar_Ochar__size,type,
c_String_Ochar_Ochar__size: $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_Type_Oshift,type,
c_Type_Oshift: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xabs__typeE__1__1,type,
c_Type_Osko__Type__Xabs__typeE__1__1: $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xabs__typeE__1__2,type,
c_Type_Osko__Type__Xabs__typeE__1__2: $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xlist__app__typeD__1__1,type,
c_Type_Osko__Type__Xlist__app__typeD__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xlist__app__typeE__1__1,type,
c_Type_Osko__Type__Xlist__app__typeE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xtype__induct__1__1,type,
c_Type_Osko__Type__Xtype__induct__1__1: $i > $i ).
thf(tp_c_Type_Osko__Type__Xtyping__elims__2__1,type,
c_Type_Osko__Type__Xtyping__elims__2__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xtyping__elims__3__1,type,
c_Type_Osko__Type__Xtyping__elims__3__1: $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xtyping__elims__3__2,type,
c_Type_Osko__Type__Xtyping__elims__3__2: $i > $i > $i > $i ).
thf(tp_c_Type_Otype_OAtom,type,
c_Type_Otype_OAtom: $i > $i ).
thf(tp_c_Type_Otype_OFun,type,
c_Type_Otype_OFun: $i ).
thf(tp_c_Type_Otype_Otype__case,type,
c_Type_Otype_Otype__case: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Otype_Otype__rec,type,
c_Type_Otype_Otype__rec: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Otyping,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(tp_c_Type_Otypings,type,
c_Type_Otypings: $i > $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_nat_Onat__size,type,
c_nat_Onat__size: $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,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Osemigroup__add,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
thf(tp_class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_class_Power_Opower,type,
class_Power_Opower: $i > $o ).
thf(tp_class_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__mono,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(tp_class_Ring__and__Field_Omult__mono1,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
thf(tp_class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(tp_class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semiring,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(tp_class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(tp_class_Ring__and__Field_Opordered__ring,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(tp_class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(tp_class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__1,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
thf(tp_tc_String_Ochar,type,
tc_String_Ochar: $i ).
thf(tp_tc_Type_Otype,type,
tc_Type_Otype: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_T_H_H____,type,
v_T_H_H____: $i ).
thf(tp_v_T_H____,type,
v_T_H____: $i ).
thf(tp_v_T____,type,
v_T____: $i ).
thf(tp_v_Ts____,type,
v_Ts____: $i ).
thf(tp_v_a____,type,
v_a____: $i ).
thf(tp_v_as____,type,
v_as____: $i ).
thf(tp_v_e____,type,
v_e____: $i ).
thf(tp_v_i____,type,
v_i____: $i ).
thf(tp_v_n____,type,
v_n____: $i ).
thf(tp_v_sko__List__Xreplicate__Xinduct__1,type,
v_sko__List__Xreplicate__Xinduct__1: $i > $i ).
thf(tp_v_sko__List__Xupt__Xinduct__1,type,
v_sko__List__Xupt__Xinduct__1: $i > $i ).
thf(tp_v_sko__Nat__Xnat__Xinduct__1,type,
v_sko__Nat__Xnat__Xinduct__1: $i > $i ).
thf(tp_v_sko__Nat__Xnat__Xinducts__1,type,
v_sko__Nat__Xnat__Xinducts__1: $i > $i ).
thf(tp_v_u____,type,
v_u____: $i ).
thf(1,axiom,
! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(4,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(5,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(6,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(7,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(8,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(9,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(10,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(11,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(12,axiom,
class_Ring__and__Field_Omult__mono @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(13,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(14,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(15,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(16,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(17,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(18,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(19,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(20,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(21,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(22,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(23,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(24,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(25,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(26,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(27,axiom,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(28,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(29,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(30,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(31,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(32,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(33,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(34,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
thf(35,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(36,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(37,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(38,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(39,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(40,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(41,axiom,
! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(42,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_H_0) ).
thf(43,axiom,
! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(44,axiom,
! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type1 = V_type1_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
thf(45,axiom,
! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( c_Lambda_Olift @ V_t @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(46,axiom,
( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_T_0) ).
thf(47,axiom,
! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).
thf(48,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).
thf(49,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ v_n____ ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_varT_0) ).
thf(50,axiom,
! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e_H @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ( c_Type_Otyping @ V_e_H @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(51,axiom,
! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).
thf(52,axiom,
! [V_e: $i,V_i: $i,V_U: $i,T_a: $i,V_T: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ T_a )
= ( c_Type_Oshift @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ T_a ) @ ( c_Suc @ V_i ) @ V_U @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__commute_0) ).
thf(53,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(54,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(55,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(56,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(57,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argT_0) ).
thf(58,axiom,
c_InductTermi_OIT @ v_u____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(59,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_headT_0) ).
thf(60,axiom,
! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
thf(61,axiom,
! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ V_Ts @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
thf(62,axiom,
! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).
thf(63,axiom,
! [V_e: $i,V_i: $i,V_T: $i,T_a: $i,V_j: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ T_a ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).
thf(64,axiom,
! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T1 )
| ~ ( c_InductTermi_OIT @ V_u )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T1 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( c_InductTermi_OIT @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI1_0) ).
thf(65,axiom,
! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T2 )
| ~ ( c_InductTermi_OIT @ V_u )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T2 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( c_InductTermi_OIT @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI2_0) ).
thf(66,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(67,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(68,axiom,
! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ 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(69,axiom,
! [V_t: $i,V_i: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) )
| ~ ( c_InductTermi_OIT @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(70,axiom,
! [V_f: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_ONil @ T_b ) @ V_a @ T_b @ T_a )
= V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(71,axiom,
! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ V_f @ V_xs @ ( c_List_Ofoldr @ V_f @ V_ys @ V_a @ T_b @ T_a ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(72,axiom,
! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ V_a @ T_b @ T_a )
= ( hAPP @ ( hAPP @ V_f @ V_x ) @ ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(73,axiom,
! [V_nat: $i,V_type1_H: $i,V_type2_H: $i] :
( ( c_Type_Otype_OAtom @ V_nat )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I3_J_0) ).
thf(74,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit_1) ).
thf(75,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_xa ) @ V_xb ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xa ) @ V_xb ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit__asm_1) ).
thf(76,axiom,
! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I6_J_0) ).
thf(77,axiom,
! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type1 @ T_a ) ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type2 @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Orecs_I2_J_0) ).
thf(78,axiom,
! [V_P: $i,V_T1a: $i,V_x: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1a ) @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T1a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__induct_0) ).
thf(79,axiom,
! [V_P: $i,V_T1: $i,V_T2: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__induct_1) ).
thf(80,axiom,
! [V_type1_H: $i,V_type2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H )
!= ( c_Type_Otype_OAtom @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I4_J_0) ).
thf(81,axiom,
! [V_e: $i,V_t: $i,V_T: $i,V_u: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) @ V_T ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).
thf(82,axiom,
! [V_e: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) @ tc_Type_Otype ) @ V_t @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_1) ).
thf(83,axiom,
! [V_e: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ V_e @ V_t ) @ tc_Type_Otype ) @ V_t @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ V_e @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__typeE_0) ).
thf(84,axiom,
! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(85,axiom,
! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(86,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_Lambda_Obeta @ V_t @ V_t_H )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(87,axiom,
c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argsT_0) ).
thf(88,axiom,
! [T_a: $i,V_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
thf(89,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
thf(90,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum__foldr_0) ).
thf(91,axiom,
! [V_pwr: $i,V_x: $i,V_r1: $i,V_add: $i,V_mul: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_r1 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__0_0) ).
thf(92,axiom,
! [V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(93,axiom,
! [V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(94,axiom,
! [V_x: $i] :
( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(95,axiom,
! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_x = V_y )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(96,axiom,
! [V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__0L_0) ).
thf(97,axiom,
! [V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__0R_0) ).
thf(98,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(99,axiom,
! [V_c: $i] :
( ( c_Nat_Osize__class_Osize @ V_c @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_size__char_0) ).
thf(100,axiom,
! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
thf(101,axiom,
! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_infinite__descent0_1) ).
thf(102,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(103,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__0_0) ).
thf(104,axiom,
! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xupt__Xinduct__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upt_Oinduct_0) ).
thf(105,axiom,
( ( c_Orderings_Obot__class_Obot @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__nat__def_0) ).
thf(106,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(107,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(108,axiom,
! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Nat__Xnat__Xinduct__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinduct_0) ).
thf(109,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(110,axiom,
! [V_c: $i] :
( ( c_String_Ochar_Ochar__size @ V_c )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_char__size_0) ).
thf(111,axiom,
( ( c_nat_Onat__size @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osize_I1_J_0) ).
thf(112,axiom,
! [V_x: $i] :
( ( c_Nitpick_Onat__gcd @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__gcd_Osimps_0) ).
thf(113,axiom,
! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Nat__Xnat__Xinducts__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinducts_0) ).
thf(114,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_f1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osplit_0) ).
thf(115,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(116,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(117,axiom,
! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xreplicate__Xinduct__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate_Oinduct_0) ).
thf(118,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= 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(119,axiom,
! [V_x: $i,V_a: $i] :
( ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(120,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(121,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(122,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ( V_m = V_n )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
thf(123,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
thf(124,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
thf(125,axiom,
! [V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0L_0) ).
thf(126,axiom,
! [V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0R_0) ).
thf(127,axiom,
! [V_f1: $i,V_f2: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_f1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__case__0_0) ).
thf(128,axiom,
! [V_x: $i,V_f: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__case @ V_x @ V_f @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Onat__case__def_0) ).
thf(129,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(130,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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(131,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
thf(132,axiom,
! [V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
thf(133,axiom,
! [V_m: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
thf(134,axiom,
! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__induct_0) ).
thf(135,axiom,
! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(136,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(137,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(138,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(139,axiom,
! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ V_P @ V_n ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__least__nat__le_2) ).
thf(140,axiom,
! [V_f1: $i,V_f2: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__rec @ V_f1 @ V_f2 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_f1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__rec__0_0) ).
thf(141,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(142,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(143,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(144,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(145,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(146,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(147,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(148,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).
thf(149,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ V_k @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).
thf(150,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_c @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(151,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_c @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(152,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(153,axiom,
! [V_xs: $i,V_x: $i,V_ts: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_x @ V_ts @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ V_ts @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(154,axiom,
! [V_zs: $i,V_x: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_zs @ V_x @ T_a ) @ V_ys @ T_a )
= ( c_List_Oappend @ V_zs @ ( c_List_Oappend @ V_x @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(155,axiom,
! [V_xs: $i,V_xs1: $i,V_us: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_xs1 @ V_us @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_xs1 @ T_a ) @ V_us @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(156,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
thf(157,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_zs @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(158,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(159,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(160,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(161,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(162,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(163,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(164,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(165,axiom,
! [T_a: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(166,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
thf(167,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
thf(168,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
thf(169,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
thf(170,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
thf(171,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
thf(172,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
thf(173,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(174,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(175,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(176,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(177,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(178,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(179,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(180,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(181,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(182,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(183,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(184,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ V_n @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).
thf(185,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
thf(186,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ V_y @ V_x @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_z @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
thf(187,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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(188,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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(189,axiom,
! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(190,axiom,
! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs = V_ys ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(191,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(192,axiom,
! [V_n: $i,V_m: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ 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(193,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) @ ( c_List_Olistsum @ V_ys @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum__append_0) ).
thf(194,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_q @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_q @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(195,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(196,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(197,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(198,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(199,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(200,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) @ ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_x @ V_z @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
thf(201,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(202,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(203,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(204,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
thf(205,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ 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(206,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(207,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(208,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(209,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(210,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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 ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(211,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(212,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(213,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(214,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(215,axiom,
! [V_n: $i,V_x: $i,T_a: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(216,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_2) ).
thf(217,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).
thf(218,axiom,
! [V_k: $i,V_i: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_i @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).
thf(219,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).
thf(220,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(221,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ 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(222,axiom,
! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(223,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
thf(224,axiom,
! [V_P: $i,V_i: $i,V_n: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ V_P @ V_n ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__least__nat__le_1) ).
thf(225,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(226,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(227,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(228,axiom,
! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
thf(229,axiom,
! [V_m: $i,V_i: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_i @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ V_m @ V_n @ tc_nat ) @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff_0) ).
thf(230,axiom,
! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(231,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(232,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(233,axiom,
! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(234,axiom,
! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(235,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(236,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_d: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(237,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(238,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(239,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(240,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(241,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(242,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(243,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).
thf(244,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).
thf(245,axiom,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(246,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(247,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(248,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(249,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(250,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(251,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(252,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(253,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(254,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(255,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(256,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(257,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(258,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
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_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(259,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(260,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(261,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(262,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(263,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(264,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_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(265,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(266,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(267,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(268,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(269,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(270,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(271,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(272,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(273,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(274,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(275,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(276,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(277,axiom,
! [V_T: $i,V_e: $i,V_t: $i] :
( ( V_T
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).
thf(278,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_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(279,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(280,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(281,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(282,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(283,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(284,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(285,axiom,
! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ 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(286,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ 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__less__le__mono_0) ).
thf(287,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(288,axiom,
! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I5_J_0) ).
thf(289,axiom,
! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(290,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_b @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(291,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_n @ tc_nat )
= V_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(292,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ V_n @ tc_nat )
= V_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(293,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
thf(294,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
thf(295,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
thf(296,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
thf(297,axiom,
! [V_i: $i,V_x: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(298,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
thf(299,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(300,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(301,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(302,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(303,axiom,
! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(304,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_m @ T_a ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_m @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(305,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(306,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_y @ ( c_Orderings_Oord__class_Omax @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
thf(307,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
thf(308,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
thf(309,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).
thf(310,axiom,
! [V_m: $i] : ( c_lessequals @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_m @ tc_nat ) @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__cube_0) ).
thf(311,axiom,
! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_l @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).
thf(312,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(313,axiom,
! [V_t: $i,V_i: $i] :
( ( c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) )
| ~ ( c_InductTermi_OIT @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(314,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) ) @ V_z )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
thf(315,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(316,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(317,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(318,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(319,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(320,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(321,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(322,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(323,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(324,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(325,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(326,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(327,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(328,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(329,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).
thf(330,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).
thf(331,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).
thf(332,axiom,
! [V_k: $i,V_i: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_i @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).
thf(333,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
thf(334,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
thf(335,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(336,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(337,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(338,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m
= ( c_Suc @ V_n ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(339,axiom,
! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omin @ V_m @ V_n @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).
thf(340,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(341,axiom,
! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(342,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ V_i @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(343,axiom,
! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(344,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(345,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(346,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(347,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(348,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(349,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).
thf(350,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ 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(351,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(352,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ 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_add__less__mono1_0) ).
thf(353,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(354,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ 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(355,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ 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(356,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(357,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ 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(358,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ 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(359,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(360,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(361,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
thf(362,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ 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(363,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ 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(364,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ 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(365,axiom,
! [T_a: $i,V_x: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(366,axiom,
! [V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ tc_nat ) ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
thf(367,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ T_a ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ 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(368,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i] :
( ( V_ys
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(369,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_ys )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(370,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(371,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(372,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(373,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
thf(374,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
thf(375,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
thf(376,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
thf(377,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).
thf(378,axiom,
! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(379,axiom,
! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(380,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(381,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(382,axiom,
! [V_r: $i,V_i: $i,V_j: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) )
| ~ ( c_InductTermi_OIT @ V_r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(383,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(384,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ 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(385,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).
thf(386,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
thf(387,axiom,
! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(388,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
thf(389,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
thf(390,axiom,
! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
thf(391,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(392,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(393,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(394,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(395,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(396,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
thf(397,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
thf(398,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
thf(399,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
thf(400,axiom,
! [T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(401,axiom,
! [T_a: $i,V_x: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ V_x @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( c_Suc @ V_q ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
thf(402,axiom,
! [T_a: $i,V_x: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( c_Suc @ V_q ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
thf(403,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Oreplicate @ V_n @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(404,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
thf(405,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
thf(406,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(407,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(408,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(409,axiom,
! [V_n: $i,V_m: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_m @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__add_0) ).
thf(410,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(411,axiom,
! [V_n: $i,V_m: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Odrop @ V_m @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__drop_0) ).
thf(412,axiom,
! [V_j: $i,V_k: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ V_i )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
thf(413,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
thf(414,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
thf(415,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
thf(416,axiom,
! [V_pwr: $i,V_x: $i,V_n: $i,V_mul: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_Suc @ V_n ) )
= ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_n ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__Suc_0) ).
thf(417,axiom,
! [V_pwr: $i,V_x: $i,V_q: $i,V_mul: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_Suc @ V_q ) )
= ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I35_J_0) ).
thf(418,axiom,
! [V_mul: $i,V_pwr: $i,V_x: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) ) @ V_x )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_Suc @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I28_J_0) ).
thf(419,axiom,
! [V_mul: $i,V_x: $i,V_pwr: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_Suc @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I27_J_0) ).
thf(420,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) @ V_n )
= V_m )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).
thf(421,axiom,
! [V_n: $i,V_m: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
= V_m )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
thf(422,axiom,
! [V_i: $i,V_j: $i] :
( ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( V_j
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) ) @ V_i ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
thf(423,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
thf(424,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
thf(425,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
thf(426,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(427,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(428,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(429,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(430,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(431,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(432,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(433,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(434,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(435,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(436,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(437,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(438,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(439,axiom,
! [V_m: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ ( c_Suc @ V_j ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
thf(440,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(441,axiom,
! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(442,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(443,axiom,
! [V_n: $i,V_i: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= V_i )
| ~ ( c_lessequals @ V_i @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(444,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ 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(445,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ 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(446,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(447,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ 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(448,axiom,
! [V_m: $i] : ( c_lessequals @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_m @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__square_0) ).
thf(449,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
thf(450,axiom,
! [V_nat: $i] :
( ( c_nat_Onat__size @ ( c_Suc @ V_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_nat_Onat__size @ V_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osize_I2_J_0) ).
thf(451,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(452,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_x @ V_z @ T_a ) @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
thf(453,axiom,
! [V_i: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( c_List_Odrop @ V_i @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ V_k @ V_i @ tc_nat ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
thf(454,axiom,
! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(455,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) )
| ( V_a = V_b )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(456,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
thf(457,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(458,axiom,
! [V_s: $i,V_u: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) @ ( hAPP @ ( hAPP @ 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(459,axiom,
! [V_u: $i,V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) @ ( hAPP @ ( hAPP @ 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(460,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(461,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(462,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ 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(463,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ 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(464,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).
thf(465,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).
thf(466,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(467,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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(468,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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(469,axiom,
! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(470,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit_0) ).
thf(471,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osplit__asm_0) ).
thf(472,axiom,
! [V_add: $i,V_mul: $i,V_a: $i,V_m: $i,V_b: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_m ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I1_J_0) ).
thf(473,axiom,
! [V_add: $i,V_mul: $i,V_a: $i,V_m: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) ) @ V_m )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I2_J_0) ).
thf(474,axiom,
! [V_add: $i,V_m: $i,V_mul: $i,V_a: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_m ) @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I3_J_0) ).
thf(475,axiom,
! [V_add: $i,V_m: $i,V_mul: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_m ) @ V_m )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_r1 ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I4_J_0) ).
thf(476,axiom,
! [V_add: $i,V_r0: $i,V_a: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_r0 ) @ V_a )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I5_J_0) ).
thf(477,axiom,
! [V_add: $i,V_a: $i,V_r0: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r0 )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I6_J_0) ).
thf(478,axiom,
! [V_mul: $i,V_a: $i,V_b: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_a ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I7_J_0) ).
thf(479,axiom,
! [V_mul: $i,V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_c ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I8_J_0) ).
thf(480,axiom,
! [V_mul: $i,V_r0: $i,V_a: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r0 ) @ V_a )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I9_J_0) ).
thf(481,axiom,
! [V_mul: $i,V_a: $i,V_r0: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_r0 )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I10_J_0) ).
thf(482,axiom,
! [V_mul: $i,V_r1: $i,V_a: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r1 ) @ V_a )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I11_J_0) ).
thf(483,axiom,
! [V_mul: $i,V_a: $i,V_r1: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_r1 )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I12_J_0) ).
thf(484,axiom,
! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I13_J_0) ).
thf(485,axiom,
! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I14_J_0) ).
thf(486,axiom,
! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I15_J_0) ).
thf(487,axiom,
! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ V_ly ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I16_J_0) ).
thf(488,axiom,
! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ V_rx ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I17_J_0) ).
thf(489,axiom,
! [V_mul: $i,V_lx: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ V_ry ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I18_J_0) ).
thf(490,axiom,
! [V_mul: $i,V_lx: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I19_J_0) ).
thf(491,axiom,
! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ V_add @ V_b ) @ V_d ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I20_J_0) ).
thf(492,axiom,
! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_b ) @ V_c ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I21_J_0) ).
thf(493,axiom,
! [V_add: $i,V_a: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ V_c ) @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_d ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I22_J_0) ).
thf(494,axiom,
! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ V_b ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I23_J_0) ).
thf(495,axiom,
! [V_add: $i,V_a: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_a ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I24_J_0) ).
thf(496,axiom,
! [V_add: $i,V_a: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ V_d ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I25_J_0) ).
thf(497,axiom,
! [V_add: $i,V_r0: $i,V_x: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_r0 ) @ V_x )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__0_0) ).
thf(498,axiom,
! [V_add: $i,V_x: $i,V_y: $i,V_z: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_x ) @ ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_x ) @ V_y ) ) @ V_z ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__a_0) ).
thf(499,axiom,
! [V_add: $i,V_x: $i,V_y: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_x ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__c_0) ).
thf(500,axiom,
! [V_mul: $i,V_r0: $i,V_x: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r0 ) @ V_x )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__0_0) ).
thf(501,axiom,
! [V_mul: $i,V_r1: $i,V_x: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r1 ) @ V_x )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__1_0) ).
thf(502,axiom,
! [V_mul: $i,V_x: $i,V_y: $i,V_z: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_mul @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ V_z ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__a_0) ).
thf(503,axiom,
! [V_mul: $i,V_x: $i,V_y: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ V_mul @ V_y ) @ V_x ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__c_0) ).
thf(504,axiom,
! [V_mul: $i,V_x: $i,V_add: $i,V_y: $i,V_z: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_z ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__d_0) ).
thf(505,axiom,
! [V_pwr: $i,V_mul: $i,V_x: $i,V_y: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ V_q )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) ) @ ( hAPP @ ( hAPP @ V_pwr @ V_y ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__mul_0) ).
thf(506,axiom,
! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(507,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(508,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
thf(509,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) ) @ V_z )
= ( c_Orderings_Oord__class_Omin @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).
thf(510,axiom,
! [V_x: $i,V_xs1: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs1 @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs1 @ T_a ) @ V_zs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(511,axiom,
! [V_x: $i,V_xa: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(512,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(513,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(514,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(515,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(516,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(517,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(518,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(519,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(520,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(521,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(522,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).
thf(523,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
thf(524,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(525,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
thf(526,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
thf(527,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
thf(528,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
thf(529,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
thf(530,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
thf(531,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
thf(532,axiom,
! [V_a: $i,V_c: $i,V_b: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_c @ V_a @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
thf(533,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(534,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(535,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(536,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(537,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).
thf(538,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
thf(539,axiom,
! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
thf(540,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
thf(541,axiom,
! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(542,axiom,
! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(543,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(544,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(545,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(546,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(547,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(548,axiom,
! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(549,axiom,
! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ 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(550,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ 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(551,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ 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(552,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ 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(553,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
thf(554,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(555,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(556,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(557,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(558,axiom,
! [V_n: $i,V_x: $i,T_a: $i,V_k: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(559,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(560,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(561,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(562,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(563,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(564,axiom,
! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(565,axiom,
! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(566,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(567,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(568,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(569,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(570,axiom,
! [T_a: $i,V_x: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_Osimps_I2_J_0) ).
thf(571,axiom,
! [V_n: $i,V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) ) @ V_m )
= ( c_Orderings_Oord__class_Omax @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__minus__add__max_0) ).
thf(572,axiom,
! [V_m: $i,V_x: $i] : ( c_lessequals @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
thf(573,axiom,
! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).
thf(574,axiom,
! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).
thf(575,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ 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(576,axiom,
! [V_s: $i,V_t: $i] : ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ 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(577,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
thf(578,axiom,
! [V_i: $i,V_k: $i] :
( ~ ( c_lessequals @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_i ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_i ) @ V_i @ tc_nat )
= V_k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).
thf(579,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(580,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(581,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(582,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(583,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(584,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(585,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(586,axiom,
! [T_a: $i,V_x: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(587,axiom,
! [V_r: $i,V_ss: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(588,axiom,
! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Orecs_I1_J_0) ).
thf(589,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(590,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(591,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
thf(592,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(593,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(594,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(595,axiom,
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
thf(596,axiom,
! [V_j: $i,V_i: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_k @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ V_i ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).
thf(597,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).
thf(598,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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 ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
thf(599,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(600,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(601,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(602,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(603,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(604,axiom,
! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(605,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(606,axiom,
! [V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) ) )
| ( V_y = V_z )
| ( V_w = V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
thf(607,axiom,
! [V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ tc_nat ) ) )
| ( V_c = V_d )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
thf(608,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) ) )
| ( V_c = V_d )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(609,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ 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(610,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
thf(611,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(612,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(613,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).
thf(614,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_1) ).
thf(615,axiom,
! [V_m: $i,V_j: $i,V_i: $i,V_u: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_0) ).
thf(616,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_1) ).
thf(617,axiom,
! [V_i: $i,V_j: $i,V_u: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_0) ).
thf(618,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ 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(619,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(620,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(621,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(622,axiom,
! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_Suc @ V_nat ) @ T_a )
= ( hAPP @ V_f2 @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__case__Suc_0) ).
thf(623,axiom,
! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(624,axiom,
! [V_f: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(625,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_InductTermi_OIT @ V_s )
| ~ ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(626,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
thf(627,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
thf(628,axiom,
! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
thf(629,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(630,axiom,
! [V_j: $i,V_k: $i,V_i: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat )
| ~ ( c_lessequals @ V_j @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
thf(631,axiom,
! [V_j: $i,V_i: $i,V_k: $i] :
( ( c_lessequals @ V_j @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
thf(632,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
thf(633,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
thf(634,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
thf(635,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
thf(636,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
thf(637,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
thf(638,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
thf(639,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
thf(640,axiom,
! [T_a: $i,V_x: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x @ V_zs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(641,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
thf(642,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
thf(643,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).
thf(644,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).
thf(645,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_Suc @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f2 @ V_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osplit_1) ).
thf(646,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_Suc @ V_xa ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f2 @ V_xa ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osplit__asm_1) ).
thf(647,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(648,axiom,
! [V_x: $i,V_xa: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(649,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
thf(650,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
thf(651,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(652,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( 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(653,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
thf(654,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
thf(655,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(656,axiom,
! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(657,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_e @ T_a ) ) @ V_c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(658,axiom,
! [V_i: $i,V_u: $i,V_j: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_k ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_u @ tc_nat ) ) @ V_k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
thf(659,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
thf(660,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).
thf(661,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
thf(662,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
thf(663,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
thf(664,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
thf(665,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
thf(666,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
thf(667,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(668,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(669,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ 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(670,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) @ 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(671,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
thf(672,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
thf(673,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
thf(674,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
thf(675,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
thf(676,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
thf(677,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
thf(678,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_1) ).
thf(679,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_0) ).
thf(680,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).
thf(681,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).
thf(682,axiom,
! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
thf(683,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ V_m ) ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_Suc @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(684,axiom,
! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(685,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
thf(686,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
thf(687,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( 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(688,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( 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(689,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
thf(690,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
thf(691,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(692,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(693,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(694,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(695,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(696,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_n @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(697,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(698,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(699,axiom,
! [V_m: $i,V_l: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_l @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(700,axiom,
! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(701,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(702,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(703,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_y @ ( c_Orderings_Oord__class_Omin @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
thf(704,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
thf(705,axiom,
! [V_P: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__induct_2) ).
thf(706,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(707,axiom,
! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ V_P ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_infinite__descent0_0) ).
thf(708,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(709,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(710,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(711,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(712,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(713,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(714,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(715,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(716,axiom,
! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
thf(717,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_z @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
thf(718,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
thf(719,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
thf(720,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
thf(721,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
thf(722,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_lessequals @ V_x @ V_z @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
thf(723,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).
thf(724,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).
thf(725,axiom,
! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_lessequals @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
thf(726,axiom,
! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_lessequals @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
thf(727,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(728,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ V_n ) @ V_x @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
thf(729,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Cons_H_0) ).
thf(730,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).
thf(731,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).
thf(732,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__add_0) ).
thf(733,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(734,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(735,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(736,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(737,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(738,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(739,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(740,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(741,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(742,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
thf(743,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(744,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(745,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(746,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(747,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( 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(748,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( 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(749,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_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(750,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(751,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ 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_0) ).
thf(752,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_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(753,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(754,axiom,
! [V_i: $i,V_j: $i,V_u: $i,V_n: $i] :
( ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_1) ).
thf(755,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
thf(756,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( V_m
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_0) ).
thf(757,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m )
= V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_0) ).
thf(758,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).
thf(759,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(760,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) @ V_d @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(761,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(762,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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_less__add__iff2_1) ).
thf(763,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(764,axiom,
! [T_a: $i,V_xs: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ V_a @ T_a @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).
thf(765,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(766,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(767,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(768,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(769,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
thf(770,axiom,
! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
thf(771,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).
thf(772,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).
thf(773,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
thf(774,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
thf(775,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
thf(776,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
thf(777,axiom,
! [V_n: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(778,axiom,
! [V_j: $i,V_i: $i,V_u: $i,V_m: $i] :
( ~ ( c_lessequals @ V_j @ V_i @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_1) ).
thf(779,axiom,
! [V_mul: $i,V_pwr: $i,V_x: $i,V_p: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_p ) ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_p ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__pwr_0) ).
thf(780,axiom,
! [V_P: $i,V_n: $i] :
( ( c_lessequals @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ V_P @ V_n ) @ V_n @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__least__nat__le_0) ).
thf(781,axiom,
! [V_n: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
thf(782,axiom,
! [T_a: $i,V_x: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_p @ T_a ) @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_p ) @ V_q ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).
thf(783,axiom,
! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ V_y @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
thf(784,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_a @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(785,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
thf(786,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
thf(787,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
thf(788,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
thf(789,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(790,axiom,
! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__induct_1) ).
thf(791,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(792,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y @ V_zs @ T_a @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(793,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
thf(794,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
thf(795,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(796,axiom,
! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_l )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ~ ( 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(797,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(798,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(799,axiom,
! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(800,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
thf(801,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
thf(802,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_e: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) @ V_d @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
thf(803,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) @ V_d @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
thf(804,axiom,
! [T_a: $i,V_c: $i,V_b: $i,V_a: $i,V_e: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ V_c @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
thf(805,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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_le__add__iff2_1) ).
thf(806,axiom,
! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ 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(807,axiom,
! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ 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(808,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(809,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ 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(810,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ 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(811,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(812,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(813,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(814,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(815,axiom,
! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate_Oinduct_1) ).
thf(816,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Type_Otype_OAtom @ V_nat )
!= ( c_Type_Otype_OAtom @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I1_J_0) ).
thf(817,axiom,
! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_upt_Oinduct_1) ).
thf(818,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(819,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(820,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
thf(821,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ V_y @ V_x @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_z @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
thf(822,axiom,
! [V_pwr: $i,V_x: $i,V_p: $i,V_q: $i,V_add: $i,V_mul: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_p ) ) @ V_q )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__pwr_0) ).
thf(823,axiom,
! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__rec @ V_f1 @ V_f2 @ ( c_Suc @ V_nat ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_nat ) @ ( c_Nat_Onat_Onat__rec @ V_f1 @ V_f2 @ V_nat @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__rec__Suc_0) ).
thf(824,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(825,axiom,
! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(826,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(827,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(828,axiom,
! [V_x: $i,T_a: $i] :
( V_x
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(829,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(830,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
thf(831,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
thf(832,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
thf(833,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
thf(834,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
thf(835,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_lessequals @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).
thf(836,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat )
| ~ ( c_lessequals @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
thf(837,axiom,
! [V_m: $i,V_x: $i] : ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_x ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(838,axiom,
! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_i ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(839,axiom,
! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_m ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(840,axiom,
! [V_P: $i,V_n: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ V_P ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_infinite__descent0_2) ).
thf(841,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(842,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(843,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(844,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(845,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
thf(846,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
thf(847,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
thf(848,axiom,
! [V_e: $i,V_u: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_u @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
thf(849,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(850,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(851,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(852,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(853,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(854,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(855,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
thf(856,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(857,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum_0) ).
thf(858,axiom,
! [V_x: $i] :
( ~ ( c_lessequals @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(859,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(860,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(861,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(862,axiom,
! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_l @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
thf(863,axiom,
! [T_a: $i,V_x: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_Suc @ V_q ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
thf(864,axiom,
! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).
thf(865,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc_0) ).
thf(866,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
thf(867,axiom,
! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinducts_1) ).
thf(868,axiom,
! [T_a: $i,V_x: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ V_x @ V_p @ T_a ) @ V_q @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ tc_nat ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
thf(869,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).
thf(870,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).
thf(871,axiom,
! [V_P: $i,V_b: $i,V_d: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_b ) @ V_d ) @ V_b @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_d ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).
thf(872,axiom,
! [V_P: $i,V_b: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_b ) @ V_x ) @ V_b @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).
thf(873,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) ) @ V_b )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(874,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq1_0) ).
thf(875,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat ) )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq2_0) ).
thf(876,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(877,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
thf(878,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(879,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(880,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(881,axiom,
! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omax @ V_m @ V_n @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__Suc__Suc_0) ).
thf(882,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(883,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(884,axiom,
! [V_x: $i,V_c: $i,V_d: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).
thf(885,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).
thf(886,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
thf(887,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(888,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
thf(889,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
thf(890,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(891,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lem0_0) ).
thf(892,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(893,axiom,
! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(894,axiom,
! [V_j: $i,V_k: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ V_m @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_j ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
thf(895,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_xs @ T_a )
!= ( c_List_Oappend @ V_zs @ V_xs @ T_a ) )
| ( V_ys = V_zs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(896,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Oappend @ V_xs @ V_zs @ T_a ) )
| ( V_ys = V_zs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(897,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
thf(898,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_z @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).
thf(899,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
thf(900,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
thf(901,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(902,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(903,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).
thf(904,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).
thf(905,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).
thf(906,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
thf(907,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
thf(908,axiom,
! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinduct_1) ).
thf(909,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
thf(910,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(911,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_Suc @ V_n ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(912,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ V_m ) ) @ V_n )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(913,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(914,axiom,
! [V_i: $i,V_j: $i,V_u: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_0) ).
thf(915,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).
thf(916,axiom,
! [V_m: $i,V_j: $i,V_i: $i,V_u: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_0) ).
thf(917,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_1) ).
thf(918,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) )
| ( V_c
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) ) @ V_d ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(919,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c )
= V_d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(920,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(921,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[920]) ).
thf(922,negated_conjecture,
~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_T_H_H____ @ tc_Type_Otype ) @ ( c_Lambda_Olift @ v_u____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(923,plain,
$false = $false,
inference(unfold_def,[status(thm)],[921]) ).
thf(924,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(925,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(926,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(927,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(928,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(929,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(930,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(931,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(932,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(933,plain,
( ( class_Ring__and__Field_Osemiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(934,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(935,plain,
( ( class_Ring__and__Field_Omult__mono @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(936,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(937,plain,
( ( class_Ring__and__Field_Omult__mono1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(938,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(939,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(940,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(941,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(942,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(943,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(944,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(945,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(946,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(947,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(948,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(949,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(950,plain,
( ( class_Ring__and__Field_Oordered__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(951,plain,
( ( class_Ring__and__Field_Opordered__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(952,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(953,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(954,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(955,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(956,plain,
( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(957,plain,
( ( class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(958,plain,
( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(959,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(960,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(961,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(962,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(963,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(964,plain,
( ( ! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(965,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(966,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(967,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type1 = V_type1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(968,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( c_Lambda_Olift @ V_t @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(969,plain,
( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(970,plain,
( ( ! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(971,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(972,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ v_n____ ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(973,plain,
( ( ! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e_H @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ( c_Type_Otyping @ V_e_H @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(974,plain,
( ( ! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(975,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,T_a: $i,V_T: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ T_a )
= ( c_Type_Oshift @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ T_a ) @ ( c_Suc @ V_i ) @ V_U @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(976,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)],[53]) ).
thf(977,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(978,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(979,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(980,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____ )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(981,plain,
( ( c_InductTermi_OIT @ v_u____ )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(982,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(983,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(984,plain,
( ( ! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ V_Ts @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(985,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(986,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i,T_a: $i,V_j: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ T_a ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(987,plain,
( ( ! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T1 )
| ~ ( c_InductTermi_OIT @ V_u )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T1 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(988,plain,
( ( ! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T2 )
| ~ ( c_InductTermi_OIT @ V_u )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T2 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(989,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)],[66]) ).
thf(990,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)],[67]) ).
thf(991,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(992,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(993,plain,
( ( ! [V_f: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_ONil @ T_b ) @ V_a @ T_b @ T_a )
= V_a ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(994,plain,
( ( ! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ V_f @ V_xs @ ( c_List_Ofoldr @ V_f @ V_ys @ V_a @ T_b @ T_a ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(995,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ V_a @ T_b @ T_a )
= ( hAPP @ ( hAPP @ V_f @ V_x ) @ ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(996,plain,
( ( ! [V_nat: $i,V_type1_H: $i,V_type2_H: $i] :
( ( c_Type_Otype_OAtom @ V_nat )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(997,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(998,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_xa ) @ V_xb ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xa ) @ V_xb ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(999,plain,
( ( ! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(1000,plain,
( ( ! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type1 @ T_a ) ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type2 @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(1001,plain,
( ( ! [V_P: $i,V_T1a: $i,V_x: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1a ) @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T1a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(1002,plain,
( ( ! [V_P: $i,V_T1: $i,V_T2: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(1003,plain,
( ( ! [V_type1_H: $i,V_type2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H )
!= ( c_Type_Otype_OAtom @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(1004,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_u: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) @ V_T ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(1005,plain,
( ( ! [V_e: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) @ tc_Type_Otype ) @ V_t @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(1006,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ V_e @ V_t ) @ tc_Type_Otype ) @ V_t @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ V_e @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(1007,plain,
( ( ! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(1008,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(1009,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_Lambda_Obeta @ V_t @ V_t_H )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(1010,plain,
( ( c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____ )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(1011,plain,
( ( ! [T_a: $i,V_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(1012,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(1013,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(1014,plain,
( ( ! [V_pwr: $i,V_x: $i,V_r1: $i,V_add: $i,V_mul: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_r1 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(1015,plain,
( ( ! [V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_m ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(1016,plain,
( ( ! [V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(1017,plain,
( ( ! [V_x: $i] :
( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(1018,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_x = V_y )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(1019,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(1020,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(1021,plain,
( ( ! [V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(1022,plain,
( ( ! [V_c: $i] :
( ( c_Nat_Osize__class_Osize @ V_c @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(1023,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(1024,plain,
( ( ! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(1025,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)],[102]) ).
thf(1026,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(1027,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xupt__Xinduct__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(1028,plain,
( ( ( c_Orderings_Obot__class_Obot @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(1029,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)],[106]) ).
thf(1030,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)],[107]) ).
thf(1031,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Nat__Xnat__Xinduct__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(1032,plain,
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(1033,plain,
( ( ! [V_c: $i] :
( ( c_String_Ochar_Ochar__size @ V_c )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(1034,plain,
( ( ( c_nat_Onat__size @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(1035,plain,
( ( ! [V_x: $i] :
( ( c_Nitpick_Onat__gcd @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(1036,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Nat__Xnat__Xinducts__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(1037,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_f1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(1038,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(1039,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(1040,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xreplicate__Xinduct__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(1041,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= V_m )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(1042,plain,
( ( ! [V_x: $i,V_a: $i] :
( ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(1043,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)],[120]) ).
thf(1044,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)],[121]) ).
thf(1045,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ( V_m = V_n )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(1046,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(1047,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(1048,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(1049,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(1050,plain,
( ( ! [V_f1: $i,V_f2: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_f1 ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(1051,plain,
( ( ! [V_x: $i,V_f: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__case @ V_x @ V_f @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(1052,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(1053,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(1054,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(1055,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(1056,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(1057,plain,
( ( ! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(1058,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(1059,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)],[136]) ).
thf(1060,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(1061,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(1062,plain,
( ( ! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ V_P @ V_n ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(1063,plain,
( ( ! [V_f1: $i,V_f2: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__rec @ V_f1 @ V_f2 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_f1 ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(1064,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)],[141]) ).
thf(1065,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)],[142]) ).
thf(1066,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(1067,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(1068,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)],[145]) ).
thf(1069,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(1070,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(1071,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(1072,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ V_k @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(1073,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_c @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(1074,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_c @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(1075,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)],[152]) ).
thf(1076,plain,
( ( ! [V_xs: $i,V_x: $i,V_ts: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_x @ V_ts @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ V_ts @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(1077,plain,
( ( ! [V_zs: $i,V_x: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_zs @ V_x @ T_a ) @ V_ys @ T_a )
= ( c_List_Oappend @ V_zs @ ( c_List_Oappend @ V_x @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(1078,plain,
( ( ! [V_xs: $i,V_xs1: $i,V_us: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_xs1 @ V_us @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_xs1 @ T_a ) @ V_us @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(1079,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(1080,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_zs @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(1081,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)],[158]) ).
thf(1082,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)],[159]) ).
thf(1083,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)],[160]) ).
thf(1084,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)],[161]) ).
thf(1085,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)],[162]) ).
thf(1086,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(1087,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(1088,plain,
( ( ! [T_a: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(1089,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(1090,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(1091,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(1092,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(1093,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(1094,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(1095,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(1096,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(1097,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(1098,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(1099,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(1100,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(1101,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(1102,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(1103,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(1104,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(1105,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(1106,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(1107,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(1108,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(1109,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ V_y @ V_x @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(1110,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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)],[187]) ).
thf(1111,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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)],[188]) ).
thf(1112,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(1113,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(1114,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)],[191]) ).
thf(1115,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
= V_m )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(1116,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) @ ( c_List_Olistsum @ V_ys @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(1117,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_q @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_q @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(1118,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(1119,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)],[196]) ).
thf(1120,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)],[197]) ).
thf(1121,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(1122,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(1123,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) @ ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_x @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(1124,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)],[201]) ).
thf(1125,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(1126,plain,
( ( ! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(1127,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(1128,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ 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)],[205]) ).
thf(1129,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)],[206]) ).
thf(1130,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)],[207]) ).
thf(1131,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)],[208]) ).
thf(1132,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)],[209]) ).
thf(1133,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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 ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(1134,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)],[211]) ).
thf(1135,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)],[212]) ).
thf(1136,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)],[213]) ).
thf(1137,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)],[214]) ).
thf(1138,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(1139,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(1140,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(1141,plain,
( ( ! [V_k: $i,V_i: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_i @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(1142,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(1143,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)],[220]) ).
thf(1144,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(1145,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(1146,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(1147,plain,
( ( ! [V_P: $i,V_i: $i,V_n: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ V_P @ V_n ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(1148,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)],[225]) ).
thf(1149,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)],[226]) ).
thf(1150,plain,
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(1151,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(1152,plain,
( ( ! [V_m: $i,V_i: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_i @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ V_m @ V_n @ tc_nat ) @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(1153,plain,
( ( ! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(1154,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(1155,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(1156,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(1157,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(1158,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)],[235]) ).
thf(1159,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_d: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(1160,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(1161,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(1162,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(1163,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(1164,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)],[241]) ).
thf(1165,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)],[242]) ).
thf(1166,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(1167,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(1168,plain,
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(1169,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(1170,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(1171,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(1172,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(1173,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(1174,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(1175,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(1176,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(1177,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)],[254]) ).
thf(1178,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)],[255]) ).
thf(1179,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)],[256]) ).
thf(1180,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(1181,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
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(1182,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)],[259]) ).
thf(1183,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)],[260]) ).
thf(1184,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)],[261]) ).
thf(1185,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)],[262]) ).
thf(1186,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)],[263]) ).
thf(1187,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(1188,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)],[265]) ).
thf(1189,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)],[266]) ).
thf(1190,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)],[267]) ).
thf(1191,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)],[268]) ).
thf(1192,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)],[269]) ).
thf(1193,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)],[270]) ).
thf(1194,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)],[271]) ).
thf(1195,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)],[272]) ).
thf(1196,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)],[273]) ).
thf(1197,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)],[274]) ).
thf(1198,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(1199,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(1200,plain,
( ( ! [V_T: $i,V_e: $i,V_t: $i] :
( ( V_T
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(1201,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_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)],[278]) ).
thf(1202,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(1203,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(1204,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(1205,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)],[282]) ).
thf(1206,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)],[283]) ).
thf(1207,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)],[284]) ).
thf(1208,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(1209,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(1210,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(1211,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(1212,plain,
( ( ! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(1213,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_b @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(1214,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_n @ tc_nat )
= V_m ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(1215,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ V_n @ tc_nat )
= V_m ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(1216,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(1217,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(1218,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(1219,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(1220,plain,
( ( ! [V_i: $i,V_x: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(1221,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(1222,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)],[299]) ).
thf(1223,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(1224,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(1225,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(1226,plain,
( ( ! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(1227,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_m @ T_a ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_m @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(1228,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(1229,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_y @ ( c_Orderings_Oord__class_Omax @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(1230,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(1231,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(1232,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(1233,plain,
( ( ! [V_m: $i] : ( c_lessequals @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_m @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(1234,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_l @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(1235,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(1236,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(1237,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) ) @ V_z )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(1238,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(1239,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)],[316]) ).
thf(1240,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)],[317]) ).
thf(1241,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)],[318]) ).
thf(1242,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)],[319]) ).
thf(1243,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)],[320]) ).
thf(1244,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)],[321]) ).
thf(1245,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)],[322]) ).
thf(1246,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)],[323]) ).
thf(1247,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)],[324]) ).
thf(1248,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(1249,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)],[326]) ).
thf(1250,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)],[327]) ).
thf(1251,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)],[328]) ).
thf(1252,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(1253,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(1254,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(1255,plain,
( ( ! [V_k: $i,V_i: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_i @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(1256,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(1257,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(1258,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)],[335]) ).
thf(1259,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)],[336]) ).
thf(1260,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)],[337]) ).
thf(1261,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m
= ( c_Suc @ V_n ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(1262,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omin @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(1263,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(1264,plain,
( ( ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(1265,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ V_i @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(1266,plain,
( ( ! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(1267,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(1268,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(1269,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(1270,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(1271,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(1272,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(1273,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(1274,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(1275,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(1276,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(1277,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(1278,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(1279,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(1280,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(1281,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(1282,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(1283,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(1284,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(1285,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ 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)],[362]) ).
thf(1286,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(1287,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(1288,plain,
( ( ! [T_a: $i,V_x: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(1289,plain,
( ( ! [V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ tc_nat ) ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(1290,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ T_a ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ T_a ) ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(1291,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
( ( V_ys
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(1292,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_ys )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(1293,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(1294,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(1295,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(1296,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(1297,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(1298,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(1299,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(1300,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(1301,plain,
( ( ! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_i @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(1302,plain,
( ( ! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_i @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(1303,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(1304,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(1305,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(1306,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)],[383]) ).
thf(1307,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ 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)],[384]) ).
thf(1308,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(1309,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(1310,plain,
( ( ! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(1311,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(1312,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(1313,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(1314,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(1315,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(1316,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)],[393]) ).
thf(1317,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)],[394]) ).
thf(1318,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)],[395]) ).
thf(1319,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(1320,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(1321,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(1322,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(1323,plain,
( ( ! [T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(1324,plain,
( ( ! [T_a: $i,V_x: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ V_x @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( c_Suc @ V_q ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(1325,plain,
( ( ! [T_a: $i,V_x: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( c_Suc @ V_q ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(1326,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Oreplicate @ V_n @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(1327,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(1328,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(1329,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)],[406]) ).
thf(1330,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)],[407]) ).
thf(1331,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)],[408]) ).
thf(1332,plain,
( ( ! [V_n: $i,V_m: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_m @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(1333,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(1334,plain,
( ( ! [V_n: $i,V_m: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Odrop @ V_m @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(1335,plain,
( ( ! [V_j: $i,V_k: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ V_i )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(1336,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(1337,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(1338,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(1339,plain,
( ( ! [V_pwr: $i,V_x: $i,V_n: $i,V_mul: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_Suc @ V_n ) )
= ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_n ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(1340,plain,
( ( ! [V_pwr: $i,V_x: $i,V_q: $i,V_mul: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_Suc @ V_q ) )
= ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(1341,plain,
( ( ! [V_mul: $i,V_pwr: $i,V_x: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) ) @ V_x )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_Suc @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(1342,plain,
( ( ! [V_mul: $i,V_x: $i,V_pwr: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_Suc @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(1343,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) @ V_n )
= V_m )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(1344,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
= V_m )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(1345,plain,
( ( ! [V_i: $i,V_j: $i] :
( ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( V_j
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) ) @ V_i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(1346,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(1347,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(1348,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(1349,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(1350,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(1351,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(1352,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(1353,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(1354,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(1355,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)],[432]) ).
thf(1356,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(1357,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(1358,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)],[435]) ).
thf(1359,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)],[436]) ).
thf(1360,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)],[437]) ).
thf(1361,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)],[438]) ).
thf(1362,plain,
( ( ! [V_m: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ ( c_Suc @ V_j ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(1363,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) @ V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1364,plain,
( ( ! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(1365,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)],[442]) ).
thf(1366,plain,
( ( ! [V_n: $i,V_i: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= V_i )
| ~ ( c_lessequals @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(1367,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)],[444]) ).
thf(1368,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)],[445]) ).
thf(1369,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)],[446]) ).
thf(1370,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)],[447]) ).
thf(1371,plain,
( ( ! [V_m: $i] : ( c_lessequals @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_m @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1372,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1373,plain,
( ( ! [V_nat: $i] :
( ( c_nat_Onat__size @ ( c_Suc @ V_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_nat_Onat__size @ V_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1374,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(1375,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_x @ V_z @ T_a ) @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(1376,plain,
( ( ! [V_i: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( c_List_Odrop @ V_i @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ V_k @ V_i @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(1377,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(1378,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) )
| ( V_a = V_b )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(1379,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(1380,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)],[457]) ).
thf(1381,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(1382,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(1383,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(1384,plain,
( ( ! [V_r: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(1385,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(1386,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(1387,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(1388,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(1389,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)],[466]) ).
thf(1390,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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)],[467]) ).
thf(1391,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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)],[468]) ).
thf(1392,plain,
( ( ! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(1393,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(1394,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xc ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(1395,plain,
( ( ! [V_add: $i,V_mul: $i,V_a: $i,V_m: $i,V_b: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_m ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(1396,plain,
( ( ! [V_add: $i,V_mul: $i,V_a: $i,V_m: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) ) @ V_m )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(1397,plain,
( ( ! [V_add: $i,V_m: $i,V_mul: $i,V_a: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_m ) @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(1398,plain,
( ( ! [V_add: $i,V_m: $i,V_mul: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_m ) @ V_m )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_r1 ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(1399,plain,
( ( ! [V_add: $i,V_r0: $i,V_a: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_r0 ) @ V_a )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(1400,plain,
( ( ! [V_add: $i,V_a: $i,V_r0: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r0 )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(1401,plain,
( ( ! [V_mul: $i,V_a: $i,V_b: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_a ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(1402,plain,
( ( ! [V_mul: $i,V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_c ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(1403,plain,
( ( ! [V_mul: $i,V_r0: $i,V_a: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r0 ) @ V_a )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(1404,plain,
( ( ! [V_mul: $i,V_a: $i,V_r0: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_r0 )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(1405,plain,
( ( ! [V_mul: $i,V_r1: $i,V_a: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r1 ) @ V_a )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(1406,plain,
( ( ! [V_mul: $i,V_a: $i,V_r1: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_r1 )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(1407,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(1408,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(1409,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(1410,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ V_ly ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(1411,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ V_rx ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(1412,plain,
( ( ! [V_mul: $i,V_lx: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ V_ry ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(1413,plain,
( ( ! [V_mul: $i,V_lx: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(1414,plain,
( ( ! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ V_add @ V_b ) @ V_d ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(1415,plain,
( ( ! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_b ) @ V_c ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(1416,plain,
( ( ! [V_add: $i,V_a: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ V_c ) @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_d ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(1417,plain,
( ( ! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ V_b ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(1418,plain,
( ( ! [V_add: $i,V_a: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_a ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(1419,plain,
( ( ! [V_add: $i,V_a: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ V_d ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(1420,plain,
( ( ! [V_add: $i,V_r0: $i,V_x: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_r0 ) @ V_x )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(1421,plain,
( ( ! [V_add: $i,V_x: $i,V_y: $i,V_z: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_x ) @ ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_x ) @ V_y ) ) @ V_z ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(1422,plain,
( ( ! [V_add: $i,V_x: $i,V_y: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_x ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(1423,plain,
( ( ! [V_mul: $i,V_r0: $i,V_x: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r0 ) @ V_x )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(1424,plain,
( ( ! [V_mul: $i,V_r1: $i,V_x: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r1 ) @ V_x )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(1425,plain,
( ( ! [V_mul: $i,V_x: $i,V_y: $i,V_z: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_mul @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ V_z ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(1426,plain,
( ( ! [V_mul: $i,V_x: $i,V_y: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ V_mul @ V_y ) @ V_x ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(1427,plain,
( ( ! [V_mul: $i,V_x: $i,V_add: $i,V_y: $i,V_z: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_z ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(1428,plain,
( ( ! [V_pwr: $i,V_mul: $i,V_x: $i,V_y: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ V_q )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) ) @ ( hAPP @ ( hAPP @ V_pwr @ V_y ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(1429,plain,
( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(1430,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(1431,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(1432,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) ) @ V_z )
= ( c_Orderings_Oord__class_Omin @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(1433,plain,
( ( ! [V_x: $i,V_xs1: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs1 @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs1 @ T_a ) @ V_zs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(1434,plain,
( ( ! [V_x: $i,V_xa: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(1435,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(1436,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(1437,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(1438,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(1439,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(1440,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(1441,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(1442,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(1443,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(1444,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)],[521]) ).
thf(1445,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(1446,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(1447,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)],[524]) ).
thf(1448,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(1449,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(1450,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(1451,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(1452,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(1453,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1454,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(1455,plain,
( ( ! [V_a: $i,V_c: $i,V_b: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_c @ V_a @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(1456,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(1457,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(1458,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)],[535]) ).
thf(1459,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(1460,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(1461,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(1462,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(1463,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(1464,plain,
( ( ! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(1465,plain,
( ( ! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(1466,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(1467,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(1468,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(1469,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(1470,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(1471,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(1472,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ 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)],[549]) ).
thf(1473,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ 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)],[550]) ).
thf(1474,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(1475,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(1476,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(1477,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(1478,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(1479,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)],[556]) ).
thf(1480,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)],[557]) ).
thf(1481,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_k: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(1482,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(1483,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(1484,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)],[561]) ).
thf(1485,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(1486,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)],[563]) ).
thf(1487,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(1488,plain,
( ( ! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(1489,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)],[566]) ).
thf(1490,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(1491,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)],[568]) ).
thf(1492,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)],[569]) ).
thf(1493,plain,
( ( ! [T_a: $i,V_x: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(1494,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) ) @ V_m )
= ( c_Orderings_Oord__class_Omax @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(1495,plain,
( ( ! [V_m: $i,V_x: $i] : ( c_lessequals @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(1496,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(1497,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(1498,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ 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)],[575]) ).
thf(1499,plain,
( ( ! [V_s: $i,V_t: $i] : ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ 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)],[576]) ).
thf(1500,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(1501,plain,
( ( ! [V_i: $i,V_k: $i] :
( ~ ( c_lessequals @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_i ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_i ) @ V_i @ tc_nat )
= V_k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(1502,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)],[579]) ).
thf(1503,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)],[580]) ).
thf(1504,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)],[581]) ).
thf(1505,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(1506,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(1507,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(1508,plain,
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(1509,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(1510,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(1511,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(1512,plain,
( ( ! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(1513,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)],[590]) ).
thf(1514,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(1515,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)],[592]) ).
thf(1516,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)],[593]) ).
thf(1517,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)],[594]) ).
thf(1518,plain,
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(1519,plain,
( ( ! [V_j: $i,V_i: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_k @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ V_i ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(1520,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(1521,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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 ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(1522,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)],[599]) ).
thf(1523,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)],[600]) ).
thf(1524,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)],[601]) ).
thf(1525,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(1526,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(1527,plain,
( ( ! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(1528,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)],[605]) ).
thf(1529,plain,
( ( ! [V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(1530,plain,
( ( ! [V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ tc_nat ) ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(1531,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(1532,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(1533,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(1534,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(1535,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(1536,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(1537,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(1538,plain,
( ( ! [V_m: $i,V_j: $i,V_i: $i,V_u: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(1539,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(1540,plain,
( ( ! [V_i: $i,V_j: $i,V_u: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(1541,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(1542,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)],[619]) ).
thf(1543,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(1544,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(1545,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_Suc @ V_nat ) @ T_a )
= ( hAPP @ V_f2 @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(1546,plain,
( ( ! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(1547,plain,
( ( ! [V_f: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_a ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(1548,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_InductTermi_OIT @ V_s )
| ~ ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[625]) ).
thf(1549,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[626]) ).
thf(1550,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(1551,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(1552,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(1553,plain,
( ( ! [V_j: $i,V_k: $i,V_i: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat )
| ~ ( c_lessequals @ V_j @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(1554,plain,
( ( ! [V_j: $i,V_i: $i,V_k: $i] :
( ( c_lessequals @ V_j @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(1555,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(1556,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(1557,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[634]) ).
thf(1558,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(1559,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(1560,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(1561,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(1562,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(1563,plain,
( ( ! [T_a: $i,V_x: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x @ V_zs @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(1564,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641]) ).
thf(1565,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(1566,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(1567,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(1568,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_Suc @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f2 @ V_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(1569,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_Suc @ V_xa ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f2 @ V_xa ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(1570,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(1571,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(1572,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(1573,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(1574,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(1575,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( 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)],[652]) ).
thf(1576,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(1577,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654]) ).
thf(1578,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(1579,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[656]) ).
thf(1580,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_e @ T_a ) ) @ V_c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(1581,plain,
( ( ! [V_i: $i,V_u: $i,V_j: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_k ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_u @ tc_nat ) ) @ V_k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[658]) ).
thf(1582,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(1583,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(1584,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(1585,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(1586,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663]) ).
thf(1587,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(1588,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(1589,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(1590,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)],[667]) ).
thf(1591,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)],[668]) ).
thf(1592,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(1593,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(1594,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[671]) ).
thf(1595,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(1596,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[673]) ).
thf(1597,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[674]) ).
thf(1598,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[675]) ).
thf(1599,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[676]) ).
thf(1600,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(1601,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[678]) ).
thf(1602,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[679]) ).
thf(1603,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(1604,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(1605,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[682]) ).
thf(1606,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ V_m ) ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_Suc @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[683]) ).
thf(1607,plain,
( ( ! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[684]) ).
thf(1608,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[685]) ).
thf(1609,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(1610,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( 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)],[687]) ).
thf(1611,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( 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)],[688]) ).
thf(1612,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[689]) ).
thf(1613,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[690]) ).
thf(1614,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(1615,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)],[692]) ).
thf(1616,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)],[693]) ).
thf(1617,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[694]) ).
thf(1618,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[695]) ).
thf(1619,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_n @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(1620,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(1621,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(1622,plain,
( ( ! [V_m: $i,V_l: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_l @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(1623,plain,
( ( ! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[700]) ).
thf(1624,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[701]) ).
thf(1625,plain,
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[702]) ).
thf(1626,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_y @ ( c_Orderings_Oord__class_Omin @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[703]) ).
thf(1627,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[704]) ).
thf(1628,plain,
( ( ! [V_P: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[705]) ).
thf(1629,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)],[706]) ).
thf(1630,plain,
( ( ! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ V_P ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[707]) ).
thf(1631,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[708]) ).
thf(1632,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[709]) ).
thf(1633,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[710]) ).
thf(1634,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[711]) ).
thf(1635,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[712]) ).
thf(1636,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[713]) ).
thf(1637,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[714]) ).
thf(1638,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[715]) ).
thf(1639,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[716]) ).
thf(1640,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_z @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[717]) ).
thf(1641,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[718]) ).
thf(1642,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[719]) ).
thf(1643,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[720]) ).
thf(1644,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[721]) ).
thf(1645,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_lessequals @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[722]) ).
thf(1646,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[723]) ).
thf(1647,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[724]) ).
thf(1648,plain,
( ( ! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_lessequals @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[725]) ).
thf(1649,plain,
( ( ! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_lessequals @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[726]) ).
thf(1650,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ) )
= $true ),
inference(unfold_def,[status(thm)],[727]) ).
thf(1651,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ V_n ) @ V_x @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[728]) ).
thf(1652,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[729]) ).
thf(1653,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[730]) ).
thf(1654,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[731]) ).
thf(1655,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[732]) ).
thf(1656,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[733]) ).
thf(1657,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[734]) ).
thf(1658,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[735]) ).
thf(1659,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[736]) ).
thf(1660,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[737]) ).
thf(1661,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[738]) ).
thf(1662,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[739]) ).
thf(1663,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[740]) ).
thf(1664,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[741]) ).
thf(1665,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[742]) ).
thf(1666,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)],[743]) ).
thf(1667,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)],[744]) ).
thf(1668,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)],[745]) ).
thf(1669,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)],[746]) ).
thf(1670,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[747]) ).
thf(1671,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( 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)],[748]) ).
thf(1672,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_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)],[749]) ).
thf(1673,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[750]) ).
thf(1674,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[751]) ).
thf(1675,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_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)],[752]) ).
thf(1676,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)],[753]) ).
thf(1677,plain,
( ( ! [V_i: $i,V_j: $i,V_u: $i,V_n: $i] :
( ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[754]) ).
thf(1678,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[755]) ).
thf(1679,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( V_m
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[756]) ).
thf(1680,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m )
= V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[757]) ).
thf(1681,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(unfold_def,[status(thm)],[758]) ).
thf(1682,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[759]) ).
thf(1683,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) @ V_d @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[760]) ).
thf(1684,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[761]) ).
thf(1685,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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)],[762]) ).
thf(1686,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)],[763]) ).
thf(1687,plain,
( ( ! [T_a: $i,V_xs: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ V_a @ T_a @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[764]) ).
thf(1688,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)],[765]) ).
thf(1689,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)],[766]) ).
thf(1690,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[767]) ).
thf(1691,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[768]) ).
thf(1692,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[769]) ).
thf(1693,plain,
( ( ! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[770]) ).
thf(1694,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[771]) ).
thf(1695,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[772]) ).
thf(1696,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[773]) ).
thf(1697,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[774]) ).
thf(1698,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[775]) ).
thf(1699,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[776]) ).
thf(1700,plain,
( ( ! [V_n: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[777]) ).
thf(1701,plain,
( ( ! [V_j: $i,V_i: $i,V_u: $i,V_m: $i] :
( ~ ( c_lessequals @ V_j @ V_i @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[778]) ).
thf(1702,plain,
( ( ! [V_mul: $i,V_pwr: $i,V_x: $i,V_p: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_p ) ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_p ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[779]) ).
thf(1703,plain,
( ( ! [V_P: $i,V_n: $i] :
( ( c_lessequals @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ V_P @ V_n ) @ V_n @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[780]) ).
thf(1704,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[781]) ).
thf(1705,plain,
( ( ! [T_a: $i,V_x: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_p @ T_a ) @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_p ) @ V_q ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[782]) ).
thf(1706,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ V_y @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[783]) ).
thf(1707,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_a @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[784]) ).
thf(1708,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[785]) ).
thf(1709,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[786]) ).
thf(1710,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[787]) ).
thf(1711,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[788]) ).
thf(1712,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)],[789]) ).
thf(1713,plain,
( ( ! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[790]) ).
thf(1714,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)],[791]) ).
thf(1715,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y @ V_zs @ T_a @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[792]) ).
thf(1716,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[793]) ).
thf(1717,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[794]) ).
thf(1718,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[795]) ).
thf(1719,plain,
( ( ! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_l )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ~ ( 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)],[796]) ).
thf(1720,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[797]) ).
thf(1721,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[798]) ).
thf(1722,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[799]) ).
thf(1723,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[800]) ).
thf(1724,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[801]) ).
thf(1725,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_e: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) @ V_d @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[802]) ).
thf(1726,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) @ V_d @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[803]) ).
thf(1727,plain,
( ( ! [T_a: $i,V_c: $i,V_b: $i,V_a: $i,V_e: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ V_c @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[804]) ).
thf(1728,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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)],[805]) ).
thf(1729,plain,
( ( ! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[806]) ).
thf(1730,plain,
( ( ! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[807]) ).
thf(1731,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[808]) ).
thf(1732,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[809]) ).
thf(1733,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[810]) ).
thf(1734,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[811]) ).
thf(1735,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[812]) ).
thf(1736,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[813]) ).
thf(1737,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[814]) ).
thf(1738,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[815]) ).
thf(1739,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Type_Otype_OAtom @ V_nat )
!= ( c_Type_Otype_OAtom @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[816]) ).
thf(1740,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[817]) ).
thf(1741,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[818]) ).
thf(1742,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[819]) ).
thf(1743,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[820]) ).
thf(1744,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ V_y @ V_x @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[821]) ).
thf(1745,plain,
( ( ! [V_pwr: $i,V_x: $i,V_p: $i,V_q: $i,V_add: $i,V_mul: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_p ) ) @ V_q )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[822]) ).
thf(1746,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__rec @ V_f1 @ V_f2 @ ( c_Suc @ V_nat ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_nat ) @ ( c_Nat_Onat_Onat__rec @ V_f1 @ V_f2 @ V_nat @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[823]) ).
thf(1747,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[824]) ).
thf(1748,plain,
( ( ! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[825]) ).
thf(1749,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(unfold_def,[status(thm)],[826]) ).
thf(1750,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[827]) ).
thf(1751,plain,
( ( ! [V_x: $i,T_a: $i] :
( V_x
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[828]) ).
thf(1752,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[829]) ).
thf(1753,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[830]) ).
thf(1754,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[831]) ).
thf(1755,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[832]) ).
thf(1756,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[833]) ).
thf(1757,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[834]) ).
thf(1758,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_lessequals @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[835]) ).
thf(1759,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat )
| ~ ( c_lessequals @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[836]) ).
thf(1760,plain,
( ( ! [V_m: $i,V_x: $i] : ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_x ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[837]) ).
thf(1761,plain,
( ( ! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_i ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[838]) ).
thf(1762,plain,
( ( ! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_m ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[839]) ).
thf(1763,plain,
( ( ! [V_P: $i,V_n: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ V_P ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[840]) ).
thf(1764,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[841]) ).
thf(1765,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[842]) ).
thf(1766,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[843]) ).
thf(1767,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[844]) ).
thf(1768,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[845]) ).
thf(1769,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[846]) ).
thf(1770,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[847]) ).
thf(1771,plain,
( ( ! [V_e: $i,V_u: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_u @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[848]) ).
thf(1772,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)],[849]) ).
thf(1773,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)],[850]) ).
thf(1774,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[851]) ).
thf(1775,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)],[852]) ).
thf(1776,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)],[853]) ).
thf(1777,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[854]) ).
thf(1778,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[855]) ).
thf(1779,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)],[856]) ).
thf(1780,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[857]) ).
thf(1781,plain,
( ( ! [V_x: $i] :
( ~ ( c_lessequals @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[858]) ).
thf(1782,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[859]) ).
thf(1783,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[860]) ).
thf(1784,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[861]) ).
thf(1785,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_l @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[862]) ).
thf(1786,plain,
( ( ! [T_a: $i,V_x: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_Suc @ V_q ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[863]) ).
thf(1787,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[864]) ).
thf(1788,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[865]) ).
thf(1789,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[866]) ).
thf(1790,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[867]) ).
thf(1791,plain,
( ( ! [T_a: $i,V_x: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ V_x @ V_p @ T_a ) @ V_q @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ tc_nat ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[868]) ).
thf(1792,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[869]) ).
thf(1793,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[870]) ).
thf(1794,plain,
( ( ! [V_P: $i,V_b: $i,V_d: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_b ) @ V_d ) @ V_b @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_d ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[871]) ).
thf(1795,plain,
( ( ! [V_P: $i,V_b: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_b ) @ V_x ) @ V_b @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[872]) ).
thf(1796,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) ) @ V_b )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[873]) ).
thf(1797,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[874]) ).
thf(1798,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat ) )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[875]) ).
thf(1799,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)],[876]) ).
thf(1800,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[877]) ).
thf(1801,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[878]) ).
thf(1802,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[879]) ).
thf(1803,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)],[880]) ).
thf(1804,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omax @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[881]) ).
thf(1805,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[882]) ).
thf(1806,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[883]) ).
thf(1807,plain,
( ( ! [V_x: $i,V_c: $i,V_d: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[884]) ).
thf(1808,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[885]) ).
thf(1809,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[886]) ).
thf(1810,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)],[887]) ).
thf(1811,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[888]) ).
thf(1812,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[889]) ).
thf(1813,plain,
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[890]) ).
thf(1814,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[891]) ).
thf(1815,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[892]) ).
thf(1816,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[893]) ).
thf(1817,plain,
( ( ! [V_j: $i,V_k: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ V_m @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_j ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[894]) ).
thf(1818,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_xs @ T_a )
!= ( c_List_Oappend @ V_zs @ V_xs @ T_a ) )
| ( V_ys = V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[895]) ).
thf(1819,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Oappend @ V_xs @ V_zs @ T_a ) )
| ( V_ys = V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[896]) ).
thf(1820,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[897]) ).
thf(1821,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_z @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[898]) ).
thf(1822,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[899]) ).
thf(1823,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[900]) ).
thf(1824,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[901]) ).
thf(1825,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[902]) ).
thf(1826,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[903]) ).
thf(1827,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[904]) ).
thf(1828,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[905]) ).
thf(1829,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[906]) ).
thf(1830,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[907]) ).
thf(1831,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[908]) ).
thf(1832,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[909]) ).
thf(1833,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[910]) ).
thf(1834,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_Suc @ V_n ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[911]) ).
thf(1835,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ V_m ) ) @ V_n )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[912]) ).
thf(1836,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[913]) ).
thf(1837,plain,
( ( ! [V_i: $i,V_j: $i,V_u: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[914]) ).
thf(1838,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[915]) ).
thf(1839,plain,
( ( ! [V_m: $i,V_j: $i,V_i: $i,V_u: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[916]) ).
thf(1840,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[917]) ).
thf(1841,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) )
| ( V_c
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) ) @ V_d ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[918]) ).
thf(1842,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c )
= V_d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[919]) ).
thf(1843,plain,
( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_T_H_H____ @ tc_Type_Otype ) @ ( c_Lambda_Olift @ v_u____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[922]) ).
thf(1844,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[923]) ).
thf(1845,plain,
( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_T_H_H____ @ tc_Type_Otype ) @ ( c_Lambda_Olift @ v_u____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(copy,[status(thm)],[1843]) ).
thf(1846,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c )
= V_d ) ) )
= $true ),
inference(copy,[status(thm)],[1842]) ).
thf(1847,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) )
| ( V_c
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) ) @ V_d ) ) ) )
= $true ),
inference(copy,[status(thm)],[1841]) ).
thf(1848,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1840]) ).
thf(1849,plain,
( ( ! [V_m: $i,V_j: $i,V_i: $i,V_u: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1839]) ).
thf(1850,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1838]) ).
thf(1851,plain,
( ( ! [V_i: $i,V_j: $i,V_u: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1837]) ).
thf(1852,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) ) ) )
= $true ),
inference(copy,[status(thm)],[1836]) ).
thf(1853,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ V_m ) ) @ V_n )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1835]) ).
thf(1854,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_Suc @ V_n ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1834]) ).
thf(1855,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1833]) ).
thf(1856,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1832]) ).
thf(1857,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1831]) ).
thf(1858,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1830]) ).
thf(1859,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1829]) ).
thf(1860,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1828]) ).
thf(1861,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1827]) ).
thf(1862,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1826]) ).
thf(1863,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1825]) ).
thf(1864,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1824]) ).
thf(1865,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1823]) ).
thf(1866,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1822]) ).
thf(1867,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_z @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1821]) ).
thf(1868,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1820]) ).
thf(1869,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Oappend @ V_xs @ V_zs @ T_a ) )
| ( V_ys = V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[1819]) ).
thf(1870,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_xs @ T_a )
!= ( c_List_Oappend @ V_zs @ V_xs @ T_a ) )
| ( V_ys = V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[1818]) ).
thf(1871,plain,
( ( ! [V_j: $i,V_k: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ V_m @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_j ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1817]) ).
thf(1872,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1816]) ).
thf(1873,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1815]) ).
thf(1874,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1814]) ).
thf(1875,plain,
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1813]) ).
thf(1876,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1812]) ).
thf(1877,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1811]) ).
thf(1878,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)],[1810]) ).
thf(1879,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1809]) ).
thf(1880,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1808]) ).
thf(1881,plain,
( ( ! [V_x: $i,V_c: $i,V_d: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1807]) ).
thf(1882,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1806]) ).
thf(1883,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1805]) ).
thf(1884,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omax @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1804]) ).
thf(1885,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)],[1803]) ).
thf(1886,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1802]) ).
thf(1887,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1801]) ).
thf(1888,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1800]) ).
thf(1889,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)],[1799]) ).
thf(1890,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat ) )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1798]) ).
thf(1891,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1797]) ).
thf(1892,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) ) @ V_b )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1796]) ).
thf(1893,plain,
( ( ! [V_P: $i,V_b: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_b ) @ V_x ) @ V_b @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1795]) ).
thf(1894,plain,
( ( ! [V_P: $i,V_b: $i,V_d: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_b ) @ V_d ) @ V_b @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_d ) ) ) )
= $true ),
inference(copy,[status(thm)],[1794]) ).
thf(1895,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1793]) ).
thf(1896,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1792]) ).
thf(1897,plain,
( ( ! [T_a: $i,V_x: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ V_x @ V_p @ T_a ) @ V_q @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ tc_nat ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1791]) ).
thf(1898,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1790]) ).
thf(1899,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1789]) ).
thf(1900,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1788]) ).
thf(1901,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1787]) ).
thf(1902,plain,
( ( ! [T_a: $i,V_x: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_Suc @ V_q ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1786]) ).
thf(1903,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_l @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1785]) ).
thf(1904,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1784]) ).
thf(1905,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1783]) ).
thf(1906,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1782]) ).
thf(1907,plain,
( ( ! [V_x: $i] :
( ~ ( c_lessequals @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1781]) ).
thf(1908,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1780]) ).
thf(1909,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)],[1779]) ).
thf(1910,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1778]) ).
thf(1911,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1777]) ).
thf(1912,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)],[1776]) ).
thf(1913,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)],[1775]) ).
thf(1914,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1774]) ).
thf(1915,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)],[1773]) ).
thf(1916,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)],[1772]) ).
thf(1917,plain,
( ( ! [V_e: $i,V_u: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_u @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[1771]) ).
thf(1918,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1770]) ).
thf(1919,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1769]) ).
thf(1920,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1768]) ).
thf(1921,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1767]) ).
thf(1922,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1766]) ).
thf(1923,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1765]) ).
thf(1924,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[1764]) ).
thf(1925,plain,
( ( ! [V_P: $i,V_n: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ V_P ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1763]) ).
thf(1926,plain,
( ( ! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_m ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1762]) ).
thf(1927,plain,
( ( ! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_i ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1761]) ).
thf(1928,plain,
( ( ! [V_m: $i,V_x: $i] : ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_x ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1760]) ).
thf(1929,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat )
| ~ ( c_lessequals @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1759]) ).
thf(1930,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_lessequals @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1758]) ).
thf(1931,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1757]) ).
thf(1932,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1756]) ).
thf(1933,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1755]) ).
thf(1934,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1754]) ).
thf(1935,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1753]) ).
thf(1936,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[1752]) ).
thf(1937,plain,
( ( ! [V_x: $i,T_a: $i] :
( V_x
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1751]) ).
thf(1938,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1750]) ).
thf(1939,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(copy,[status(thm)],[1749]) ).
thf(1940,plain,
( ( ! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1748]) ).
thf(1941,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1747]) ).
thf(1942,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__rec @ V_f1 @ V_f2 @ ( c_Suc @ V_nat ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_nat ) @ ( c_Nat_Onat_Onat__rec @ V_f1 @ V_f2 @ V_nat @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1746]) ).
thf(1943,plain,
( ( ! [V_pwr: $i,V_x: $i,V_p: $i,V_q: $i,V_add: $i,V_mul: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_p ) ) @ V_q )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1745]) ).
thf(1944,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ V_y @ V_x @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1744]) ).
thf(1945,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1743]) ).
thf(1946,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1742]) ).
thf(1947,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1741]) ).
thf(1948,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1740]) ).
thf(1949,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Type_Otype_OAtom @ V_nat )
!= ( c_Type_Otype_OAtom @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1739]) ).
thf(1950,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1738]) ).
thf(1951,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1737]) ).
thf(1952,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1736]) ).
thf(1953,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1735]) ).
thf(1954,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1734]) ).
thf(1955,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1733]) ).
thf(1956,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1732]) ).
thf(1957,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1731]) ).
thf(1958,plain,
( ( ! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1730]) ).
thf(1959,plain,
( ( ! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1729]) ).
thf(1960,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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)],[1728]) ).
thf(1961,plain,
( ( ! [T_a: $i,V_c: $i,V_b: $i,V_a: $i,V_e: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ V_c @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1727]) ).
thf(1962,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) @ V_d @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1726]) ).
thf(1963,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_e: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) @ V_d @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1725]) ).
thf(1964,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1724]) ).
thf(1965,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1723]) ).
thf(1966,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1722]) ).
thf(1967,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1721]) ).
thf(1968,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1720]) ).
thf(1969,plain,
( ( ! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_l )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ~ ( 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)],[1719]) ).
thf(1970,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1718]) ).
thf(1971,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1717]) ).
thf(1972,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1716]) ).
thf(1973,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y @ V_zs @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1715]) ).
thf(1974,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)],[1714]) ).
thf(1975,plain,
( ( ! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ V_P ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1713]) ).
thf(1976,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)],[1712]) ).
thf(1977,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1711]) ).
thf(1978,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1710]) ).
thf(1979,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1709]) ).
thf(1980,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1708]) ).
thf(1981,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_a @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1707]) ).
thf(1982,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ V_y @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1706]) ).
thf(1983,plain,
( ( ! [T_a: $i,V_x: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_p @ T_a ) @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_p ) @ V_q ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1705]) ).
thf(1984,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1704]) ).
thf(1985,plain,
( ( ! [V_P: $i,V_n: $i] :
( ( c_lessequals @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ V_P @ V_n ) @ V_n @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1703]) ).
thf(1986,plain,
( ( ! [V_mul: $i,V_pwr: $i,V_x: $i,V_p: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_p ) ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_p ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1702]) ).
thf(1987,plain,
( ( ! [V_j: $i,V_i: $i,V_u: $i,V_m: $i] :
( ~ ( c_lessequals @ V_j @ V_i @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1701]) ).
thf(1988,plain,
( ( ! [V_n: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1700]) ).
thf(1989,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1699]) ).
thf(1990,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1698]) ).
thf(1991,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1697]) ).
thf(1992,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1696]) ).
thf(1993,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1695]) ).
thf(1994,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1694]) ).
thf(1995,plain,
( ( ! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1693]) ).
thf(1996,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1692]) ).
thf(1997,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1691]) ).
thf(1998,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1690]) ).
thf(1999,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1689]) ).
thf(2000,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)],[1688]) ).
thf(2001,plain,
( ( ! [T_a: $i,V_xs: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ V_a @ T_a @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1687]) ).
thf(2002,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)],[1686]) ).
thf(2003,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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)],[1685]) ).
thf(2004,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1684]) ).
thf(2005,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) @ V_d @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1683]) ).
thf(2006,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) ) @ V_c ) @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_d ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1682]) ).
thf(2007,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(copy,[status(thm)],[1681]) ).
thf(2008,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m )
= V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1680]) ).
thf(2009,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( V_m
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1679]) ).
thf(2010,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1678]) ).
thf(2011,plain,
( ( ! [V_i: $i,V_j: $i,V_u: $i,V_n: $i] :
( ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1677]) ).
thf(2012,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)],[1676]) ).
thf(2013,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_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)],[1675]) ).
thf(2014,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1674]) ).
thf(2015,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1673]) ).
thf(2016,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_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)],[1672]) ).
thf(2017,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( 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)],[1671]) ).
thf(2018,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1670]) ).
thf(2019,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)],[1669]) ).
thf(2020,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)],[1668]) ).
thf(2021,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)],[1667]) ).
thf(2022,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)],[1666]) ).
thf(2023,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1665]) ).
thf(2024,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1664]) ).
thf(2025,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1663]) ).
thf(2026,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1662]) ).
thf(2027,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1661]) ).
thf(2028,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ) )
= $true ),
inference(copy,[status(thm)],[1660]) ).
thf(2029,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1659]) ).
thf(2030,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1658]) ).
thf(2031,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1657]) ).
thf(2032,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1656]) ).
thf(2033,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1655]) ).
thf(2034,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1654]) ).
thf(2035,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1653]) ).
thf(2036,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1652]) ).
thf(2037,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ V_n ) @ V_x @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1651]) ).
thf(2038,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ) )
= $true ),
inference(copy,[status(thm)],[1650]) ).
thf(2039,plain,
( ( ! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_lessequals @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1649]) ).
thf(2040,plain,
( ( ! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_lessequals @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1648]) ).
thf(2041,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1647]) ).
thf(2042,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1646]) ).
thf(2043,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_lessequals @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1645]) ).
thf(2044,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1644]) ).
thf(2045,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1643]) ).
thf(2046,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1642]) ).
thf(2047,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1641]) ).
thf(2048,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_z @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1640]) ).
thf(2049,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[1639]) ).
thf(2050,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1638]) ).
thf(2051,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1637]) ).
thf(2052,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1636]) ).
thf(2053,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1635]) ).
thf(2054,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1634]) ).
thf(2055,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1633]) ).
thf(2056,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1632]) ).
thf(2057,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1631]) ).
thf(2058,plain,
( ( ! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ V_P ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1630]) ).
thf(2059,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)],[1629]) ).
thf(2060,plain,
( ( ! [V_P: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1628]) ).
thf(2061,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1627]) ).
thf(2062,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_y @ ( c_Orderings_Oord__class_Omin @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1626]) ).
thf(2063,plain,
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1625]) ).
thf(2064,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1624]) ).
thf(2065,plain,
( ( ! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1623]) ).
thf(2066,plain,
( ( ! [V_m: $i,V_l: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_l @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1622]) ).
thf(2067,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1621]) ).
thf(2068,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1620]) ).
thf(2069,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_n @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1619]) ).
thf(2070,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1618]) ).
thf(2071,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1617]) ).
thf(2072,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)],[1616]) ).
thf(2073,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)],[1615]) ).
thf(2074,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1614]) ).
thf(2075,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1613]) ).
thf(2076,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1612]) ).
thf(2077,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( 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)],[1611]) ).
thf(2078,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) )
| ( 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)],[1610]) ).
thf(2079,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1609]) ).
thf(2080,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1608]) ).
thf(2081,plain,
( ( ! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1607]) ).
thf(2082,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ V_m ) ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_Suc @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[1606]) ).
thf(2083,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1605]) ).
thf(2084,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1604]) ).
thf(2085,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1603]) ).
thf(2086,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1602]) ).
thf(2087,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1601]) ).
thf(2088,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1600]) ).
thf(2089,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1599]) ).
thf(2090,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1598]) ).
thf(2091,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1597]) ).
thf(2092,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1596]) ).
thf(2093,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1595]) ).
thf(2094,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1594]) ).
thf(2095,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1593]) ).
thf(2096,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1592]) ).
thf(2097,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)],[1591]) ).
thf(2098,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)],[1590]) ).
thf(2099,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1589]) ).
thf(2100,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1588]) ).
thf(2101,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1587]) ).
thf(2102,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1586]) ).
thf(2103,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1585]) ).
thf(2104,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1584]) ).
thf(2105,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1583]) ).
thf(2106,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1582]) ).
thf(2107,plain,
( ( ! [V_i: $i,V_u: $i,V_j: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_k ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_u @ tc_nat ) ) @ V_k ) ) )
= $true ),
inference(copy,[status(thm)],[1581]) ).
thf(2108,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_e @ T_a ) ) @ V_c ) ) ) )
= $true ),
inference(copy,[status(thm)],[1580]) ).
thf(2109,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1579]) ).
thf(2110,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ) )
= $true ),
inference(copy,[status(thm)],[1578]) ).
thf(2111,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1577]) ).
thf(2112,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1576]) ).
thf(2113,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( 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)],[1575]) ).
thf(2114,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1574]) ).
thf(2115,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1573]) ).
thf(2116,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1572]) ).
thf(2117,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1571]) ).
thf(2118,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1570]) ).
thf(2119,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_Suc @ V_xa ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f2 @ V_xa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1569]) ).
thf(2120,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_Suc @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f2 @ V_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1568]) ).
thf(2121,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1567]) ).
thf(2122,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1566]) ).
thf(2123,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1565]) ).
thf(2124,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1564]) ).
thf(2125,plain,
( ( ! [T_a: $i,V_x: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x @ V_zs @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1563]) ).
thf(2126,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1562]) ).
thf(2127,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1561]) ).
thf(2128,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1560]) ).
thf(2129,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1559]) ).
thf(2130,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1558]) ).
thf(2131,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1557]) ).
thf(2132,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1556]) ).
thf(2133,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1555]) ).
thf(2134,plain,
( ( ! [V_j: $i,V_i: $i,V_k: $i] :
( ( c_lessequals @ V_j @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1554]) ).
thf(2135,plain,
( ( ! [V_j: $i,V_k: $i,V_i: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat )
| ~ ( c_lessequals @ V_j @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1553]) ).
thf(2136,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1552]) ).
thf(2137,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1551]) ).
thf(2138,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1550]) ).
thf(2139,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1549]) ).
thf(2140,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_InductTermi_OIT @ V_s )
| ~ ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[1548]) ).
thf(2141,plain,
( ( ! [V_f: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_a ) )
= $true ),
inference(copy,[status(thm)],[1547]) ).
thf(2142,plain,
( ( ! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[1546]) ).
thf(2143,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_Suc @ V_nat ) @ T_a )
= ( hAPP @ V_f2 @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1545]) ).
thf(2144,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1544]) ).
thf(2145,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1543]) ).
thf(2146,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)],[1542]) ).
thf(2147,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1541]) ).
thf(2148,plain,
( ( ! [V_i: $i,V_j: $i,V_u: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1540]) ).
thf(2149,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) ) @ V_m ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1539]) ).
thf(2150,plain,
( ( ! [V_m: $i,V_j: $i,V_i: $i,V_u: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1538]) ).
thf(2151,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1537]) ).
thf(2152,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1536]) ).
thf(2153,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1535]) ).
thf(2154,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1534]) ).
thf(2155,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1533]) ).
thf(2156,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1532]) ).
thf(2157,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1531]) ).
thf(2158,plain,
( ( ! [V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ tc_nat ) ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1530]) ).
thf(2159,plain,
( ( ! [V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1529]) ).
thf(2160,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)],[1528]) ).
thf(2161,plain,
( ( ! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1527]) ).
thf(2162,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1526]) ).
thf(2163,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1525]) ).
thf(2164,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)],[1524]) ).
thf(2165,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)],[1523]) ).
thf(2166,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)],[1522]) ).
thf(2167,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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 ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1521]) ).
thf(2168,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1520]) ).
thf(2169,plain,
( ( ! [V_j: $i,V_i: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_k @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ V_i ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1519]) ).
thf(2170,plain,
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1518]) ).
thf(2171,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)],[1517]) ).
thf(2172,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)],[1516]) ).
thf(2173,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)],[1515]) ).
thf(2174,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1514]) ).
thf(2175,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)],[1513]) ).
thf(2176,plain,
( ( ! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ) )
= $true ),
inference(copy,[status(thm)],[1512]) ).
thf(2177,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1511]) ).
thf(2178,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[1510]) ).
thf(2179,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1509]) ).
thf(2180,plain,
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1508]) ).
thf(2181,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1507]) ).
thf(2182,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1506]) ).
thf(2183,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1505]) ).
thf(2184,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)],[1504]) ).
thf(2185,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)],[1503]) ).
thf(2186,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)],[1502]) ).
thf(2187,plain,
( ( ! [V_i: $i,V_k: $i] :
( ~ ( c_lessequals @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_i ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_i ) @ V_i @ tc_nat )
= V_k ) ) )
= $true ),
inference(copy,[status(thm)],[1501]) ).
thf(2188,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1500]) ).
thf(2189,plain,
( ( ! [V_s: $i,V_t: $i] : ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ 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)],[1499]) ).
thf(2190,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ 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)],[1498]) ).
thf(2191,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1497]) ).
thf(2192,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1496]) ).
thf(2193,plain,
( ( ! [V_m: $i,V_x: $i] : ( c_lessequals @ V_m @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1495]) ).
thf(2194,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) ) @ V_m )
= ( c_Orderings_Oord__class_Omax @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1494]) ).
thf(2195,plain,
( ( ! [T_a: $i,V_x: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1493]) ).
thf(2196,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)],[1492]) ).
thf(2197,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)],[1491]) ).
thf(2198,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1490]) ).
thf(2199,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)],[1489]) ).
thf(2200,plain,
( ( ! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1488]) ).
thf(2201,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[1487]) ).
thf(2202,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)],[1486]) ).
thf(2203,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1485]) ).
thf(2204,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)],[1484]) ).
thf(2205,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1483]) ).
thf(2206,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1482]) ).
thf(2207,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_k: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1481]) ).
thf(2208,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)],[1480]) ).
thf(2209,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)],[1479]) ).
thf(2210,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1478]) ).
thf(2211,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1477]) ).
thf(2212,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1476]) ).
thf(2213,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1475]) ).
thf(2214,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(copy,[status(thm)],[1474]) ).
thf(2215,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ 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)],[1473]) ).
thf(2216,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ 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)],[1472]) ).
thf(2217,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1471]) ).
thf(2218,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1470]) ).
thf(2219,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1469]) ).
thf(2220,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1468]) ).
thf(2221,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(copy,[status(thm)],[1467]) ).
thf(2222,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(copy,[status(thm)],[1466]) ).
thf(2223,plain,
( ( ! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ) )
= $true ),
inference(copy,[status(thm)],[1465]) ).
thf(2224,plain,
( ( ! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1464]) ).
thf(2225,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1463]) ).
thf(2226,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1462]) ).
thf(2227,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1461]) ).
thf(2228,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1460]) ).
thf(2229,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1459]) ).
thf(2230,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)],[1458]) ).
thf(2231,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1457]) ).
thf(2232,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1456]) ).
thf(2233,plain,
( ( ! [V_a: $i,V_c: $i,V_b: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_c @ V_a @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1455]) ).
thf(2234,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1454]) ).
thf(2235,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1453]) ).
thf(2236,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1452]) ).
thf(2237,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1451]) ).
thf(2238,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1450]) ).
thf(2239,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1449]) ).
thf(2240,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1448]) ).
thf(2241,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)],[1447]) ).
thf(2242,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1446]) ).
thf(2243,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1445]) ).
thf(2244,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)],[1444]) ).
thf(2245,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1443]) ).
thf(2246,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1442]) ).
thf(2247,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[1441]) ).
thf(2248,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1440]) ).
thf(2249,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1439]) ).
thf(2250,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[1438]) ).
thf(2251,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1437]) ).
thf(2252,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1436]) ).
thf(2253,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1435]) ).
thf(2254,plain,
( ( ! [V_x: $i,V_xa: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1434]) ).
thf(2255,plain,
( ( ! [V_x: $i,V_xs1: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs1 @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs1 @ T_a ) @ V_zs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1433]) ).
thf(2256,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) ) @ V_z )
= ( c_Orderings_Oord__class_Omin @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1432]) ).
thf(2257,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1431]) ).
thf(2258,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1430]) ).
thf(2259,plain,
( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1429]) ).
thf(2260,plain,
( ( ! [V_pwr: $i,V_mul: $i,V_x: $i,V_y: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ V_q )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) ) @ ( hAPP @ ( hAPP @ V_pwr @ V_y ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1428]) ).
thf(2261,plain,
( ( ! [V_mul: $i,V_x: $i,V_add: $i,V_y: $i,V_z: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_z ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1427]) ).
thf(2262,plain,
( ( ! [V_mul: $i,V_x: $i,V_y: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ V_mul @ V_y ) @ V_x ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1426]) ).
thf(2263,plain,
( ( ! [V_mul: $i,V_x: $i,V_y: $i,V_z: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_mul @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ V_z ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1425]) ).
thf(2264,plain,
( ( ! [V_mul: $i,V_r1: $i,V_x: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r1 ) @ V_x )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1424]) ).
thf(2265,plain,
( ( ! [V_mul: $i,V_r0: $i,V_x: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r0 ) @ V_x )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1423]) ).
thf(2266,plain,
( ( ! [V_add: $i,V_x: $i,V_y: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_x ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1422]) ).
thf(2267,plain,
( ( ! [V_add: $i,V_x: $i,V_y: $i,V_z: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_x ) @ ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_x ) @ V_y ) ) @ V_z ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1421]) ).
thf(2268,plain,
( ( ! [V_add: $i,V_r0: $i,V_x: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_r0 ) @ V_x )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1420]) ).
thf(2269,plain,
( ( ! [V_add: $i,V_a: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ V_d ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1419]) ).
thf(2270,plain,
( ( ! [V_add: $i,V_a: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_a ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1418]) ).
thf(2271,plain,
( ( ! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ V_b ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1417]) ).
thf(2272,plain,
( ( ! [V_add: $i,V_a: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ V_c ) @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_d ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1416]) ).
thf(2273,plain,
( ( ! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_b ) @ V_c ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1415]) ).
thf(2274,plain,
( ( ! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ V_add @ V_b ) @ V_d ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1414]) ).
thf(2275,plain,
( ( ! [V_mul: $i,V_lx: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1413]) ).
thf(2276,plain,
( ( ! [V_mul: $i,V_lx: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ V_ry ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1412]) ).
thf(2277,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ V_rx ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1411]) ).
thf(2278,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ V_ly ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1410]) ).
thf(2279,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1409]) ).
thf(2280,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1408]) ).
thf(2281,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1407]) ).
thf(2282,plain,
( ( ! [V_mul: $i,V_a: $i,V_r1: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_r1 )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1406]) ).
thf(2283,plain,
( ( ! [V_mul: $i,V_r1: $i,V_a: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r1 ) @ V_a )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1405]) ).
thf(2284,plain,
( ( ! [V_mul: $i,V_a: $i,V_r0: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_r0 )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1404]) ).
thf(2285,plain,
( ( ! [V_mul: $i,V_r0: $i,V_a: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r0 ) @ V_a )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1403]) ).
thf(2286,plain,
( ( ! [V_mul: $i,V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_c ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1402]) ).
thf(2287,plain,
( ( ! [V_mul: $i,V_a: $i,V_b: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_a ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1401]) ).
thf(2288,plain,
( ( ! [V_add: $i,V_a: $i,V_r0: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r0 )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1400]) ).
thf(2289,plain,
( ( ! [V_add: $i,V_r0: $i,V_a: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_r0 ) @ V_a )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1399]) ).
thf(2290,plain,
( ( ! [V_add: $i,V_m: $i,V_mul: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_m ) @ V_m )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_r1 ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1398]) ).
thf(2291,plain,
( ( ! [V_add: $i,V_m: $i,V_mul: $i,V_a: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_m ) @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1397]) ).
thf(2292,plain,
( ( ! [V_add: $i,V_mul: $i,V_a: $i,V_m: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) ) @ V_m )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1396]) ).
thf(2293,plain,
( ( ! [V_add: $i,V_mul: $i,V_a: $i,V_m: $i,V_b: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_m ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1395]) ).
thf(2294,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xc ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1394]) ).
thf(2295,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1393]) ).
thf(2296,plain,
( ( ! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(copy,[status(thm)],[1392]) ).
thf(2297,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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)],[1391]) ).
thf(2298,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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)],[1390]) ).
thf(2299,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)],[1389]) ).
thf(2300,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1388]) ).
thf(2301,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1387]) ).
thf(2302,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1386]) ).
thf(2303,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) ) @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1385]) ).
thf(2304,plain,
( ( ! [V_r: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(copy,[status(thm)],[1384]) ).
thf(2305,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1383]) ).
thf(2306,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[1382]) ).
thf(2307,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[1381]) ).
thf(2308,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)],[1380]) ).
thf(2309,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1379]) ).
thf(2310,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) )
| ( V_a = V_b )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1378]) ).
thf(2311,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1377]) ).
thf(2312,plain,
( ( ! [V_i: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( c_List_Odrop @ V_i @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ V_k @ V_i @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1376]) ).
thf(2313,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_x @ V_z @ T_a ) @ T_a ) @ ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1375]) ).
thf(2314,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1374]) ).
thf(2315,plain,
( ( ! [V_nat: $i] :
( ( c_nat_Onat__size @ ( c_Suc @ V_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_nat_Onat__size @ V_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1373]) ).
thf(2316,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1372]) ).
thf(2317,plain,
( ( ! [V_m: $i] : ( c_lessequals @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_m @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1371]) ).
thf(2318,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)],[1370]) ).
thf(2319,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)],[1369]) ).
thf(2320,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)],[1368]) ).
thf(2321,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)],[1367]) ).
thf(2322,plain,
( ( ! [V_n: $i,V_i: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= V_i )
| ~ ( c_lessequals @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1366]) ).
thf(2323,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)],[1365]) ).
thf(2324,plain,
( ( ! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ) )
= $true ),
inference(copy,[status(thm)],[1364]) ).
thf(2325,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) @ V_t ) )
= $true ),
inference(copy,[status(thm)],[1363]) ).
thf(2326,plain,
( ( ! [V_m: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k ) @ ( c_Suc @ V_j ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1362]) ).
thf(2327,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)],[1361]) ).
thf(2328,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)],[1360]) ).
thf(2329,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)],[1359]) ).
thf(2330,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)],[1358]) ).
thf(2331,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1357]) ).
thf(2332,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1356]) ).
thf(2333,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)],[1355]) ).
thf(2334,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1354]) ).
thf(2335,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1353]) ).
thf(2336,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1352]) ).
thf(2337,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1351]) ).
thf(2338,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1350]) ).
thf(2339,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1349]) ).
thf(2340,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1348]) ).
thf(2341,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1347]) ).
thf(2342,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1346]) ).
thf(2343,plain,
( ( ! [V_i: $i,V_j: $i] :
( ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( V_j
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) ) @ V_i ) ) ) )
= $true ),
inference(copy,[status(thm)],[1345]) ).
thf(2344,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
= V_m )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1344]) ).
thf(2345,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) @ V_n )
= V_m )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1343]) ).
thf(2346,plain,
( ( ! [V_mul: $i,V_x: $i,V_pwr: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_Suc @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1342]) ).
thf(2347,plain,
( ( ! [V_mul: $i,V_pwr: $i,V_x: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) ) @ V_x )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_Suc @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1341]) ).
thf(2348,plain,
( ( ! [V_pwr: $i,V_x: $i,V_q: $i,V_mul: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_Suc @ V_q ) )
= ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1340]) ).
thf(2349,plain,
( ( ! [V_pwr: $i,V_x: $i,V_n: $i,V_mul: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_Suc @ V_n ) )
= ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_n ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1339]) ).
thf(2350,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1338]) ).
thf(2351,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1337]) ).
thf(2352,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1336]) ).
thf(2353,plain,
( ( ! [V_j: $i,V_k: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ V_i )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1335]) ).
thf(2354,plain,
( ( ! [V_n: $i,V_m: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Odrop @ V_m @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1334]) ).
thf(2355,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1333]) ).
thf(2356,plain,
( ( ! [V_n: $i,V_m: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_m @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1332]) ).
thf(2357,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)],[1331]) ).
thf(2358,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)],[1330]) ).
thf(2359,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)],[1329]) ).
thf(2360,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1328]) ).
thf(2361,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1327]) ).
thf(2362,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Oreplicate @ V_n @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1326]) ).
thf(2363,plain,
( ( ! [T_a: $i,V_x: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( c_Suc @ V_q ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1325]) ).
thf(2364,plain,
( ( ! [T_a: $i,V_x: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ V_x @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( c_Suc @ V_q ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1324]) ).
thf(2365,plain,
( ( ! [T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1323]) ).
thf(2366,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1322]) ).
thf(2367,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1321]) ).
thf(2368,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1320]) ).
thf(2369,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1319]) ).
thf(2370,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)],[1318]) ).
thf(2371,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)],[1317]) ).
thf(2372,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)],[1316]) ).
thf(2373,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1315]) ).
thf(2374,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1314]) ).
thf(2375,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[1313]) ).
thf(2376,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1312]) ).
thf(2377,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1311]) ).
thf(2378,plain,
( ( ! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1310]) ).
thf(2379,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1309]) ).
thf(2380,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1308]) ).
thf(2381,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ 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)],[1307]) ).
thf(2382,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)],[1306]) ).
thf(2383,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(copy,[status(thm)],[1305]) ).
thf(2384,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1304]) ).
thf(2385,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1303]) ).
thf(2386,plain,
( ( ! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_i @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1302]) ).
thf(2387,plain,
( ( ! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_i @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1301]) ).
thf(2388,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1300]) ).
thf(2389,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1299]) ).
thf(2390,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1298]) ).
thf(2391,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1297]) ).
thf(2392,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1296]) ).
thf(2393,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1295]) ).
thf(2394,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1294]) ).
thf(2395,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1293]) ).
thf(2396,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_ys )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1292]) ).
thf(2397,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
( ( V_ys
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1291]) ).
thf(2398,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 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ T_a ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ T_a ) ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1290]) ).
thf(2399,plain,
( ( ! [V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ tc_nat ) ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1289]) ).
thf(2400,plain,
( ( ! [T_a: $i,V_x: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1288]) ).
thf(2401,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1287]) ).
thf(2402,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1286]) ).
thf(2403,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ 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)],[1285]) ).
thf(2404,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1284]) ).
thf(2405,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[1283]) ).
thf(2406,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1282]) ).
thf(2407,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1281]) ).
thf(2408,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1280]) ).
thf(2409,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1279]) ).
thf(2410,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1278]) ).
thf(2411,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1277]) ).
thf(2412,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1276]) ).
thf(2413,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1275]) ).
thf(2414,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1274]) ).
thf(2415,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1273]) ).
thf(2416,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1272]) ).
thf(2417,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1271]) ).
thf(2418,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1270]) ).
thf(2419,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1269]) ).
thf(2420,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1268]) ).
thf(2421,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1267]) ).
thf(2422,plain,
( ( ! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1266]) ).
thf(2423,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ V_i @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1265]) ).
thf(2424,plain,
( ( ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1264]) ).
thf(2425,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1263]) ).
thf(2426,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omin @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1262]) ).
thf(2427,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m
= ( c_Suc @ V_n ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1261]) ).
thf(2428,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)],[1260]) ).
thf(2429,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)],[1259]) ).
thf(2430,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)],[1258]) ).
thf(2431,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1257]) ).
thf(2432,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1256]) ).
thf(2433,plain,
( ( ! [V_k: $i,V_i: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_i @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1255]) ).
thf(2434,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1254]) ).
thf(2435,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1253]) ).
thf(2436,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1252]) ).
thf(2437,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)],[1251]) ).
thf(2438,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)],[1250]) ).
thf(2439,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)],[1249]) ).
thf(2440,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1248]) ).
thf(2441,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)],[1247]) ).
thf(2442,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)],[1246]) ).
thf(2443,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)],[1245]) ).
thf(2444,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)],[1244]) ).
thf(2445,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)],[1243]) ).
thf(2446,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)],[1242]) ).
thf(2447,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)],[1241]) ).
thf(2448,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)],[1240]) ).
thf(2449,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)],[1239]) ).
thf(2450,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1238]) ).
thf(2451,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) ) @ V_z )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1237]) ).
thf(2452,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[1236]) ).
thf(2453,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1235]) ).
thf(2454,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_l @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1234]) ).
thf(2455,plain,
( ( ! [V_m: $i] : ( c_lessequals @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_m @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1233]) ).
thf(2456,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1232]) ).
thf(2457,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1231]) ).
thf(2458,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1230]) ).
thf(2459,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_y @ ( c_Orderings_Oord__class_Omax @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1229]) ).
thf(2460,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1228]) ).
thf(2461,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_m @ T_a ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_m @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1227]) ).
thf(2462,plain,
( ( ! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[1226]) ).
thf(2463,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1225]) ).
thf(2464,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1224]) ).
thf(2465,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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 ) ) )
= $true ),
inference(copy,[status(thm)],[1223]) ).
thf(2466,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)],[1222]) ).
thf(2467,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1221]) ).
thf(2468,plain,
( ( ! [V_i: $i,V_x: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1220]) ).
thf(2469,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1219]) ).
thf(2470,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1218]) ).
thf(2471,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1217]) ).
thf(2472,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1216]) ).
thf(2473,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ V_n @ tc_nat )
= V_m ) )
= $true ),
inference(copy,[status(thm)],[1215]) ).
thf(2474,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_n @ tc_nat )
= V_m ) )
= $true ),
inference(copy,[status(thm)],[1214]) ).
thf(2475,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_b @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1213]) ).
thf(2476,plain,
( ( ! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1212]) ).
thf(2477,plain,
( ( ! [V_f1: $i,V_f2: $i,V_nat: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( c_Type_Otype_OAtom @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1211]) ).
thf(2478,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1210]) ).
thf(2479,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1209]) ).
thf(2480,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1208]) ).
thf(2481,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)],[1207]) ).
thf(2482,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)],[1206]) ).
thf(2483,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)],[1205]) ).
thf(2484,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1204]) ).
thf(2485,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1203]) ).
thf(2486,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1202]) ).
thf(2487,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1201]) ).
thf(2488,plain,
( ( ! [V_T: $i,V_e: $i,V_t: $i] :
( ( V_T
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[1200]) ).
thf(2489,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1199]) ).
thf(2490,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1198]) ).
thf(2491,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)],[1197]) ).
thf(2492,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)],[1196]) ).
thf(2493,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)],[1195]) ).
thf(2494,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)],[1194]) ).
thf(2495,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)],[1193]) ).
thf(2496,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)],[1192]) ).
thf(2497,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)],[1191]) ).
thf(2498,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)],[1190]) ).
thf(2499,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)],[1189]) ).
thf(2500,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)],[1188]) ).
thf(2501,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1187]) ).
thf(2502,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)],[1186]) ).
thf(2503,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)],[1185]) ).
thf(2504,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)],[1184]) ).
thf(2505,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)],[1183]) ).
thf(2506,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)],[1182]) ).
thf(2507,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
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1181]) ).
thf(2508,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1180]) ).
thf(2509,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)],[1179]) ).
thf(2510,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)],[1178]) ).
thf(2511,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)],[1177]) ).
thf(2512,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1176]) ).
thf(2513,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1175]) ).
thf(2514,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1174]) ).
thf(2515,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1173]) ).
thf(2516,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1172]) ).
thf(2517,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1171]) ).
thf(2518,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1170]) ).
thf(2519,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1169]) ).
thf(2520,plain,
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[1168]) ).
thf(2521,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1167]) ).
thf(2522,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1166]) ).
thf(2523,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)],[1165]) ).
thf(2524,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)],[1164]) ).
thf(2525,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1163]) ).
thf(2526,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1162]) ).
thf(2527,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1161]) ).
thf(2528,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1160]) ).
thf(2529,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_d: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1159]) ).
thf(2530,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)],[1158]) ).
thf(2531,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(copy,[status(thm)],[1157]) ).
thf(2532,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ) )
= $true ),
inference(copy,[status(thm)],[1156]) ).
thf(2533,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(copy,[status(thm)],[1155]) ).
thf(2534,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1154]) ).
thf(2535,plain,
( ( ! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ) )
= $true ),
inference(copy,[status(thm)],[1153]) ).
thf(2536,plain,
( ( ! [V_m: $i,V_i: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_i @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ V_m @ V_n @ tc_nat ) @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1152]) ).
thf(2537,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1151]) ).
thf(2538,plain,
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1150]) ).
thf(2539,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)],[1149]) ).
thf(2540,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)],[1148]) ).
thf(2541,plain,
( ( ! [V_P: $i,V_i: $i,V_n: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ V_P @ V_n ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1147]) ).
thf(2542,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1146]) ).
thf(2543,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1145]) ).
thf(2544,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[1144]) ).
thf(2545,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)],[1143]) ).
thf(2546,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1142]) ).
thf(2547,plain,
( ( ! [V_k: $i,V_i: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_i @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1141]) ).
thf(2548,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1140]) ).
thf(2549,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1139]) ).
thf(2550,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1138]) ).
thf(2551,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)],[1137]) ).
thf(2552,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)],[1136]) ).
thf(2553,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)],[1135]) ).
thf(2554,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)],[1134]) ).
thf(2555,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( 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 ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1133]) ).
thf(2556,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)],[1132]) ).
thf(2557,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)],[1131]) ).
thf(2558,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)],[1130]) ).
thf(2559,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)],[1129]) ).
thf(2560,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ 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)],[1128]) ).
thf(2561,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1127]) ).
thf(2562,plain,
( ( ! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1126]) ).
thf(2563,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1125]) ).
thf(2564,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)],[1124]) ).
thf(2565,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) @ ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_x @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1123]) ).
thf(2566,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1122]) ).
thf(2567,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1121]) ).
thf(2568,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)],[1120]) ).
thf(2569,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)],[1119]) ).
thf(2570,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1118]) ).
thf(2571,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_q @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_q @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1117]) ).
thf(2572,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) @ ( c_List_Olistsum @ V_ys @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1116]) ).
thf(2573,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
= V_m )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1115]) ).
thf(2574,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)],[1114]) ).
thf(2575,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(copy,[status(thm)],[1113]) ).
thf(2576,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1112]) ).
thf(2577,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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)],[1111]) ).
thf(2578,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( 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)],[1110]) ).
thf(2579,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ V_y @ V_x @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1109]) ).
thf(2580,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1108]) ).
thf(2581,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1107]) ).
thf(2582,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1106]) ).
thf(2583,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1105]) ).
thf(2584,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1104]) ).
thf(2585,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1103]) ).
thf(2586,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1102]) ).
thf(2587,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1101]) ).
thf(2588,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1100]) ).
thf(2589,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1099]) ).
thf(2590,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1098]) ).
thf(2591,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1097]) ).
thf(2592,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1096]) ).
thf(2593,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1095]) ).
thf(2594,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1094]) ).
thf(2595,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1093]) ).
thf(2596,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1092]) ).
thf(2597,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1091]) ).
thf(2598,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1090]) ).
thf(2599,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1089]) ).
thf(2600,plain,
( ( ! [T_a: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1088]) ).
thf(2601,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1087]) ).
thf(2602,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1086]) ).
thf(2603,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)],[1085]) ).
thf(2604,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)],[1084]) ).
thf(2605,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)],[1083]) ).
thf(2606,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)],[1082]) ).
thf(2607,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)],[1081]) ).
thf(2608,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_zs @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1080]) ).
thf(2609,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1079]) ).
thf(2610,plain,
( ( ! [V_xs: $i,V_xs1: $i,V_us: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_xs1 @ V_us @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_xs1 @ T_a ) @ V_us @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1078]) ).
thf(2611,plain,
( ( ! [V_zs: $i,V_x: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_zs @ V_x @ T_a ) @ V_ys @ T_a )
= ( c_List_Oappend @ V_zs @ ( c_List_Oappend @ V_x @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1077]) ).
thf(2612,plain,
( ( ! [V_xs: $i,V_x: $i,V_ts: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_x @ V_ts @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ V_ts @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1076]) ).
thf(2613,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)],[1075]) ).
thf(2614,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_c @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1074]) ).
thf(2615,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_c @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1073]) ).
thf(2616,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ V_k @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1072]) ).
thf(2617,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1071]) ).
thf(2618,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1070]) ).
thf(2619,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)],[1069]) ).
thf(2620,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)],[1068]) ).
thf(2621,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1067]) ).
thf(2622,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1066]) ).
thf(2623,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)],[1065]) ).
thf(2624,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)],[1064]) ).
thf(2625,plain,
( ( ! [V_f1: $i,V_f2: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__rec @ V_f1 @ V_f2 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_f1 ) )
= $true ),
inference(copy,[status(thm)],[1063]) ).
thf(2626,plain,
( ( ! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ V_P @ V_n ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1062]) ).
thf(2627,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1061]) ).
thf(2628,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1060]) ).
thf(2629,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)],[1059]) ).
thf(2630,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1058]) ).
thf(2631,plain,
( ( ! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1057]) ).
thf(2632,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1056]) ).
thf(2633,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1055]) ).
thf(2634,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1054]) ).
thf(2635,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1053]) ).
thf(2636,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1052]) ).
thf(2637,plain,
( ( ! [V_x: $i,V_f: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__case @ V_x @ V_f @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[1051]) ).
thf(2638,plain,
( ( ! [V_f1: $i,V_f2: $i,T_a: $i] :
( ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_f1 ) )
= $true ),
inference(copy,[status(thm)],[1050]) ).
thf(2639,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1049]) ).
thf(2640,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1048]) ).
thf(2641,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1047]) ).
thf(2642,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1046]) ).
thf(2643,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ( V_m = V_n )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1045]) ).
thf(2644,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)],[1044]) ).
thf(2645,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)],[1043]) ).
thf(2646,plain,
( ( ! [V_x: $i,V_a: $i] :
( ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1042]) ).
thf(2647,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= V_m )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1041]) ).
thf(2648,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xreplicate__Xinduct__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1040]) ).
thf(2649,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1039]) ).
thf(2650,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1038]) ).
thf(2651,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Nat_Onat_Onat__case @ V_f1 @ V_f2 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_f1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1037]) ).
thf(2652,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Nat__Xnat__Xinducts__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1036]) ).
thf(2653,plain,
( ( ! [V_x: $i] :
( ( c_Nitpick_Onat__gcd @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[1035]) ).
thf(2654,plain,
( ( ( c_nat_Onat__size @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1034]) ).
thf(2655,plain,
( ( ! [V_c: $i] :
( ( c_String_Ochar_Ochar__size @ V_c )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1033]) ).
thf(2656,plain,
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1032]) ).
thf(2657,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Nat__Xnat__Xinduct__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1031]) ).
thf(2658,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)],[1030]) ).
thf(2659,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)],[1029]) ).
thf(2660,plain,
( ( ( c_Orderings_Obot__class_Obot @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1028]) ).
thf(2661,plain,
( ( ! [V_P: $i,V_nat: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_nat ) )
| ( hBOOL @ ( hAPP @ V_P @ ( v_sko__List__Xupt__Xinduct__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1027]) ).
thf(2662,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[1026]) ).
thf(2663,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)],[1025]) ).
thf(2664,plain,
( ( ! [V_P: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_n ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1024]) ).
thf(2665,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1023]) ).
thf(2666,plain,
( ( ! [V_c: $i] :
( ( c_Nat_Osize__class_Osize @ V_c @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1022]) ).
thf(2667,plain,
( ( ! [V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1021]) ).
thf(2668,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[1020]) ).
thf(2669,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[1019]) ).
thf(2670,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_x = V_y )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1018]) ).
thf(2671,plain,
( ( ! [V_x: $i] :
( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1017]) ).
thf(2672,plain,
( ( ! [V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[1016]) ).
thf(2673,plain,
( ( ! [V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_m ) )
= $true ),
inference(copy,[status(thm)],[1015]) ).
thf(2674,plain,
( ( ! [V_pwr: $i,V_x: $i,V_r1: $i,V_add: $i,V_mul: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_r1 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1014]) ).
thf(2675,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1013]) ).
thf(2676,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1012]) ).
thf(2677,plain,
( ( ! [T_a: $i,V_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1011]) ).
thf(2678,plain,
( ( c_Type_Otypings @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_as____ @ v_Ts____ )
= $true ),
inference(copy,[status(thm)],[1010]) ).
thf(2679,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_Lambda_Obeta @ V_t @ V_t_H )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[1009]) ).
thf(2680,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[1008]) ).
thf(2681,plain,
( ( ! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1007]) ).
thf(2682,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ V_e @ V_t ) @ tc_Type_Otype ) @ V_t @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ V_e @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[1006]) ).
thf(2683,plain,
( ( ! [V_e: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ V_T @ V_e @ V_t ) @ tc_Type_Otype ) @ V_t @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ V_T @ V_e @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[1005]) ).
thf(2684,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_u: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ V_T @ V_e @ V_t @ V_u ) ) @ V_T ) )
| ~ ( c_Type_Otyping @ V_e @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[1004]) ).
thf(2685,plain,
( ( ! [V_type1_H: $i,V_type2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H )
!= ( c_Type_Otype_OAtom @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1003]) ).
thf(2686,plain,
( ( ! [V_P: $i,V_T1: $i,V_T2: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1002]) ).
thf(2687,plain,
( ( ! [V_P: $i,V_T1a: $i,V_x: $i,V_T: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ V_P )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1a ) @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T ) )
| ( hBOOL @ ( hAPP @ V_P @ V_T1a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1001]) ).
thf(2688,plain,
( ( ! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type1 @ T_a ) ) @ ( c_Type_Otype_Otype__rec @ V_f1 @ V_f2 @ V_type2 @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(2689,plain,
( ( ! [V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i,T_a: $i] :
( ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) )
= $true ),
inference(copy,[status(thm)],[999]) ).
thf(2690,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_xa: $i,V_xb: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_xa ) @ V_xb ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xa ) @ V_xb ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[998]) ).
thf(2691,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_type1: $i,V_type2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Type_Otype_Otype__case @ V_f1 @ V_f2 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_type1 ) @ V_type2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[997]) ).
thf(2692,plain,
( ( ! [V_nat: $i,V_type1_H: $i,V_type2_H: $i] :
( ( c_Type_Otype_OAtom @ V_nat )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) ) )
= $true ),
inference(copy,[status(thm)],[996]) ).
thf(2693,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ V_a @ T_b @ T_a )
= ( hAPP @ ( hAPP @ V_f @ V_x ) @ ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[995]) ).
thf(2694,plain,
( ( ! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ V_f @ V_xs @ ( c_List_Ofoldr @ V_f @ V_ys @ V_a @ T_b @ T_a ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[994]) ).
thf(2695,plain,
( ( ! [V_f: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_ONil @ T_b ) @ V_a @ T_b @ T_a )
= V_a ) )
= $true ),
inference(copy,[status(thm)],[993]) ).
thf(2696,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[992]) ).
thf(2697,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[991]) ).
thf(2698,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)],[990]) ).
thf(2699,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)],[989]) ).
thf(2700,plain,
( ( ! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T2 )
| ~ ( c_InductTermi_OIT @ V_u )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T2 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[988]) ).
thf(2701,plain,
( ( ! [V_T1: $i,V_T2: $i,V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_Ta: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T1 ) @ V_T2 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T1 )
| ~ ( c_InductTermi_OIT @ V_u )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_T1 @ tc_Type_Otype ) @ V_t @ V_Ta )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[987]) ).
thf(2702,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i,T_a: $i,V_j: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ T_a ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[986]) ).
thf(2703,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[985]) ).
thf(2704,plain,
( ( ! [V_e: $i,V_t: $i,V_ts: $i,V_T: $i,V_Ts: $i] :
( ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ V_Ts @ V_T @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(copy,[status(thm)],[984]) ).
thf(2705,plain,
( ( ! [V_e: $i,V_t: $i,V_T: $i,V_ts: $i] :
( ( c_Type_Otyping @ V_e @ V_t @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ V_T @ V_e @ V_t @ V_ts ) @ V_T @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[983]) ).
thf(2706,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ v_n____ ) ) @ v_a____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ),
inference(copy,[status(thm)],[982]) ).
thf(2707,plain,
( ( c_InductTermi_OIT @ v_u____ )
= $true ),
inference(copy,[status(thm)],[981]) ).
thf(2708,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_a____ @ v_T_H_H____ )
= $true ),
inference(copy,[status(thm)],[980]) ).
thf(2709,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[979]) ).
thf(2710,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[978]) ).
thf(2711,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[977]) ).
thf(2712,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)],[976]) ).
thf(2713,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,T_a: $i,V_T: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ T_a )
= ( c_Type_Oshift @ ( c_Type_Oshift @ V_e @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ T_a ) @ ( c_Suc @ V_i ) @ V_U @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[975]) ).
thf(2714,plain,
( ( ! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) ) ) )
= $true ),
inference(copy,[status(thm)],[974]) ).
thf(2715,plain,
( ( ! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e_H @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ( c_Type_Otyping @ V_e_H @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[973]) ).
thf(2716,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ ( c_Lambda_OdB_OVar @ v_n____ ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(copy,[status(thm)],[972]) ).
thf(2717,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(copy,[status(thm)],[971]) ).
thf(2718,plain,
( ( ! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_T ) @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ) )
= $true ),
inference(copy,[status(thm)],[970]) ).
thf(2719,plain,
( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(copy,[status(thm)],[969]) ).
thf(2720,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( c_Lambda_Olift @ V_t @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[968]) ).
thf(2721,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type1 = V_type1_H ) ) )
= $true ),
inference(copy,[status(thm)],[967]) ).
thf(2722,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1 ) @ V_type2 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ V_type1_H ) @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ) )
= $true ),
inference(copy,[status(thm)],[966]) ).
thf(2723,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(2724,plain,
( ( ! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ) )
= $true ),
inference(copy,[status(thm)],[964]) ).
thf(2725,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[963]) ).
thf(2726,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[962]) ).
thf(2727,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[961]) ).
thf(2728,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[960]) ).
thf(2729,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[959]) ).
thf(2730,plain,
( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat )
= $true ),
inference(copy,[status(thm)],[958]) ).
thf(2731,plain,
( ( class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[957]) ).
thf(2732,plain,
( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_nat )
= $true ),
inference(copy,[status(thm)],[956]) ).
thf(2733,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[955]) ).
thf(2734,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[954]) ).
thf(2735,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[953]) ).
thf(2736,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[952]) ).
thf(2737,plain,
( ( class_Ring__and__Field_Opordered__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[951]) ).
thf(2738,plain,
( ( class_Ring__and__Field_Oordered__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[950]) ).
thf(2739,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(copy,[status(thm)],[949]) ).
thf(2740,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(2741,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[947]) ).
thf(2742,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(2743,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[945]) ).
thf(2744,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(2745,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(2746,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[942]) ).
thf(2747,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(2748,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(2749,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[939]) ).
thf(2750,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(2751,plain,
( ( class_Ring__and__Field_Omult__mono1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[937]) ).
thf(2752,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(copy,[status(thm)],[936]) ).
thf(2753,plain,
( ( class_Ring__and__Field_Omult__mono @ tc_nat )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(2754,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[934]) ).
thf(2755,plain,
( ( class_Ring__and__Field_Osemiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(2756,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(2757,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(2758,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(2759,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(2760,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(2761,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(2762,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(2763,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(2764,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(2765,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[1844]) ).
thf(2766,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_lessequals @ SX2 @ SX1 @ SX0 )
| ~ ( c_lessequals @ SX4 @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2567]) ).
thf(2767,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2531]) ).
thf(2768,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SX0 @ SX2 @ tc_nat ) )
| ( SX1 = SX2 )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2643]) ).
thf(2769,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2249]) ).
thf(2770,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2247]) ).
thf(2771,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat ) ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX1 @ tc_nat ) ) @ SX4 ) )
| ~ ( c_lessequals @ SX3 @ SX0 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SX0 @ SX3 @ tc_nat ) @ SX1 @ tc_nat ) ) @ SX2 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2008]) ).
thf(2772,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= SX0 )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2394]) ).
thf(2773,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX2 ) @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2214]) ).
thf(2774,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SX2 @ SX1 @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2641]) ).
thf(2775,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2146]) ).
thf(2776,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2221]) ).
thf(2777,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SX0 ) @ SX1 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SX0 ) @ SX2 @ tc_nat ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2561]) ).
thf(2778,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 ) )
| ( SX1
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2077]) ).
thf(2779,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Ring__and__Field_Oring @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) ) @ SX3 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX4 @ SX2 @ SX0 ) ) @ SX5 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SX1 @ SX4 @ SX0 ) @ SX2 @ SX0 ) ) @ SX3 )
= SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1846]) ).
thf(2780,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX0 ) ) @ SX1 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2462]) ).
thf(2781,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2635]) ).
thf(2782,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2646]) ).
thf(2783,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX3 ) @ SX2 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2253]) ).
thf(2784,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oappend @ SX1 @ SX2 @ SX0 ) )
| ( SX2
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2145]) ).
thf(2785,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( 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)],[2297]) ).
thf(2786,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( 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)],[2578]) ).
thf(2787,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX1 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1870]) ).
thf(2788,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SX0 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX3 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2686]) ).
thf(2789,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)],[2568]) ).
thf(2790,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)],[2498]) ).
thf(2791,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX0
!= ( c_List_Olist_OCons @ SX1 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2425]) ).
thf(2792,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_Power_Opower__class_Opower @ SX3 @ SX2 @ SX0 ) )
| ( SX1 = SX3 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SX2 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX3 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2310]) ).
thf(2793,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2251]) ).
thf(2794,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2078]) ).
thf(2795,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX2 ) @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2722]) ).
thf(2796,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[2405]) ).
thf(2797,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2002]) ).
thf(2798,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_Lambda_OdB_OAbs @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2544]) ).
thf(2799,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX0
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1971]) ).
thf(2800,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 )
!= ( c_Type_Otype_OAtom @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2685]) ).
thf(2801,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX0 @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX2 @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2296]) ).
thf(2802,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( SX1
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2507]) ).
thf(2803,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX3 @ SX0 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX4 @ SX0 ) ) )
| ( SX3 = SX4 )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2398]) ).
thf(2804,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oreplicate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oreplicate @ SX3 @ SX4 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1872]) ).
thf(2805,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( 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)],[2577]) ).
thf(2806,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2650]) ).
thf(2807,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)],[2569]) ).
thf(2808,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX0 )
| ( ( c_Orderings_Oord__class_Omax @ SX1 @ SX2 @ SX0 )
!= SX2 )
| ( c_lessequals @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1919]) ).
thf(2809,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 )
!= ( c_List_Oappend @ SX3 @ ( c_List_Olist_OCons @ SX4 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 ) )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2576]) ).
thf(2810,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2636]) ).
thf(2811,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX0 @ SX3 @ SX2 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1869]) ).
thf(2812,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Type_Otype_OAtom @ SX0 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2692]) ).
thf(2813,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX3 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX3 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX1 @ tc_nat ) ) )
| ( SX1 = SX3 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2158]) ).
thf(2814,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2627]) ).
thf(2815,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oreplicate @ SX1 @ SX2 @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2365]) ).
thf(2816,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX4 @ SX0 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX4 @ SX0 ) ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX2 @ SX0 ) ) )
| ( SX2 = SX4 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2156]) ).
thf(2817,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX1
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1972]) ).
thf(2818,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_lessequals @ SX4 @ SX3 @ SX0 )
| ~ ( c_lessequals @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2566]) ).
thf(2819,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)],[2500]) ).
thf(2820,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2000]) ).
thf(2821,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ~ ( class_Ring__and__Field_Omult__zero @ SX0 )
| ~ ( class_Power_Opower @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2711]) ).
thf(2822,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX2 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1998]) ).
thf(2823,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SX0 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX3 ) )
| ( hBOOL @ ( hAPP @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2687]) ).
thf(2824,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SX2 @ SX1 @ tc_nat ) )
| ~ ( c_lessequals @ SX1 @ SX2 @ tc_nat )
| ~ ( c_lessequals @ SX1 @ SX0 @ tc_nat )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2074]) ).
thf(2825,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX2 ) @ SX3 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX2 ) @ SX4 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX3 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2038]) ).
thf(2826,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX1 @ SX0 ) ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX2 @ SX0 ) )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2401]) ).
thf(2827,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)],[2073]) ).
thf(2828,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat ) ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX1 @ tc_nat ) ) @ SX4 ) )
| ~ ( c_lessequals @ SX0 @ SX3 @ tc_nat )
| ( SX2
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SX3 @ SX0 @ tc_nat ) @ SX1 @ tc_nat ) ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2009]) ).
thf(2829,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX2 ) @ SX3 ) )
| ~ ( c_HOL_Oord__class_Oless @ SX2 @ SX1 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SX0 @ SX3 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1969]) ).
thf(2830,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2222]) ).
thf(2831,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2154]) ).
thf(2832,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SX0 @ SX2 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SX0 @ tc_nat )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2076]) ).
thf(2833,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX2 ) @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2248]) ).
thf(2834,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2540]) ).
thf(2835,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX4 @ SX0 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX4 @ SX0 ) ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX2 @ SX0 ) ) )
| ( SX2 = SX4 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2157]) ).
thf(2836,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2533]) ).
thf(2837,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Ring__and__Field_Oring @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) ) @ SX3 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX4 @ SX2 @ SX0 ) ) @ SX5 ) )
| ( SX3
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SX4 @ SX1 @ SX0 ) @ SX2 @ SX0 ) ) @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1847]) ).
thf(2838,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SX0 @ SX2 @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2642]) ).
thf(2839,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)],[2509]) ).
thf(2840,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SX0 @ SX1 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1866]) ).
thf(2841,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX3 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX3 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX1 @ tc_nat ) ) )
| ( SX1 = SX3 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2159]) ).
thf(2842,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2545]) ).
thf(2843,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)],[2629]) ).
thf(2844,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX1 @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2176]) ).
thf(2845,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)],[2499]) ).
thf(2846,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( 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)],[2298]) ).
thf(2847,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2142]) ).
thf(2848,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2534]) ).
thf(2849,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2252]) ).
thf(2850,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)],[1976]) ).
thf(2851,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX1 @ SX0 ) ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX2 @ SX0 ) )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2402]) ).
thf(2852,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ ( c_Suc @ SX2 ) @ SX0 )
!= ( c_Power_Opower__class_Opower @ SX3 @ ( c_Suc @ SX2 ) @ SX0 ) )
| ( SX1 = SX3 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX3 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2453]) ).
thf(2853,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= SX1 )
| ( SX0
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2396]) ).
thf(2854,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2535]) ).
thf(2855,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Oappend @ SX1 @ SX0 @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2397]) ).
thf(2856,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1999]) ).
thf(2857,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2259]) ).
thf(2858,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2258]) ).
thf(2859,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX2 ) @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2213]) ).
thf(2860,plain,
( ( ! [SX0: $i] :
( SX0
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2406]) ).
thf(2861,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2250]) ).
thf(2862,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oreplicate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2362]) ).
thf(2863,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX0 )
| ( ( c_Orderings_Oord__class_Omin @ SX1 @ SX2 @ SX0 )
!= SX1 )
| ( c_lessequals @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2046]) ).
thf(2864,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2634]) ).
thf(2865,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX0 @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SX2 ) )
| ( SX0
= ( c_Lambda_OdB_OAbs @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2223]) ).
thf(2866,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oreplicate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oreplicate @ SX3 @ SX4 @ SX2 ) )
| ( SX1 = SX4 )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2670]) ).
thf(2867,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SX2 @ SX3 @ SX4 ) )
| ~ ( c_Type_Otyping @ SX5 @ SX3 @ SX1 )
| ~ ( c_InductTermi_OIT @ SX3 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SX5 @ SX4 @ SX1 @ tc_Type_Otype ) @ SX2 @ SX6 )
| ~ ( c_InductTermi_OIT @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2700]) ).
thf(2868,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ~ ( class_Ring__and__Field_Omult__zero @ SX0 )
| ~ ( class_Power_Opower @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2489]) ).
thf(2869,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX1 @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2110]) ).
thf(2870,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 )
!= ( c_List_Oappend @ SX3 @ ( c_List_Olist_OCons @ SX4 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2575]) ).
thf(2871,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Oappend @ SX0 @ SX1 @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2395]) ).
thf(2872,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2161]) ).
thf(2873,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2649]) ).
thf(2874,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 ) )
| ( 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)],[2017]) ).
thf(2875,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2490]) ).
thf(2876,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Olist_OCons @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2224]) ).
thf(2877,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2532]) ).
thf(2878,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oappend @ SX1 @ SX2 @ SX0 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2144]) ).
thf(2879,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Type_Otype_OAtom @ SX0 )
!= ( c_Type_Otype_OAtom @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1949]) ).
thf(2880,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2018]) ).
thf(2881,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2501]) ).
thf(2882,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX2 ) @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2721]) ).
thf(2883,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_Lambda_OdB_OVar @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2480]) ).
thf(2884,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX2 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1997]) ).
thf(2885,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)],[2510]) ).
thf(2886,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2153]) ).
thf(2887,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)],[2072]) ).
thf(2888,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[2324]) ).
thf(2889,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= SX0 )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2647]) ).
thf(2890,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX3 @ tc_nat ) ) )
| ( SX2 = SX3 )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2399]) ).
thf(2891,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2628]) ).
thf(2892,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SX0 ) @ SX1 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SX2 @ SX3 @ SX4 ) )
| ~ ( c_Type_Otyping @ SX5 @ SX3 @ SX0 )
| ~ ( c_InductTermi_OIT @ SX3 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SX5 @ SX4 @ SX0 @ tc_Type_Otype ) @ SX2 @ SX6 )
| ~ ( c_InductTermi_OIT @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2701]) ).
thf(2893,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)],[2511]) ).
thf(2894,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_T_H_H____ @ tc_Type_Otype ) @ ( c_Lambda_Olift @ v_u____ @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ v_T_H_H____ ) @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ v_Ts____ @ v_T_H____ @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(2895,plain,
! [SV1: $i] :
( ( ! [SY2876: $i,SY2877: $i,SY2878: $i,SY2879: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1 @ SY2876 @ tc_nat ) ) @ SY2877 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2878 @ SY2876 @ tc_nat ) ) @ SY2879 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2877 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2878 @ SV1 @ tc_nat ) @ SY2876 @ tc_nat ) ) @ SY2879 ) @ tc_nat )
| ~ ( c_lessequals @ SV1 @ SY2878 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2896,plain,
! [SV2: $i] :
( ( ! [SY2880: $i,SY2881: $i,SY2882: $i,SY2883: $i] :
( ( c_HOL_Oord__class_Oless @ SV2 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2880 @ SY2881 @ tc_nat ) @ SY2882 @ tc_nat ) ) @ SY2883 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2881 @ SY2882 @ tc_nat ) ) @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2880 @ SY2882 @ tc_nat ) ) @ SY2883 ) @ tc_nat )
| ~ ( c_lessequals @ SY2881 @ SY2880 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2897,plain,
! [SV3: $i] :
( ( ! [SY2884: $i,SY2885: $i,SY2886: $i,SY2887: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV3 @ SY2884 @ tc_nat ) ) @ SY2885 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2886 @ SY2884 @ tc_nat ) ) @ SY2887 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV3 @ SY2886 @ tc_nat ) @ SY2884 @ tc_nat ) ) @ SY2885 ) @ SY2887 @ tc_nat )
| ~ ( c_lessequals @ SY2886 @ SV3 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2898,plain,
! [SV4: $i] :
( ( ! [SY2888: $i,SY2889: $i,SY2890: $i,SY2891: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SY2888 @ tc_nat ) @ SY2889 @ tc_nat ) ) @ SY2890 ) @ SY2891 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV4 @ SY2889 @ tc_nat ) ) @ SY2890 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2888 @ SY2889 @ tc_nat ) ) @ SY2891 ) @ tc_nat )
| ~ ( c_lessequals @ SY2888 @ SV4 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2899,plain,
! [SV5: $i] :
( ( ! [SY2892: $i,SY2893: $i,SY2894: $i,SY2895: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV5 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SY2892 @ SY2893 @ SV5 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2894 @ SY2892 @ SV5 ) @ SY2893 @ SV5 ) ) @ SY2895 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SY2894 @ SY2893 @ SV5 ) ) @ SY2895 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2900,plain,
! [SV6: $i] :
( ( ! [SY2896: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV6 ) ) @ SY2896 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV6 ) @ SY2896 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2901,plain,
! [SV7: $i] :
( ( ! [SY2897: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV7 ) @ ( c_Suc @ SY2897 ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV7 ) @ SY2897 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2902,plain,
! [SV8: $i] :
( ( ! [SY2898: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV8 )
| ~ ( class_Power_Opower @ SV8 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ ( c_Suc @ SY2898 ) @ SV8 )
= ( c_HOL_Ozero__class_Ozero @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2903,plain,
! [SV9: $i] :
( ( ! [SY2899: $i,SY2900: $i,SY2901: $i,SY2902: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2899 @ SY2900 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SY2901 @ SY2902 @ SV9 ) @ SV9 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SY2900 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SY2901 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SY2900 @ SY2902 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SY2899 @ SY2901 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2904,plain,
! [SV10: $i] :
( ( ! [SY2903: $i] :
( ( hBOOL @ ( hAPP @ SV10 @ SY2903 ) )
| ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV10 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2905,plain,
! [SV11: $i] :
( ( ! [SY2904: $i,SY2905: $i] :
( ~ ( class_Orderings_Olinorder @ SV11 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY2904 @ SY2905 @ SV11 ) @ SY2904 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2906,plain,
! [SV12: $i] :
( ( ! [SY2906: $i,SY2907: $i] :
( ~ ( class_Orderings_Olinorder @ SV12 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY2906 @ SY2907 @ SV12 ) @ SY2907 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2907,plain,
! [SV13: $i] :
( ( ! [SY2908: $i,SY2909: $i,SY2910: $i] :
( ~ ( class_Orderings_Olinorder @ SV13 )
| ( c_lessequals @ SY2908 @ ( c_Orderings_Oord__class_Omin @ SY2909 @ SY2910 @ SV13 ) @ SV13 )
| ~ ( c_lessequals @ SY2908 @ SY2910 @ SV13 )
| ~ ( c_lessequals @ SY2908 @ SY2909 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2908,plain,
! [SV14: $i] :
( ( ! [SY2911: $i,SY2912: $i,SY2913: $i] :
( ~ ( class_Orderings_Olinorder @ SV14 )
| ( c_lessequals @ SY2911 @ ( c_Orderings_Oord__class_Omin @ SY2912 @ SY2913 @ SV14 ) @ SV14 )
| ~ ( c_lessequals @ SY2911 @ SY2913 @ SV14 )
| ~ ( c_lessequals @ SY2911 @ SY2912 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2909,plain,
! [SV15: $i] :
( ( ! [SY2914: $i,SY2915: $i,SY2916: $i] :
( ~ ( class_Orderings_Olinorder @ SV15 )
| ( c_lessequals @ SY2914 @ ( c_Orderings_Oord__class_Omin @ SY2915 @ SY2916 @ SV15 ) @ SV15 )
| ~ ( c_lessequals @ SY2914 @ SY2916 @ SV15 )
| ~ ( c_lessequals @ SY2914 @ SY2915 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2910,plain,
! [SV16: $i] :
( ( ! [SY2917: $i,SY2918: $i,SY2919: $i,SY2920: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV16 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SY2917 @ SY2918 @ SV16 ) ) @ SY2919 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SY2920 @ SY2918 @ SV16 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2917 @ SY2920 @ SV16 ) @ SY2918 @ SV16 ) ) @ SY2919 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2911,plain,
! [SV17: $i] :
( ( ! [SY2921: $i,SY2922: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV17 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SY2921 @ SY2922 @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SY2921 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2912,plain,
! [SV18: $i] :
( ( ! [SY2923: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV18 @ SY2923 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV18 @ SY2923 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2913,plain,
! [SV19: $i] :
( ( ! [SY2924: $i,SY2925: $i,SY2926: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV19 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SY2924 @ SY2925 @ SV19 ) @ SY2926 @ SV19 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SY2924 @ SY2926 @ SV19 ) @ ( c_HOL_Ominus__class_Ominus @ SY2925 @ SY2926 @ SV19 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2914,plain,
! [SV20: $i] :
( ( ! [SY2927: $i,SY2928: $i,SY2929: $i] :
( ~ ( class_Orderings_Olinorder @ SV20 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY2927 @ SY2928 @ SV20 ) @ SY2929 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SY2928 @ SY2929 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SY2927 @ SY2929 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2915,plain,
! [SV21: $i] :
( ( ! [SY2930: $i,SY2931: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV21 @ SY2930 @ tc_nat ) ) @ SY2931 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV21 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2930 ) @ SY2931 ) @ tc_nat ) )
| ~ ( c_lessequals @ SY2930 @ SV21 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2916,plain,
! [SV22: $i] :
( ( ! [SY2932: $i,SY2933: $i,SY2934: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV22 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV22 )
| ( c_HOL_Oord__class_Oless @ SY2932 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SY2933 ) @ SY2934 ) @ SV22 )
| ~ ( c_lessequals @ SY2932 @ SY2934 @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SY2933 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2917,plain,
! [SV23: $i] :
( ( ! [SY2935: $i,SY2936: $i] :
( ( c_HOL_Oord__class_Oless @ SV23 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2935 ) @ SY2936 ) @ tc_nat )
| ~ ( c_lessequals @ SV23 @ SY2935 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2936 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2918,plain,
! [SV24: $i] :
( ( ! [SY2937: $i,SY2938: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV24 )
| ( c_lessequals @ SY2937 @ SY2938 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2937 @ SV24 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2938 @ SV24 ) @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2919,plain,
! [SV25: $i] :
( ( ! [SY2939: $i,SY2940: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV25 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2939 @ SV25 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2940 @ SV25 ) @ SV25 )
| ~ ( c_lessequals @ SY2939 @ SY2940 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2920,plain,
! [SV26: $i] :
( ( ! [SY2941: $i,SY2942: $i,SY2943: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV26 @ SY2941 @ SY2942 ) @ ( c_Lambda_Osubst @ SY2943 @ SY2941 @ SY2942 ) )
| ~ ( c_Lambda_Obeta @ SV26 @ SY2943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2921,plain,
! [SV27: $i] :
( ( ! [SY2944: $i,SY2945: $i,SY2946: $i] :
( ~ ( class_Orderings_Olinorder @ SV27 )
| ( c_HOL_Oord__class_Oless @ SY2944 @ ( c_Orderings_Oord__class_Omin @ SY2945 @ SY2946 @ SV27 ) @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SY2944 @ SY2946 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SY2944 @ SY2945 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2922,plain,
! [SV28: $i] :
( ( ! [SY2947: $i,SY2948: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV28 @ SY2947 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV28 @ SY2948 @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV28 @ SY2948 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV28 @ SY2947 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2923,plain,
! [SV29: $i] :
( ( ! [SY2949: $i,SY2950: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV29 @ SY2949 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV29 @ SY2950 @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV29 @ SY2950 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV29 @ SY2949 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2924,plain,
! [SV30: $i] :
( ( ! [SY2951: $i,SY2952: $i,SY2953: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV30 )
| ~ ( class_Int_Onumber__ring @ SV30 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SY2951 @ SY2952 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY2951 @ SY2953 @ SV30 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SY2951 @ SY2953 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY2951 @ SY2952 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2925,plain,
! [SV31: $i] :
( ( ! [SY2954: $i,SY2955: $i,SY2956: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV31 )
| ~ ( class_Int_Onumber__ring @ SV31 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SY2954 @ SY2955 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY2954 @ SY2956 @ SV31 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SY2954 @ SY2956 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY2954 @ SY2955 @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2926,plain,
! [SV32: $i] :
( ( ! [SY2957: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_Suc @ SV32 ) @ ( c_Suc @ SY2957 ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omax @ SV32 @ SY2957 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2927,plain,
! [SV33: $i] :
( ( ( SV33
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV33 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2928,plain,
! [SV34: $i] :
( ( ! [SY2958: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV34 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SY2958 @ SV34 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SY2958 ) @ SY2958 ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2929,plain,
! [SV35: $i] :
( ( ! [SY2959: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV35 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV35 ) @ SY2959 ) @ SY2959 ) @ SV35 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SY2959 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2930,plain,
! [SV36: $i] :
( ( ! [SY2960: $i,SY2961: $i] :
( ~ ( class_Orderings_Olinorder @ SV36 )
| ( ( c_Orderings_Oord__class_Omin @ SY2960 @ ( c_Orderings_Oord__class_Omin @ SY2960 @ SY2961 @ SV36 ) @ SV36 )
= ( c_Orderings_Oord__class_Omin @ SY2960 @ SY2961 @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2931,plain,
! [SV37: $i] :
( ( ! [SY2962: $i,SY2963: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV37 ) @ SY2962 @ SY2963 )
= ( c_Lambda_OdB_OVar @ SV37 ) )
| ( SV37 = SY2963 )
| ( c_HOL_Oord__class_Oless @ SY2963 @ SV37 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2932,plain,
! [SV38: $i] :
( ( ! [SY2964: $i,SY2965: $i,SY2966: $i,SY2967: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV38 @ SY2964 @ tc_nat ) ) @ SY2965 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2966 @ SY2964 @ tc_nat ) ) @ SY2967 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SY2965 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2966 @ SV38 @ tc_nat ) @ SY2964 @ tc_nat ) ) @ SY2967 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV38 @ SY2966 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2933,plain,
! [SV39: $i] :
( ( ! [SY2968: $i,SY2969: $i,SY2970: $i,SY2971: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV39 @ SY2968 @ tc_nat ) ) @ SY2969 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2970 @ SY2968 @ tc_nat ) ) @ SY2971 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SY2970 @ tc_nat ) @ SY2968 @ tc_nat ) ) @ SY2969 ) @ SY2971 @ tc_nat ) )
| ~ ( c_lessequals @ SY2970 @ SV39 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2934,plain,
! [SV40: $i] :
( ( ! [SY2972: $i,SY2973: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV40 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ ( c_HOL_Ominus__class_Ominus @ SY2972 @ SY2973 @ SV40 ) ) @ SY2973 )
= SY2972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2935,plain,
! [SV41: $i] :
( ( ! [SY2974: $i,SY2975: $i] :
( ~ ( hBOOL @ ( hAPP @ SV41 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2974 ) @ SY2975 ) @ SY2974 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV41 @ SY2975 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2936,plain,
! [SV42: $i] :
( ( ! [SY2976: $i,SY2977: $i] :
( ~ ( hBOOL @ ( hAPP @ SV42 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2976 ) @ SY2977 ) @ SY2976 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV42 @ SY2977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2937,plain,
! [SV43: $i] :
( ( ! [SY2978: $i,SY2979: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV43 @ SY2978 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2979 @ SY2978 @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2978 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2938,plain,
! [SV44: $i] :
( ( ! [SY2980: $i,SY2981: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV44 @ SY2980 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV44 @ SY2981 @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV44 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2939,plain,
! [SV45: $i] :
( ( ! [SY2982: $i,SY2983: $i,SY2984: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV45 )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SY2982 @ SY2983 @ SV45 ) @ SY2984 @ SV45 )
= ( c_Power_Opower__class_Opower @ SY2982 @ ( c_HOL_Otimes__class_Otimes @ SY2983 @ SY2984 @ tc_nat ) @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2940,plain,
! [SV46: $i] :
( ( ! [SY2985: $i] :
( ( hBOOL @ ( hAPP @ SV46 @ SY2985 ) )
| ~ ( hBOOL @ ( hAPP @ SV46 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ SV46 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV46 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2941,plain,
! [SV47: $i] :
( ( ! [SY2986: $i,SY2987: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV47 )
| ( ( c_Power_Opower__class_Opower @ SY2986 @ ( c_Suc @ SY2987 ) @ SV47 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY2986 @ SY2987 @ SV47 ) @ SY2986 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2942,plain,
! [SV48: $i] :
( ( ! [SY2988: $i,SY2989: $i] :
( ~ ( class_Power_Opower @ SV48 )
| ( ( c_Power_Opower__class_Opower @ SY2988 @ ( c_Suc @ SY2989 ) @ SV48 )
= ( c_HOL_Otimes__class_Otimes @ SY2988 @ ( c_Power_Opower__class_Opower @ SY2988 @ SY2989 @ SV48 ) @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2943,plain,
! [SV49: $i] :
( ( ! [SY2990: $i,SY2991: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
| ( ( c_Power_Opower__class_Opower @ SY2990 @ ( c_Suc @ SY2991 ) @ SV49 )
= ( c_HOL_Otimes__class_Otimes @ SY2990 @ ( c_Power_Opower__class_Opower @ SY2990 @ SY2991 @ SV49 ) @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2944,plain,
! [SV50: $i] :
( ( ! [SY2992: $i,SY2993: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
| ( ( c_Power_Opower__class_Opower @ SY2992 @ ( c_Suc @ SY2993 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ SY2992 @ ( c_Power_Opower__class_Opower @ SY2992 @ SY2993 @ SV50 ) @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2945,plain,
! [SV51: $i] :
( ( ! [SY2994: $i,SY2995: $i,SY2996: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SY2994 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2995 ) @ SY2996 ) @ tc_nat )
| ~ ( c_lessequals @ SY2994 @ SY2996 @ tc_nat )
| ~ ( c_lessequals @ SV51 @ SY2995 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2946,plain,
! [SV52: $i] :
( ( ! [SY2997: $i,SY2998: $i,SY2999: $i,SY3000: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV52 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SY2997 ) @ SY2998 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SY2999 ) @ SY3000 ) @ SV52 )
| ~ ( c_lessequals @ SY2998 @ SY3000 @ SV52 )
| ~ ( c_lessequals @ SY2997 @ SY2999 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2947,plain,
! [SV53: $i] :
( ( ! [SY3001: $i] :
( ( c_HOL_Oord__class_Oless @ SV53 @ ( c_Suc @ SY3001 ) @ tc_nat )
| ~ ( c_lessequals @ SV53 @ SY3001 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2948,plain,
! [SV54: $i] :
( ( ! [SY3002: $i] :
( ( c_lessequals @ SV54 @ SY3002 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ ( c_Suc @ SY3002 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2949,plain,
! [SV55: $i] :
( ( ~ ( c_lessequals @ SV55 @ SV55 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV55 @ ( c_Suc @ SV55 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2950,plain,
! [SV56: $i] :
( ( ! [SY3003: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV56 )
| ( ( c_List_Olistsum @ SY3003 @ SV56 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ ( c_HOL_Ozero__class_Ozero @ SV56 ) @ SY3003 @ SV56 @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2951,plain,
! [SV57: $i] :
( ( ! [SY3004: $i,SY3005: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV57 )
| ( ( c_HOL_Otimes__class_Otimes @ SY3004 @ SY3005 @ SV57 )
= ( c_HOL_Otimes__class_Otimes @ SY3005 @ SY3004 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2952,plain,
! [SV58: $i] :
( ( ! [SY3006: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV58 @ SY3006 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SY3006 @ SV58 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2953,plain,
! [SV59: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV59 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) )
= ( c_HOL_Ozero__class_Ozero @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2954,plain,
! [SV60: $i] :
( ( ! [SY3007: $i,SY3008: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV60 )
| ( ( c_HOL_Otimes__class_Otimes @ SY3007 @ SY3008 @ SV60 )
= ( c_HOL_Otimes__class_Otimes @ SY3008 @ SY3007 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2955,plain,
! [SV61: $i] :
( ( ! [SY3009: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV61 @ SY3009 @ tc_nat ) @ ( c_Suc @ SV61 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2956,plain,
! [SV62: $i] :
( ( ! [SY3010: $i,SY3011: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV62 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SY3010 ) @ SY3011 ) @ SV62 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SY3011 @ SV62 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SY3010 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2957,plain,
! [SV63: $i] :
( ( ! [SY3012: $i,SY3013: $i,SY3014: $i] :
( ~ ( class_Orderings_Opreorder @ SV63 )
| ( c_HOL_Oord__class_Oless @ SY3012 @ SY3013 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SY3014 @ SY3013 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SY3012 @ SY3014 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2958,plain,
! [SV64: $i] :
( ( ! [SY3015: $i,SY3016: $i,SY3017: $i] :
( ~ ( class_Orderings_Oorder @ SV64 )
| ( c_HOL_Oord__class_Oless @ SY3015 @ SY3016 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SY3015 @ SY3017 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SY3017 @ SY3016 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2959,plain,
! [SV65: $i] :
( ( ! [SY3018: $i,SY3019: $i,SY3020: $i] :
( ( c_Type_Otyping @ SV65 @ SY3018 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY3019 @ SV65 @ SY3020 @ SY3018 ) )
| ~ ( c_Type_Otyping @ SV65 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3020 ) @ SY3018 ) @ SY3019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2960,plain,
! [SV66: $i] :
( ( ! [SY3021: $i,SY3022: $i] :
( ~ ( class_Orderings_Olinorder @ SV66 )
| ( ( c_Orderings_Oord__class_Omax @ SY3021 @ SY3022 @ SV66 )
= SY3022 )
| ~ ( c_lessequals @ SY3021 @ SY3022 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2961,plain,
! [SV67: $i] :
( ( ! [SY3023: $i,SY3024: $i] :
( ~ ( class_Orderings_Olinorder @ SV67 )
| ( ( c_Orderings_Oord__class_Omax @ SY3023 @ SY3024 @ SV67 )
= SY3023 )
| ~ ( c_lessequals @ SY3024 @ SY3023 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2962,plain,
! [SV68: $i] :
( ( ! [SY3025: $i,SY3026: $i,SY3027: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SY3025 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SY3026 ) @ SY3027 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SY3025 ) @ SY3026 ) ) @ SY3027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2963,plain,
! [SV69: $i] :
( ( ! [SY3028: $i,SY3029: $i,SY3030: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV69 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SY3028 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SY3029 ) @ SY3030 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SY3029 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SY3028 ) @ SY3030 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2964,plain,
! [SV70: $i] :
( ( ! [SY3031: $i,SY3032: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV70 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3031 ) @ SY3032 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3031 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV70 ) @ SY3032 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2965,plain,
! [SV71: $i] :
( ( ! [SY3033: $i,SY3034: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV71 ) @ SY3033 ) ) @ SY3034 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3033 ) @ SY3034 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2966,plain,
! [SV72: $i] :
( ( ! [SY3035: $i,SY3036: $i] :
( ( hBOOL @ ( hAPP @ SV72 @ SY3035 ) )
| ( hBOOL @ ( hAPP @ SV72 @ SY3036 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3036 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV72 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV72 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2967,plain,
! [SV73: $i] :
( ( ! [SY3037: $i] : ( c_HOL_Oord__class_Oless @ SV73 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV73 ) @ SY3037 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2968,plain,
! [SV74: $i] :
( ( ! [SY3038: $i] : ( c_HOL_Oord__class_Oless @ SV74 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3038 ) @ SV74 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2969,plain,
! [SV75: $i] :
( ( ! [SY3039: $i] : ( c_HOL_Oord__class_Oless @ SV75 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV75 ) @ SY3039 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2970,plain,
! [SV76: $i] :
( ( ! [SY3040: $i,SY3041: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV76 ) @ SY3040 ) @ SY3041 @ tc_nat )
| ~ ( c_lessequals @ SV76 @ ( c_HOL_Ominus__class_Ominus @ SY3041 @ SY3040 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3040 @ SY3041 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2971,plain,
! [SV77: $i] :
( ( ! [SY3042: $i,SY3043: $i] :
( ( c_lessequals @ SV77 @ ( c_HOL_Ominus__class_Ominus @ SY3042 @ SY3043 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV77 ) @ SY3043 ) @ SY3042 @ tc_nat )
| ~ ( c_lessequals @ SY3043 @ SY3042 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2972,plain,
! [SV78: $i] :
( ( ! [SY3044: $i,SY3045: $i,SY3046: $i] :
( ~ ( class_Orderings_Olinorder @ SV78 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY3044 @ SY3045 @ SV78 ) @ SY3046 @ SV78 )
| ~ ( c_lessequals @ SY3045 @ SY3046 @ SV78 )
| ~ ( c_lessequals @ SY3044 @ SY3046 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2973,plain,
! [SV79: $i] :
( ( ! [SY3047: $i,SY3048: $i,SY3049: $i] :
( ~ ( class_Orderings_Olinorder @ SV79 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY3047 @ SY3048 @ SV79 ) @ SY3049 @ SV79 )
| ~ ( c_lessequals @ SY3048 @ SY3049 @ SV79 )
| ~ ( c_lessequals @ SY3047 @ SY3049 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2974,plain,
! [SV80: $i] :
( ( ! [SY3050: $i,SY3051: $i,SY3052: $i] :
( ~ ( class_Orderings_Olinorder @ SV80 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY3050 @ SY3051 @ SV80 ) @ SY3052 @ SV80 )
| ~ ( c_lessequals @ SY3051 @ SY3052 @ SV80 )
| ~ ( c_lessequals @ SY3050 @ SY3052 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2975,plain,
! [SV81: $i] :
( ( ! [SY3053: $i,SY3054: $i] :
( ~ ( class_Orderings_Olinorder @ SV81 )
| ( c_lessequals @ SY3053 @ ( c_Orderings_Oord__class_Omax @ SY3053 @ SY3054 @ SV81 ) @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2976,plain,
! [SV82: $i] :
( ( ! [SY3055: $i,SY3056: $i] :
( ~ ( class_Orderings_Olinorder @ SV82 )
| ( c_lessequals @ SY3055 @ ( c_Orderings_Oord__class_Omax @ SY3056 @ SY3055 @ SV82 ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2977,plain,
! [SV83: $i] :
( ( ! [SY3057: $i] :
( ( c_List_Oappend @ SV83 @ ( c_List_Olist_ONil @ SY3057 ) @ SY3057 )
= SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2978,plain,
! [SV84: $i] :
( ( ! [SY3058: $i] :
( SV84
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY3058 ) @ SV84 @ SY3058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2979,plain,
! [SV85: $i] :
( ( ! [SY3059: $i] :
( SV85
= ( c_List_Oappend @ SV85 @ ( c_List_Olist_ONil @ SY3059 ) @ SY3059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2980,plain,
! [SV86: $i] :
( ( ! [SY3060: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV86 ) @ SY3060 @ SV86 )
= SY3060 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2981,plain,
! [SV87: $i] :
( ( ! [SY3061: $i] :
( SV87
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY3061 ) @ SV87 @ SY3061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2982,plain,
! [SV88: $i] :
( ( ! [SY3062: $i] :
( ~ ( class_Orderings_Obot @ SV88 )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV88 ) @ SY3062 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2983,plain,
! [SV89: $i] :
( ( ! [SY3063: $i,SY3064: $i,SY3065: $i] :
( ( c_Nat_Onat_Onat__rec @ SV89 @ SY3063 @ ( c_Suc @ SY3064 ) @ SY3065 )
= ( hAPP @ ( hAPP @ SY3063 @ SY3064 ) @ ( c_Nat_Onat_Onat__rec @ SV89 @ SY3063 @ SY3064 @ SY3065 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2984,plain,
! [SV90: $i] :
( ( ! [SY3066: $i,SY3067: $i,SY3068: $i,SY3069: $i,SY3070: $i,SY3071: $i,SY3072: $i,SY3073: $i] :
( ( ( hAPP @ ( hAPP @ SV90 @ ( hAPP @ ( hAPP @ SV90 @ SY3066 ) @ SY3067 ) ) @ SY3068 )
= ( hAPP @ ( hAPP @ SV90 @ SY3066 ) @ ( c_HOL_Otimes__class_Otimes @ SY3067 @ SY3068 @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3069 @ SY3070 @ SV90 @ SY3071 @ SY3072 @ SY3073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2985,plain,
! [SV91: $i] :
( ( ! [SY3074: $i,SY3075: $i,SY3076: $i] :
( ~ ( class_Orderings_Olinorder @ SV91 )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SY3074 @ SY3075 @ SV91 ) @ SY3076 @ SV91 )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SY3074 @ SY3076 @ SV91 ) @ ( c_Orderings_Oord__class_Omin @ SY3075 @ SY3076 @ SV91 ) @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2986,plain,
! [SV92: $i] :
( ( ! [SY3077: $i,SY3078: $i,SY3079: $i] :
( ~ ( class_Orderings_Olinorder @ SV92 )
| ( ( c_Orderings_Oord__class_Omin @ SY3077 @ ( c_Orderings_Oord__class_Omax @ SY3078 @ SY3079 @ SV92 ) @ SV92 )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SY3077 @ SY3078 @ SV92 ) @ ( c_Orderings_Oord__class_Omin @ SY3077 @ SY3079 @ SV92 ) @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2987,plain,
! [SV93: $i] :
( ( ! [SY3080: $i,SY3081: $i,SY3082: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV93 )
| ( c_lessequals @ SY3080 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SY3081 ) @ SY3082 ) @ SV93 )
| ~ ( c_lessequals @ SY3080 @ SY3082 @ SV93 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SY3081 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2988,plain,
! [SV94: $i] :
( ( ! [SY3083: $i,SY3084: $i,SY3085: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV94 )
| ( c_lessequals @ SY3083 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SY3084 ) @ SY3085 ) @ SV94 )
| ~ ( c_lessequals @ SY3083 @ SY3084 @ SV94 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SY3085 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2989,plain,
! [SV95: $i] :
( ( ! [SY3086: $i] :
( ( hBOOL @ ( hAPP @ SV95 @ SY3086 ) )
| ~ ( hBOOL @ ( hAPP @ SV95 @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV95 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2990,plain,
! [SV96: $i] :
( ( ! [SY3087: $i] :
( ( hBOOL @ ( hAPP @ SV96 @ SY3087 ) )
| ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ SV96 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2991,plain,
! [SV97: $i] :
( ( ! [SY3088: $i] :
( ( c_lessequals @ ( c_Suc @ SV97 ) @ SY3088 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV97 @ SY3088 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2992,plain,
! [SV98: $i] :
( ( ! [SY3089: $i] :
( ( c_HOL_Oord__class_Oless @ SV98 @ SY3089 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV98 ) @ SY3089 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2993,plain,
! [SV99: $i] :
( ( ! [SY3090: $i] :
( ( c_lessequals @ ( c_Suc @ SV99 ) @ SY3090 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV99 @ SY3090 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2994,plain,
! [SV100: $i] :
( ( ! [SY3091: $i] :
( ( c_HOL_Oord__class_Oless @ SV100 @ SY3091 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV100 ) @ SY3091 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2995,plain,
! [SV101: $i] :
( ( ! [SY3092: $i,SY3093: $i] :
( ( c_HOL_Oord__class_Oless @ SV101 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3092 ) @ SY3093 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV101 @ SY3092 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2996,plain,
! [SV102: $i] :
( ( ! [SY3094: $i,SY3095: $i] :
( ( c_HOL_Oord__class_Oless @ SV102 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3094 ) @ SY3095 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV102 @ SY3095 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2997,plain,
! [SV103: $i] :
( ( ! [SY3096: $i,SY3097: $i] :
( ( c_HOL_Oord__class_Oless @ SV103 @ SY3096 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV103 ) @ SY3097 ) @ SY3096 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2998,plain,
! [SV104: $i] :
( ( ! [SY3098: $i,SY3099: $i] :
( ( c_HOL_Oord__class_Oless @ SV104 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3098 ) @ SY3099 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV104 @ SY3098 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2999,plain,
! [SV105: $i] :
( ( ! [SY3100: $i,SY3101: $i] :
( ( c_HOL_Oord__class_Oless @ SV105 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3100 ) @ SY3101 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV105 @ SY3101 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(3000,plain,
! [SV106: $i] :
( ( ! [SY3102: $i,SY3103: $i,SY3104: $i,SY3105: $i,SY3106: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV106 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SY3102 @ SY3103 @ SV106 ) ) @ SY3104 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SY3105 @ SY3103 @ SV106 ) ) @ SY3106 ) @ SV106 )
| ~ ( c_lessequals @ SY3104 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3105 @ SY3102 @ SV106 ) @ SY3103 @ SV106 ) ) @ SY3106 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(3001,plain,
! [SV107: $i] :
( ( ! [SY3107: $i,SY3108: $i,SY3109: $i,SY3110: $i,SY3111: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV107 )
| ( c_lessequals @ SY3107 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3108 @ SY3109 @ SV107 ) @ SY3110 @ SV107 ) ) @ SY3111 ) @ SV107 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SY3109 @ SY3110 @ SV107 ) ) @ SY3107 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SY3108 @ SY3110 @ SV107 ) ) @ SY3111 ) @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(3002,plain,
! [SV108: $i] :
( ( ! [SY3112: $i,SY3113: $i,SY3114: $i,SY3115: $i,SY3116: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV108 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SY3112 @ SY3113 @ SV108 ) ) @ SY3114 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SY3115 @ SY3113 @ SV108 ) ) @ SY3116 ) @ SV108 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3112 @ SY3115 @ SV108 ) @ SY3113 @ SV108 ) ) @ SY3114 ) @ SY3116 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(3003,plain,
! [SV109: $i] :
( ( ! [SY3117: $i,SY3118: $i,SY3119: $i,SY3120: $i,SY3121: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV109 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3117 @ SY3118 @ SV109 ) @ SY3119 @ SV109 ) ) @ SY3120 ) @ SY3121 @ SV109 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SY3117 @ SY3119 @ SV109 ) ) @ SY3120 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SY3118 @ SY3119 @ SV109 ) ) @ SY3121 ) @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(3004,plain,
! [SV110: $i] :
( ( ! [SY3122: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV110 ) @ SY3122 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV110 @ SY3122 @ tc_nat ) ) )
| ~ ( c_lessequals @ SY3122 @ SV110 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(3005,plain,
! [SV111: $i] :
( ( ! [SY3123: $i,SY3124: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV111 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ ( c_HOL_Otimes__class_Otimes @ SY3123 @ SY3123 @ SV111 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY3124 @ SY3124 @ SV111 ) ) @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(3006,plain,
! [SV112: $i] :
( ( ! [SY3125: $i,SY3126: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV112 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SY3125 ) @ SY3126 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SY3126 ) @ SY3125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(3007,plain,
! [SV113: $i] :
( ( ! [SY3127: $i,SY3128: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SY3127 ) @ SY3128 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SY3128 ) @ SY3127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(3008,plain,
! [SV114: $i] :
( ( ! [SY3129: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV114 ) @ SY3129 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3129 ) @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(3009,plain,
! [SV115: $i] :
( ( ! [SY3130: $i,SY3131: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SY3130 ) @ SY3131 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SY3131 ) @ SY3130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(3010,plain,
! [SV116: $i] :
( ( ! [SY3132: $i,SY3133: $i,SY3134: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV116 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SY3132 ) @ SY3133 ) @ SY3134 @ SV116 @ SV116 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SY3132 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SY3133 @ SY3134 @ SV116 @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(3011,plain,
! [SV117: $i] :
( ( ! [SY3135: $i,SY3136: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SY3135 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SY3136 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3136 @ SV117 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3136 @ SY3135 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(3012,plain,
! [SV118: $i] :
( ( ! [SY3137: $i] :
( ( hBOOL @ ( hAPP @ SV118 @ SY3137 ) )
| ~ ( hBOOL @ ( hAPP @ SV118 @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ SV118 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV118 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(3013,plain,
! [SV119: $i] :
( ( ! [SY3138: $i,SY3139: $i,SY3140: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV119 )
| ( c_HOL_Oord__class_Oless @ SY3138 @ SY3139 @ SV119 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SY3140 @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3138 @ SY3140 @ SV119 ) @ ( c_HOL_Otimes__class_Otimes @ SY3139 @ SY3140 @ SV119 ) @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(3014,plain,
! [SV120: $i] :
( ( ! [SY3141: $i,SY3142: $i,SY3143: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV120 )
| ( c_HOL_Oord__class_Oless @ SY3141 @ SY3142 @ SV120 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SY3143 @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3143 @ SY3141 @ SV120 ) @ ( c_HOL_Otimes__class_Otimes @ SY3143 @ SY3142 @ SV120 ) @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(3015,plain,
! [SV121: $i] :
( ( ! [SY3144: $i,SY3145: $i,SY3146: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ SV121 )
| ( c_HOL_Oord__class_Oless @ SY3144 @ SY3145 @ SV121 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SY3146 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3144 @ SY3146 @ SV121 ) @ ( c_HOL_Otimes__class_Otimes @ SY3145 @ SY3146 @ SV121 ) @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(3016,plain,
! [SV122: $i] :
( ( ! [SY3147: $i,SY3148: $i,SY3149: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ SV122 )
| ( c_HOL_Oord__class_Oless @ SY3147 @ SY3148 @ SV122 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SY3149 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3149 @ SY3147 @ SV122 ) @ ( c_HOL_Otimes__class_Otimes @ SY3149 @ SY3148 @ SV122 ) @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(3017,plain,
! [SV123: $i] :
( ( ! [SY3150: $i,SY3151: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV123 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY3150 @ SY3151 @ SV123 ) @ SY3150 @ SV123 )
= ( c_HOL_Otimes__class_Otimes @ SY3150 @ ( c_Power_Opower__class_Opower @ SY3150 @ SY3151 @ SV123 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(3018,plain,
! [SV124: $i] :
( ( ! [SY3152: $i,SY3153: $i,SY3154: $i] :
( ~ ( class_Orderings_Olinorder @ SV124 )
| ( c_lessequals @ SY3152 @ SY3153 @ SV124 )
| ( c_lessequals @ SY3152 @ SY3154 @ SV124 )
| ~ ( c_lessequals @ SY3152 @ ( c_Orderings_Oord__class_Omax @ SY3154 @ SY3153 @ SV124 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(3019,plain,
! [SV125: $i] :
( ( ! [SY3155: $i,SY3156: $i,SY3157: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY3155 @ SY3156 @ SV125 ) @ ( c_Power_Opower__class_Opower @ SY3155 @ SY3157 @ SV125 ) @ SV125 )
= ( c_Power_Opower__class_Opower @ SY3155 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3156 ) @ SY3157 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(3020,plain,
! [SV126: $i] :
( ( ! [SY3158: $i] :
( ( c_List_Odrop @ SV126 @ ( c_List_Olist_ONil @ SY3158 ) @ SY3158 )
= ( c_List_Olist_ONil @ SY3158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(3021,plain,
! [SV127: $i] :
( ( ! [SY3159: $i] :
( ( c_lessequals @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV127 @ SY3159 ) @ SY3159 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV127 @ SY3159 ) )
| ( hBOOL @ ( hAPP @ SV127 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(3022,plain,
! [SV128: $i] :
( ( ! [SY3160: $i,SY3161: $i,SY3162: $i,SY3163: $i,SY3164: $i,SY3165: $i,SY3166: $i,SY3167: $i] :
( ( ( hAPP @ ( hAPP @ SV128 @ ( hAPP @ ( hAPP @ SY3160 @ SY3161 ) @ SY3162 ) ) @ ( hAPP @ ( hAPP @ SY3160 @ SY3161 ) @ SY3163 ) )
= ( hAPP @ ( hAPP @ SY3160 @ SY3161 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3162 ) @ SY3163 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3164 @ SV128 @ SY3160 @ SY3165 @ SY3166 @ SY3167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(3023,plain,
! [SV129: $i] :
( ( ! [SY3168: $i,SY3169: $i,SY3170: $i] :
( ~ ( c_lessequals @ SV129 @ SY3168 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3168 @ SY3169 @ tc_nat ) ) @ SY3170 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV129 @ SY3169 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3168 @ SV129 @ tc_nat ) @ SY3169 @ tc_nat ) ) @ SY3170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(3024,plain,
! [SV130: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(3025,plain,
! [SV131: $i] :
( ( ! [SY3171: $i,SY3172: $i,SY3173: $i] :
( ~ ( class_Orderings_Olinorder @ SV131 )
| ( c_lessequals @ SY3171 @ SY3172 @ SV131 )
| ~ ( c_lessequals @ SY3171 @ ( c_Orderings_Oord__class_Omin @ SY3173 @ SY3172 @ SV131 ) @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(3026,plain,
! [SV132: $i] :
( ( ! [SY3174: $i,SY3175: $i,SY3176: $i] :
( ~ ( class_Orderings_Olinorder @ SV132 )
| ( c_lessequals @ SY3174 @ SY3175 @ SV132 )
| ~ ( c_lessequals @ SY3174 @ ( c_Orderings_Oord__class_Omin @ SY3175 @ SY3176 @ SV132 ) @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(3027,plain,
! [SV133: $i] :
( ( ! [SY3177: $i,SY3178: $i,SY3179: $i] :
( ~ ( class_Orderings_Olinorder @ SV133 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY3177 @ SY3178 @ SV133 ) @ SY3179 @ SV133 )
| ~ ( c_lessequals @ SY3178 @ SY3179 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(3028,plain,
! [SV134: $i] :
( ( ! [SY3180: $i,SY3181: $i,SY3182: $i] :
( ~ ( class_Orderings_Olinorder @ SV134 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY3180 @ SY3181 @ SV134 ) @ SY3182 @ SV134 )
| ~ ( c_lessequals @ SY3180 @ SY3182 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(3029,plain,
! [SV135: $i] :
( ( ! [SY3183: $i,SY3184: $i,SY3185: $i] :
( ~ ( class_Orderings_Olinorder @ SV135 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY3183 @ SY3184 @ SV135 ) @ SY3185 @ SV135 )
| ~ ( c_lessequals @ SY3184 @ SY3185 @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(3030,plain,
! [SV136: $i] :
( ( ! [SY3186: $i,SY3187: $i,SY3188: $i] :
( ~ ( class_Orderings_Olinorder @ SV136 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY3186 @ SY3187 @ SV136 ) @ SY3188 @ SV136 )
| ~ ( c_lessequals @ SY3186 @ SY3188 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(3031,plain,
! [SV137: $i] :
( ( ! [SY3189: $i,SY3190: $i,SY3191: $i] :
( ~ ( class_Orderings_Olinorder @ SV137 )
| ( c_lessequals @ SY3189 @ SY3190 @ SV137 )
| ~ ( c_lessequals @ SY3189 @ ( c_Orderings_Oord__class_Omin @ SY3191 @ SY3190 @ SV137 ) @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(3032,plain,
! [SV138: $i] :
( ( ! [SY3192: $i,SY3193: $i,SY3194: $i] :
( ~ ( class_Orderings_Olinorder @ SV138 )
| ( c_lessequals @ SY3192 @ SY3193 @ SV138 )
| ~ ( c_lessequals @ SY3192 @ ( c_Orderings_Oord__class_Omin @ SY3193 @ SY3194 @ SV138 ) @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(3033,plain,
! [SV139: $i] :
( ( ! [SY3195: $i,SY3196: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV139 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SY3195 @ SY3196 @ SV139 @ SV139 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SY3196 @ SY3195 @ SV139 @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(3034,plain,
! [SV140: $i] :
( ( ! [SY3197: $i,SY3198: $i,SY3199: $i,SY3200: $i,SY3201: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV140 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SY3197 @ SY3198 @ SV140 ) ) @ SY3199 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SY3200 @ SY3198 @ SV140 ) ) @ SY3201 ) @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SY3199 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3200 @ SY3197 @ SV140 ) @ SY3198 @ SV140 ) ) @ SY3201 ) @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(3035,plain,
! [SV141: $i] :
( ( ! [SY3202: $i,SY3203: $i,SY3204: $i,SY3205: $i,SY3206: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV141 )
| ( c_HOL_Oord__class_Oless @ SY3202 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3203 @ SY3204 @ SV141 ) @ SY3205 @ SV141 ) ) @ SY3206 ) @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SY3204 @ SY3205 @ SV141 ) ) @ SY3202 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SY3203 @ SY3205 @ SV141 ) ) @ SY3206 ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(3036,plain,
! [SV142: $i] :
( ( ! [SY3207: $i,SY3208: $i,SY3209: $i,SY3210: $i,SY3211: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV142 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SY3207 @ SY3208 @ SV142 ) ) @ SY3209 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SY3210 @ SY3208 @ SV142 ) ) @ SY3211 ) @ SV142 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3207 @ SY3210 @ SV142 ) @ SY3208 @ SV142 ) ) @ SY3209 ) @ SY3211 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(3037,plain,
! [SV143: $i] :
( ( ! [SY3212: $i,SY3213: $i,SY3214: $i,SY3215: $i,SY3216: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV143 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3212 @ SY3213 @ SV143 ) @ SY3214 @ SV143 ) ) @ SY3215 ) @ SY3216 @ SV143 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SY3212 @ SY3214 @ SV143 ) ) @ SY3215 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SY3213 @ SY3214 @ SV143 ) ) @ SY3216 ) @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(3038,plain,
! [SV144: $i] :
( ( ! [SY3217: $i,SY3218: $i,SY3219: $i] :
( ~ ( class_Orderings_Olinorder @ SV144 )
| ( c_lessequals @ SY3217 @ SY3218 @ SV144 )
| ( c_lessequals @ SY3219 @ SY3218 @ SV144 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY3219 @ SY3217 @ SV144 ) @ SY3218 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(3039,plain,
! [SV145: $i] :
( ( ! [SY3220: $i,SY3221: $i,SY3222: $i] :
( ~ ( c_lessequals @ SV145 @ SY3220 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV145 @ SY3221 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3220 @ SV145 @ tc_nat ) @ SY3221 @ tc_nat ) ) @ SY3222 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3220 @ SY3221 @ tc_nat ) ) @ SY3222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(3040,plain,
! [SV146: $i] :
( ( ! [SY3223: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV146 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SY3223 ) @ SY3223 ) @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SY3223 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(3041,plain,
! [SV147: $i] :
( ( ! [SY3224: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV147 )
| ( c_HOL_Oord__class_Oless @ SY3224 @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY3224 ) @ SY3224 ) @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(3042,plain,
! [SV148: $i] :
( ( ! [SY3225: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV148 )
| ( c_HOL_Oord__class_Oless @ SY3225 @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SY3225 ) @ SY3225 ) @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(3043,plain,
! [SV149: $i] :
( ( ! [SY3226: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV149 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SY3226 ) @ SY3226 ) @ ( c_HOL_Ozero__class_Ozero @ SV149 ) @ SV149 )
| ~ ( c_HOL_Oord__class_Oless @ SY3226 @ ( c_HOL_Ozero__class_Ozero @ SV149 ) @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(3044,plain,
! [SV150: $i] :
( ( ! [SY3227: $i,SY3228: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV150 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SY3227 @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SY3228 @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ ( c_HOL_Otimes__class_Otimes @ SY3227 @ SY3228 @ SV150 ) @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(3045,plain,
! [SV151: $i] :
( ( ! [SY3229: $i,SY3230: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV151 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SY3229 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SY3230 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ ( c_HOL_Otimes__class_Otimes @ SY3230 @ SY3229 @ SV151 ) @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(3046,plain,
! [SV152: $i] :
( ( ! [SY3231: $i,SY3232: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV152 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SY3231 @ SY3232 @ SV152 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SY3232 @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SY3231 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(3047,plain,
! [SV153: $i] :
( ( ! [SY3233: $i,SY3234: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV153 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SY3233 @ SY3234 @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SY3234 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SY3233 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(3048,plain,
! [SV154: $i] :
( ( ! [SY3235: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV154 @ SY3235 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3235 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV154 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(3049,plain,
! [SV155: $i] :
( ( ! [SY3236: $i,SY3237: $i,SY3238: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV155 )
| ( c_HOL_Oord__class_Oless @ SY3236 @ SY3237 @ SV155 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SY3237 @ SV155 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3236 @ SY3238 @ SV155 ) @ ( c_Power_Opower__class_Opower @ SY3237 @ SY3238 @ SV155 ) @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(3050,plain,
! [SV156: $i] :
( ( ! [SY3239: $i,SY3240: $i,SY3241: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV156 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY3239 ) @ SY3240 ) ) @ SY3241 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY3239 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY3240 ) @ SY3241 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(3051,plain,
! [SV157: $i] :
( ( ! [SY3242: $i,SY3243: $i,SY3244: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY3242 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY3243 ) @ SY3244 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY3243 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY3242 ) @ SY3244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(3052,plain,
! [SV158: $i] :
( ( ! [SY3245: $i,SY3246: $i,SY3247: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV158 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SY3245 ) @ SY3246 ) ) @ SY3247 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SY3245 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SY3246 ) @ SY3247 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(3053,plain,
! [SV159: $i] :
( ( ! [SY3248: $i,SY3249: $i,SY3250: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV159 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SY3248 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SY3249 ) @ SY3250 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SY3248 ) @ SY3249 ) ) @ SY3250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(3054,plain,
! [SV160: $i] :
( ( ! [SY3251: $i,SY3252: $i,SY3253: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV160 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SY3251 ) @ SY3252 ) ) @ SY3253 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SY3251 ) @ SY3253 ) ) @ SY3252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(3055,plain,
! [SV161: $i] :
( ( ! [SY3254: $i,SY3255: $i,SY3256: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV161 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SY3254 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SY3255 ) @ SY3256 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SY3255 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SY3254 ) @ SY3256 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(3056,plain,
! [SV162: $i] :
( ( ! [SY3257: $i,SY3258: $i,SY3259: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SY3257 ) @ SY3258 ) ) @ SY3259 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SY3257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SY3258 ) @ SY3259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(3057,plain,
! [SV163: $i] :
( ( ! [SY3260: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV163 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3260 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3260 ) @ SV163 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(3058,plain,
! [SV164: $i] :
( ( ! [SY3261: $i,SY3262: $i,SY3263: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV164 )
| ( ( c_Power_Opower__class_Opower @ SY3261 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3262 ) @ SY3263 ) @ SV164 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY3261 @ SY3262 @ SV164 ) @ ( c_Power_Opower__class_Opower @ SY3261 @ SY3263 @ SV164 ) @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(3059,plain,
! [SV165: $i] :
( ( ! [SY3264: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV165 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SY3264 @ SV165 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(3060,plain,
! [SV166: $i] :
( ( ! [SY3265: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV166 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV166 @ SY3265 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(3061,plain,
! [SV167: $i] :
( ( ! [SY3266: $i,SY3267: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV167 @ SY3266 @ SY3267 ) @ SY3267 )
= ( c_List_Olist_OCons @ SV167 @ SY3266 @ SY3267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(3062,plain,
! [SV168: $i] :
( ( ! [SY3268: $i,SY3269: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ SV168 ) @ SY3268 @ SY3269 )
= ( c_List_Olist_OCons @ SY3268 @ ( c_List_Oreplicate @ SV168 @ SY3268 @ SY3269 ) @ SY3269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(3063,plain,
! [SV169: $i] :
( ( ! [SY3270: $i,SY3271: $i] :
( ( c_lessequals @ SV169 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3270 ) @ SY3271 ) @ tc_nat )
| ~ ( c_lessequals @ SV169 @ SY3271 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(3064,plain,
! [SV170: $i] :
( ( ! [SY3272: $i,SY3273: $i] :
( ( c_lessequals @ SV170 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3272 ) @ SY3273 ) @ tc_nat )
| ~ ( c_lessequals @ SV170 @ SY3272 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(3065,plain,
! [SV171: $i] :
( ( ! [SY3274: $i,SY3275: $i] :
( ( c_lessequals @ SV171 @ SY3274 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3275 ) @ SV171 ) @ SY3274 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(3066,plain,
! [SV172: $i] :
( ( ! [SY3276: $i,SY3277: $i] :
( ( c_lessequals @ SV172 @ SY3276 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV172 ) @ SY3277 ) @ SY3276 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(3067,plain,
! [SV173: $i] :
( ( ! [SY3278: $i,SY3279: $i] :
( ( c_lessequals @ SV173 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3278 ) @ SY3279 ) @ tc_nat )
| ~ ( c_lessequals @ SV173 @ SY3279 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(3068,plain,
! [SV174: $i] :
( ( ! [SY3280: $i,SY3281: $i] :
( ( c_lessequals @ SV174 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3280 ) @ SY3281 ) @ tc_nat )
| ~ ( c_lessequals @ SV174 @ SY3280 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(3069,plain,
! [SV175: $i] :
( ( ! [SY3282: $i,SY3283: $i] :
( ~ ( class_Orderings_Olinorder @ SV175 )
| ( ( c_Orderings_Oord__class_Omin @ SY3282 @ SY3283 @ SV175 )
= SY3282 )
| ~ ( c_lessequals @ SY3282 @ SY3283 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(3070,plain,
! [SV176: $i] :
( ( ! [SY3284: $i,SY3285: $i] :
( ~ ( class_Orderings_Olinorder @ SV176 )
| ( ( c_Orderings_Oord__class_Omin @ SY3284 @ SY3285 @ SV176 )
= SY3285 )
| ~ ( c_lessequals @ SY3285 @ SY3284 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(3071,plain,
! [SV177: $i] :
( ( ! [SY3286: $i,SY3287: $i,SY3288: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV177 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ SY3286 @ SY3287 @ SV177 ) @ SY3288 @ SV177 )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ SY3286 @ SY3288 @ SV177 ) @ ( c_HOL_Ominus__class_Ominus @ SY3287 @ SY3288 @ SV177 ) @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(3072,plain,
! [SV178: $i] :
( ( ! [SY3289: $i,SY3290: $i,SY3291: $i] :
( ( c_Type_Otypings @ SV178 @ SY3289 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY3290 @ SV178 @ SY3291 @ SY3289 ) )
| ~ ( c_Type_Otyping @ SV178 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3291 @ SY3289 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY3290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(3073,plain,
! [SV179: $i] :
( ( ! [SY3292: $i,SY3293: $i] :
( ~ ( class_Orderings_Olinorder @ SV179 )
| ( c_HOL_Oord__class_Oless @ SY3292 @ SY3293 @ SV179 )
| ( c_lessequals @ SY3293 @ SY3292 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(3074,plain,
! [SV180: $i] :
( ( ! [SY3294: $i] :
( ~ ( class_Orderings_Olinorder @ SV180 )
| ~ ( c_lessequals @ SY3294 @ SY3294 @ SV180 )
| ~ ( c_HOL_Oord__class_Oless @ SY3294 @ SY3294 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(3075,plain,
! [SV181: $i] :
( ( ! [SY3295: $i] :
( ~ ( class_Orderings_Olinorder @ SV181 )
| ( c_HOL_Oord__class_Oless @ SY3295 @ SY3295 @ SV181 )
| ( c_lessequals @ SY3295 @ SY3295 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(3076,plain,
! [SV182: $i] :
( ( ! [SY3296: $i,SY3297: $i] :
( ~ ( class_Orderings_Olinorder @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SY3296 @ SY3297 @ SV182 )
| ~ ( c_lessequals @ SY3297 @ SY3296 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(3077,plain,
! [SV183: $i] :
( ( ! [SY3298: $i,SY3299: $i] :
( ~ ( class_Orderings_Olinorder @ SV183 )
| ( c_lessequals @ SY3298 @ SY3299 @ SV183 )
| ( c_HOL_Oord__class_Oless @ SY3299 @ SY3298 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(3078,plain,
! [SV184: $i] :
( ( ! [SY3300: $i,SY3301: $i] :
( ~ ( class_Orderings_Olinorder @ SV184 )
| ~ ( c_lessequals @ SY3300 @ SY3301 @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ SY3301 @ SY3300 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(3079,plain,
! [SV185: $i] :
( ( ! [SY3302: $i,SY3303: $i] :
( ~ ( class_Orderings_Olinorder @ SV185 )
| ( c_HOL_Oord__class_Oless @ SY3302 @ SY3303 @ SV185 )
| ( c_lessequals @ SY3303 @ SY3302 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(3080,plain,
! [SV186: $i] :
( ( ! [SY3304: $i,SY3305: $i] :
( ~ ( class_Orderings_Opreorder @ SV186 )
| ~ ( c_lessequals @ SY3304 @ SY3305 @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SY3305 @ SY3304 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(3081,plain,
! [SV187: $i] :
( ( ! [SY3306: $i] :
( ( hBOOL @ ( hAPP @ SV187 @ SY3306 ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV187 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV187 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(3082,plain,
! [SV188: $i] :
( ( ! [SY3307: $i] :
( ( c_HOL_Oord__class_Oless @ SV188 @ SV188 @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV188 ) @ SY3307 @ SV188 )
= SY3307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(3083,plain,
! [SV189: $i] :
( ( ! [SY3308: $i] :
( ( hBOOL @ ( hAPP @ SV189 @ SY3308 ) )
| ~ ( hBOOL @ ( hAPP @ SV189 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(3084,plain,
! [SV190: $i] :
( ( ! [SY3309: $i,SY3310: $i,SY3311: $i] :
( ~ ( class_Orderings_Olinorder @ SV190 )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ SY3309 @ SY3310 @ SV190 ) @ SY3311 @ SV190 )
= ( c_Orderings_Oord__class_Omin @ SY3309 @ ( c_Orderings_Oord__class_Omin @ SY3310 @ SY3311 @ SV190 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(3085,plain,
! [SV191: $i] :
( ( ! [SY3312: $i,SY3313: $i,SY3314: $i] :
( ~ ( class_Orderings_Olinorder @ SV191 )
| ( ( c_Orderings_Oord__class_Omin @ SY3312 @ ( c_Orderings_Oord__class_Omin @ SY3313 @ SY3314 @ SV191 ) @ SV191 )
= ( c_Orderings_Oord__class_Omin @ SY3313 @ ( c_Orderings_Oord__class_Omin @ SY3312 @ SY3314 @ SV191 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(3086,plain,
! [SV192: $i] :
( ( ! [SY3315: $i,SY3316: $i,SY3317: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV192 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV192 )
| ( c_HOL_Oord__class_Oless @ SY3315 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SY3316 ) @ SY3317 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SY3315 @ SY3317 @ SV192 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SY3316 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(3087,plain,
! [SV193: $i] :
( ( ! [SY3318: $i,SY3319: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV193 @ SY3318 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV193 @ SY3319 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3319 @ SY3318 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(3088,plain,
! [SV194: $i] :
( ( ! [SY3320: $i,SY3321: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV194 @ SY3320 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3321 @ SY3320 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV194 @ SY3321 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(3089,plain,
! [SV195: $i] :
( ( ! [SY3322: $i,SY3323: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV195 @ SY3322 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3323 @ SY3322 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV195 @ SY3323 @ tc_nat )
| ~ ( c_lessequals @ SY3322 @ SY3323 @ tc_nat )
| ~ ( c_lessequals @ SY3322 @ SV195 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(3090,plain,
! [SV196: $i] :
( ( ! [SY3324: $i,SY3325: $i] :
( ( c_lessequals @ SV196 @ SY3324 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV196 @ SY3325 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3324 @ SY3325 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3325 @ SY3324 @ tc_nat )
| ~ ( c_lessequals @ SY3325 @ SV196 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(3091,plain,
! [SV197: $i] :
( ( ! [SY3326: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV197 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV197 ) @ SY3326 ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(3092,plain,
! [SV198: $i] :
( ( ! [SY3327: $i,SY3328: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV198 @ SY3327 @ tc_nat ) @ SY3328 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV198 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3327 ) @ SY3328 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(3093,plain,
! [SV199: $i] :
( ( ! [SY3329: $i,SY3330: $i,SY3331: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV199 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY3329 @ SY3330 @ SV199 ) @ ( c_Power_Opower__class_Opower @ SY3331 @ SY3330 @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SY3329 @ SV199 )
| ~ ( c_lessequals @ SY3329 @ SY3331 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(3094,plain,
! [SV200: $i] :
( ( ! [SY3332: $i,SY3333: $i] :
( ~ ( class_Orderings_Olinorder @ SV200 )
| ( ( c_Orderings_Oord__class_Omin @ SY3332 @ ( c_Orderings_Oord__class_Omax @ SY3332 @ SY3333 @ SV200 ) @ SV200 )
= SY3332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(3095,plain,
! [SV201: $i] :
( ( ! [SY3334: $i,SY3335: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV201 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3334 @ SV201 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3335 @ SV201 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(3096,plain,
! [SV202: $i] :
( ( ! [SY3336: $i,SY3337: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV202 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SY3336 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SY3337 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(3097,plain,
! [SV203: $i] :
( ( ! [SY3338: $i,SY3339: $i,SY3340: $i,SY3341: $i,SY3342: $i] :
( ( c_List_Ofoldl @ SV203 @ SY3338 @ ( c_List_Olist_OCons @ SY3339 @ SY3340 @ SY3341 ) @ SY3342 @ SY3341 )
= ( c_List_Ofoldl @ SV203 @ ( hAPP @ ( hAPP @ SV203 @ SY3338 ) @ SY3339 ) @ SY3340 @ SY3342 @ SY3341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(3098,plain,
! [SV204: $i] :
( ( ! [SY3343: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV204 ) ) @ SY3343 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV204 ) @ ( c_Suc @ SY3343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(3099,plain,
! [SV205: $i] :
( ( ! [SY3344: $i,SY3345: $i,SY3346: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV205 ) @ ( c_List_Olist_OCons @ SY3344 @ SY3345 @ SY3346 ) @ SY3346 )
= ( c_List_Odrop @ SV205 @ SY3345 @ SY3346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(3100,plain,
! [SV206: $i] :
( ( ! [SY3347: $i,SY3348: $i] :
( ( c_lessequals @ SV206 @ SY3347 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3348 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV206 @ SY3348 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3347 @ SY3348 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(3101,plain,
! [SV207: $i] :
( ( ! [SY3349: $i,SY3350: $i] :
( ( c_lessequals @ SV207 @ SY3349 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3350 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3350 @ SV207 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3350 @ SY3349 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(3102,plain,
! [SV208: $i] :
( ( ! [SY3351: $i,SY3352: $i] :
( ( c_lessequals @ SV208 @ SY3351 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3352 @ SV208 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3352 @ SY3351 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3352 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(3103,plain,
! [SV209: $i] :
( ( ! [SY3353: $i,SY3354: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SY3353 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SY3354 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3353 @ SY3354 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV209 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(3104,plain,
! [SV210: $i] :
( ( ! [SY3355: $i,SY3356: $i,SY3357: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV210 )
| ( c_lessequals @ SY3355 @ SY3356 @ SV210 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3357 @ SY3356 @ SV210 ) @ ( c_HOL_Otimes__class_Otimes @ SY3357 @ SY3355 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SY3357 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(3105,plain,
! [SV211: $i] :
( ( ! [SY3358: $i,SY3359: $i,SY3360: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV211 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3358 @ SY3359 @ SV211 ) @ ( c_HOL_Otimes__class_Otimes @ SY3358 @ SY3360 @ SV211 ) @ SV211 )
| ~ ( c_lessequals @ SY3360 @ SY3359 @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ SY3358 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(3106,plain,
! [SV212: $i] :
( ( ! [SY3361: $i,SY3362: $i,SY3363: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV212 )
| ( c_lessequals @ SY3361 @ SY3362 @ SV212 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3363 @ SY3361 @ SV212 ) @ ( c_HOL_Otimes__class_Otimes @ SY3363 @ SY3362 @ SV212 ) @ SV212 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SY3363 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(3107,plain,
! [SV213: $i] :
( ( ! [SY3364: $i,SY3365: $i,SY3366: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV213 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3364 @ SY3365 @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SY3364 @ SY3366 @ SV213 ) @ SV213 )
| ~ ( c_lessequals @ SY3365 @ SY3366 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SY3364 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(3108,plain,
! [SV214: $i] :
( ( ! [SY3367: $i,SY3368: $i,SY3369: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV214 )
| ( c_lessequals @ SY3367 @ SY3368 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SY3369 @ SV214 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3369 @ SY3367 @ SV214 ) @ ( c_HOL_Otimes__class_Otimes @ SY3369 @ SY3368 @ SV214 ) @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(3109,plain,
! [SV215: $i] :
( ( ! [SY3370: $i,SY3371: $i,SY3372: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV215 )
| ( c_lessequals @ SY3370 @ SY3371 @ SV215 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SY3372 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3370 @ SY3372 @ SV215 ) @ ( c_HOL_Otimes__class_Otimes @ SY3371 @ SY3372 @ SV215 ) @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(3110,plain,
! [SV216: $i] :
( ( ! [SY3373: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV216 @ SY3373 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV216 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY3373 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(3111,plain,
! [SV217: $i] :
( ( ! [SY3374: $i,SY3375: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV217 ) @ SY3374 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3375 ) @ SY3374 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV217 @ SY3375 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(3112,plain,
! [SV218: $i] :
( ( ! [SY3376: $i,SY3377: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV218 ) @ SY3376 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV218 ) @ SY3377 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SY3376 @ SY3377 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(3113,plain,
! [SV219: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV219 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(3114,plain,
! [SV220: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV220 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(3115,plain,
! [SV221: $i] :
( ( ! [SY3378: $i,SY3379: $i,SY3380: $i] :
( ~ ( class_Orderings_Olinorder @ SV221 )
| ( c_HOL_Oord__class_Oless @ SY3378 @ ( c_Orderings_Oord__class_Omax @ SY3379 @ SY3380 @ SV221 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SY3378 @ SY3379 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(3116,plain,
! [SV222: $i] :
( ( ! [SY3381: $i,SY3382: $i,SY3383: $i] :
( ~ ( class_Orderings_Olinorder @ SV222 )
| ( c_HOL_Oord__class_Oless @ SY3381 @ ( c_Orderings_Oord__class_Omax @ SY3382 @ SY3383 @ SV222 ) @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ SY3381 @ SY3383 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(3117,plain,
! [SV223: $i] :
( ( ! [SY3384: $i,SY3385: $i,SY3386: $i] :
( ~ ( class_Orderings_Olinorder @ SV223 )
| ( c_HOL_Oord__class_Oless @ SY3384 @ ( c_Orderings_Oord__class_Omax @ SY3385 @ SY3386 @ SV223 ) @ SV223 )
| ~ ( c_HOL_Oord__class_Oless @ SY3384 @ SY3385 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(3118,plain,
! [SV224: $i] :
( ( ! [SY3387: $i,SY3388: $i,SY3389: $i] :
( ~ ( class_Orderings_Olinorder @ SV224 )
| ( c_HOL_Oord__class_Oless @ SY3387 @ ( c_Orderings_Oord__class_Omax @ SY3388 @ SY3389 @ SV224 ) @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ SY3387 @ SY3389 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(3119,plain,
! [SV225: $i] :
( ( ! [SY3390: $i,SY3391: $i,SY3392: $i] :
( ~ ( class_Orderings_Olinorder @ SV225 )
| ( c_HOL_Oord__class_Oless @ SY3390 @ SY3391 @ SV225 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY3390 @ SY3392 @ SV225 ) @ SY3391 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(3120,plain,
! [SV226: $i] :
( ( ! [SY3393: $i,SY3394: $i,SY3395: $i] :
( ~ ( class_Orderings_Olinorder @ SV226 )
| ( c_HOL_Oord__class_Oless @ SY3393 @ SY3394 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY3395 @ SY3393 @ SV226 ) @ SY3394 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(3121,plain,
! [SV227: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV227 )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV227 ) @ SV227 )
= ( c_HOL_Ozero__class_Ozero @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(3122,plain,
! [SV228: $i] :
( ( ! [SY3396: $i,SY3397: $i] :
( ~ ( class_Orderings_Olinorder @ SV228 )
| ( ( c_Orderings_Oord__class_Omin @ SY3396 @ SY3397 @ SV228 )
= ( c_Orderings_Oord__class_Omin @ SY3397 @ SY3396 @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(3123,plain,
! [SV229: $i] :
( ( ! [SY3398: $i,SY3399: $i,SY3400: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV229 @ SY3398 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3399 @ SY3398 @ tc_nat ) ) @ SY3400 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV229 ) @ SY3399 ) @ SY3398 @ tc_nat ) ) @ SY3400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(3124,plain,
! [SV230: $i] :
( ( ! [SY3401: $i,SY3402: $i,SY3403: $i,SY3404: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV230 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SY3401 @ SY3402 @ SV230 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SY3403 @ SY3402 @ SV230 ) ) @ SY3404 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ SY3401 ) @ SY3403 ) @ SY3402 @ SV230 ) ) @ SY3404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(3125,plain,
! [SV231: $i] :
( ( ! [SY3405: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV231 @ SY3405 @ tc_nat ) @ SV231 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(3126,plain,
! [SV232: $i] :
( ( ! [SY3406: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV232 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3406 @ SV232 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(3127,plain,
! [SV233: $i] :
( ( ! [SY3407: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV233 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV233 @ SY3407 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(3128,plain,
! [SV234: $i] :
( ( ! [SY3408: $i,SY3409: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SY3408 ) @ SY3409 ) @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SY3409 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SY3408 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(3129,plain,
! [SV235: $i] :
( ( ! [SY3410: $i,SY3411: $i,SY3412: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV235 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3410 @ SY3411 @ SV235 ) @ ( c_Power_Opower__class_Opower @ SY3412 @ SY3411 @ SV235 ) @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3411 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV235 ) @ SY3410 @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ SY3410 @ SY3412 @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(3130,plain,
! [SV236: $i] :
( ( ! [SY3413: $i,SY3414: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV236 )
| ( SY3413
= ( c_HOL_Ozero__class_Ozero @ SV236 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ ( c_HOL_Otimes__class_Otimes @ SY3413 @ SY3413 @ SV236 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY3414 @ SY3414 @ SV236 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV236 ) @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(3131,plain,
! [SV237: $i] :
( ( ! [SY3415: $i,SY3416: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV237 )
| ( SY3415
= ( c_HOL_Ozero__class_Ozero @ SV237 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( c_HOL_Otimes__class_Otimes @ SY3416 @ SY3416 @ SV237 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY3415 @ SY3415 @ SV237 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV237 ) @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(3132,plain,
! [SV238: $i] :
( ( ! [SY3417: $i,SY3418: $i,SY3419: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV238 @ SY3417 @ SY3418 ) @ SY3419 @ SY3418 )
= ( c_List_Olist_OCons @ SV238 @ ( c_List_Oappend @ SY3417 @ SY3419 @ SY3418 ) @ SY3418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(3133,plain,
! [SV239: $i] :
( ( ! [SY3420: $i,SY3421: $i,SY3422: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV239 @ SY3420 @ SY3421 ) @ SY3422 @ SY3421 )
= ( c_List_Olist_OCons @ SV239 @ ( c_List_Oappend @ SY3420 @ SY3422 @ SY3421 ) @ SY3421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(3134,plain,
! [SV240: $i] :
( ( ! [SY3423: $i,SY3424: $i,SY3425: $i] :
( ~ ( hBOOL @ ( hAPP @ SV240 @ ( c_Nat_Onat_Onat__case @ SY3423 @ SY3424 @ ( c_Suc @ SY3425 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV240 @ ( hAPP @ SY3424 @ SY3425 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(3135,plain,
! [SV241: $i] :
( ( ! [SY3426: $i,SY3427: $i,SY3428: $i] :
( ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_Nat_Onat_Onat__case @ SY3426 @ SY3427 @ ( c_Suc @ SY3428 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV241 @ ( hAPP @ SY3427 @ SY3428 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(3136,plain,
! [SV242: $i] :
( ( ! [SY3429: $i,SY3430: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV242 @ ( c_HOL_Ominus__class_Ominus @ SY3429 @ SY3430 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV242 @ SY3429 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV242 @ SY3430 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(3137,plain,
! [SV243: $i] :
( ( ! [SY3431: $i,SY3432: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV243 @ SY3431 @ tc_nat ) @ SY3432 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV243 @ SY3432 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3431 @ SY3432 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(3138,plain,
! [SV244: $i] :
( ( ! [SY3433: $i,SY3434: $i,SY3435: $i] :
( ~ ( class_Orderings_Olinorder @ SV244 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY3433 @ SY3434 @ SV244 ) @ SY3435 @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ SY3433 @ SY3435 @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(3139,plain,
! [SV245: $i] :
( ( ! [SY3436: $i,SY3437: $i,SY3438: $i] :
( ~ ( class_Orderings_Olinorder @ SV245 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY3436 @ SY3437 @ SV245 ) @ SY3438 @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ SY3437 @ SY3438 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(3140,plain,
! [SV246: $i] :
( ( ! [SY3439: $i,SY3440: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV246 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ SY3439 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ ( c_HOL_Ozero__class_Ozero @ SV246 ) @ SY3440 @ SV246 @ SV246 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ SY3439 @ SY3440 @ SV246 @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(3141,plain,
! [SV247: $i] :
( ( ! [SY3441: $i,SY3442: $i,SY3443: $i] :
( ~ ( class_Orderings_Olinorder @ SV247 )
| ( c_lessequals @ SY3441 @ SY3442 @ SV247 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY3443 @ SY3441 @ SV247 ) @ SY3442 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(3142,plain,
! [SV248: $i] :
( ( ! [SY3444: $i,SY3445: $i,SY3446: $i] :
( ~ ( class_Orderings_Olinorder @ SV248 )
| ( c_lessequals @ SY3444 @ SY3445 @ SV248 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY3444 @ SY3446 @ SV248 ) @ SY3445 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(3143,plain,
! [SV249: $i] :
( ( ! [SY3447: $i,SY3448: $i,SY3449: $i] :
( ~ ( class_Orderings_Olinorder @ SV249 )
| ( c_lessequals @ SY3447 @ ( c_Orderings_Oord__class_Omax @ SY3448 @ SY3449 @ SV249 ) @ SV249 )
| ~ ( c_lessequals @ SY3447 @ SY3449 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(3144,plain,
! [SV250: $i] :
( ( ! [SY3450: $i,SY3451: $i,SY3452: $i] :
( ~ ( class_Orderings_Olinorder @ SV250 )
| ( c_lessequals @ SY3450 @ ( c_Orderings_Oord__class_Omax @ SY3451 @ SY3452 @ SV250 ) @ SV250 )
| ~ ( c_lessequals @ SY3450 @ SY3451 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(3145,plain,
! [SV251: $i] :
( ( ! [SY3453: $i,SY3454: $i,SY3455: $i] :
( ~ ( class_Orderings_Olinorder @ SV251 )
| ( c_lessequals @ SY3453 @ ( c_Orderings_Oord__class_Omax @ SY3454 @ SY3455 @ SV251 ) @ SV251 )
| ~ ( c_lessequals @ SY3453 @ SY3455 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(3146,plain,
! [SV252: $i] :
( ( ! [SY3456: $i,SY3457: $i,SY3458: $i] :
( ~ ( class_Orderings_Olinorder @ SV252 )
| ( c_lessequals @ SY3456 @ ( c_Orderings_Oord__class_Omax @ SY3457 @ SY3458 @ SV252 ) @ SV252 )
| ~ ( c_lessequals @ SY3456 @ SY3457 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(3147,plain,
! [SV253: $i] :
( ( ! [SY3459: $i,SY3460: $i,SY3461: $i] :
( ~ ( class_Orderings_Olinorder @ SV253 )
| ( c_lessequals @ SY3459 @ SY3460 @ SV253 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY3461 @ SY3459 @ SV253 ) @ SY3460 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(3148,plain,
! [SV254: $i] :
( ( ! [SY3462: $i,SY3463: $i,SY3464: $i] :
( ~ ( class_Orderings_Olinorder @ SV254 )
| ( c_lessequals @ SY3462 @ SY3463 @ SV254 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY3462 @ SY3464 @ SV254 ) @ SY3463 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(3149,plain,
! [SV255: $i] :
( ( ! [SY3465: $i,SY3466: $i] :
( ( c_lessequals @ SV255 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3465 ) @ SY3466 ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV255 @ SY3466 @ tc_nat ) @ SY3465 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(3150,plain,
! [SV256: $i] :
( ( ! [SY3467: $i,SY3468: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV256 @ SY3467 @ tc_nat ) @ SY3468 @ tc_nat )
| ~ ( c_lessequals @ SV256 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3468 ) @ SY3467 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(3151,plain,
! [SV257: $i] :
( ( ! [SY3469: $i,SY3470: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV257 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ ( c_Power_Opower__class_Opower @ SY3469 @ SY3470 @ SV257 ) @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SY3469 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(3152,plain,
! [SV258: $i] :
( ( ! [SY3471: $i,SY3472: $i,SY3473: $i] :
( ~ ( class_Orderings_Olinorder @ SV258 )
| ( c_HOL_Oord__class_Oless @ SY3471 @ SY3472 @ SV258 )
| ( c_HOL_Oord__class_Oless @ SY3471 @ SY3473 @ SV258 )
| ~ ( c_HOL_Oord__class_Oless @ SY3471 @ ( c_Orderings_Oord__class_Omax @ SY3473 @ SY3472 @ SV258 ) @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(3153,plain,
! [SV259: $i] :
( ( ! [SY3474: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV259 @ ( c_Suc @ SY3474 ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV259 ) @ ( c_HOL_Otimes__class_Otimes @ SV259 @ SY3474 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(3154,plain,
! [SV260: $i] :
( ( ! [SY3475: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV260 ) @ SY3475 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3475 ) @ ( c_HOL_Otimes__class_Otimes @ SV260 @ SY3475 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(3155,plain,
! [SV261: $i] :
( ( ! [SY3476: $i,SY3477: $i] :
( ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV261 ) ) @ SY3476 ) @ SY3477 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_InductTermi_OIT @ SY3476 )
| ~ ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV261 @ SY3476 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY3477 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(3156,plain,
! [SV262: $i] :
( ( ! [SY3478: $i,SY3479: $i,SY3480: $i] :
( ( c_List_Ofoldl @ SV262 @ SY3478 @ ( c_List_Olist_ONil @ SY3479 ) @ SY3480 @ SY3479 )
= SY3478 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(3157,plain,
! [SV263: $i] :
( ( ! [SY3481: $i,SY3482: $i,SY3483: $i] :
( ( c_Nat_Onat_Onat__case @ SV263 @ SY3481 @ ( c_Suc @ SY3482 ) @ SY3483 )
= ( hAPP @ SY3481 @ SY3482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(3158,plain,
! [SV264: $i] :
( ( ! [SY3484: $i,SY3485: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV264 ) @ ( c_HOL_Otimes__class_Otimes @ SY3484 @ SY3484 @ SV264 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY3485 @ SY3485 @ SV264 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(3159,plain,
! [SV265: $i] :
( ( ! [SY3486: $i,SY3487: $i,SY3488: $i,SY3489: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV265 @ SY3486 @ tc_nat ) @ SY3487 @ tc_nat ) ) @ SY3488 ) @ SY3489 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV265 @ SY3487 @ tc_nat ) ) @ SY3488 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3486 @ SY3487 @ tc_nat ) ) @ SY3489 ) @ tc_nat )
| ~ ( c_lessequals @ SY3486 @ SV265 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(3160,plain,
! [SV266: $i] :
( ( ! [SY3490: $i,SY3491: $i,SY3492: $i,SY3493: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV266 @ SY3490 @ tc_nat ) ) @ SY3491 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3492 @ SY3490 @ tc_nat ) ) @ SY3493 ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV266 @ SY3492 @ tc_nat ) @ SY3490 @ tc_nat ) ) @ SY3491 ) @ SY3493 @ tc_nat )
| ~ ( c_lessequals @ SY3492 @ SV266 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(3161,plain,
! [SV267: $i] :
( ( ! [SY3494: $i,SY3495: $i,SY3496: $i,SY3497: $i] :
( ( c_lessequals @ SV267 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3494 @ SY3495 @ tc_nat ) @ SY3496 @ tc_nat ) ) @ SY3497 ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3495 @ SY3496 @ tc_nat ) ) @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3494 @ SY3496 @ tc_nat ) ) @ SY3497 ) @ tc_nat )
| ~ ( c_lessequals @ SY3495 @ SY3494 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(3162,plain,
! [SV268: $i] :
( ( ! [SY3498: $i,SY3499: $i,SY3500: $i,SY3501: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SY3498 @ tc_nat ) ) @ SY3499 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3500 @ SY3498 @ tc_nat ) ) @ SY3501 ) @ tc_nat )
| ~ ( c_lessequals @ SY3499 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3500 @ SV268 @ tc_nat ) @ SY3498 @ tc_nat ) ) @ SY3501 ) @ tc_nat )
| ~ ( c_lessequals @ SV268 @ SY3500 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(3163,plain,
! [SV269: $i] :
( ( ! [SY3502: $i,SY3503: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV269 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SY3502 @ SY3503 @ tc_nat ) @ SV269 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3502 @ SV269 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3503 @ SV269 ) @ SV269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(3164,plain,
! [SV270: $i] :
( ( ! [SY3504: $i,SY3505: $i,SY3506: $i] :
( ~ ( class_Orderings_Olinorder @ SV270 )
| ( c_HOL_Oord__class_Oless @ SY3504 @ SY3505 @ SV270 )
| ( c_HOL_Oord__class_Oless @ SY3506 @ SY3505 @ SV270 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY3506 @ SY3504 @ SV270 ) @ SY3505 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(3165,plain,
! [SV271: $i] :
( ( ! [SY3507: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV271 ) @ ( c_Suc @ SY3507 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV271 @ SY3507 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(3166,plain,
! [SV272: $i] :
( ( ! [SY3508: $i,SY3509: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV272 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SY3508 ) @ SY3509 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
| ~ ( c_HOL_Oord__class_Oless @ SY3509 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
| ~ ( c_lessequals @ SY3508 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(3167,plain,
! [SV273: $i] :
( ( ! [SY3510: $i,SY3511: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV273 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SY3510 ) @ SY3511 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
| ~ ( c_lessequals @ SY3511 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
| ~ ( c_HOL_Oord__class_Oless @ SY3510 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(3168,plain,
! [SV274: $i] :
( ( ! [SY3512: $i] :
( ( SV274 = SY3512 )
| ( c_HOL_Oord__class_Oless @ SV274 @ SY3512 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV274 @ ( c_Suc @ SY3512 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(3169,plain,
! [SV275: $i] :
( ( ! [SY3513: $i] :
( ( SV275 = SY3513 )
| ~ ( c_HOL_Oord__class_Oless @ SY3513 @ ( c_Suc @ SV275 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY3513 @ SV275 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(3170,plain,
! [SV276: $i] :
( ( ! [SY3514: $i] :
( ( SV276 = SY3514 )
| ~ ( c_HOL_Oord__class_Oless @ SV276 @ ( c_Suc @ SY3514 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV276 @ SY3514 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(3171,plain,
! [SV277: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV277 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ SV277 ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ SV277 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(3172,plain,
! [SV278: $i] :
( ( ! [SY3515: $i,SY3516: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV278 ) @ SY3515 ) @ SY3516 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV278 ) @ ( c_HOL_Ominus__class_Ominus @ SY3515 @ SY3516 @ tc_nat ) ) )
| ~ ( c_lessequals @ SY3516 @ SY3515 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(3173,plain,
! [SV279: $i] :
( ( ! [SY3517: $i,SY3518: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV279 ) @ SY3517 ) @ SY3518 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV279 @ SY3518 @ tc_nat ) ) @ SY3517 ) )
| ~ ( c_lessequals @ SY3518 @ SV279 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(3174,plain,
! [SV280: $i] :
( ( ! [SY3519: $i,SY3520: $i,SY3521: $i,SY3522: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV280 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY3519 @ SY3520 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SY3521 @ SY3522 @ SV280 ) @ SV280 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY3519 @ SY3521 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SY3520 @ SY3522 @ SV280 ) @ SV280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(3175,plain,
! [SV281: $i] :
( ( ! [SY3523: $i,SY3524: $i,SY3525: $i,SY3526: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV281 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY3523 @ SY3524 @ SV281 ) @ ( c_HOL_Otimes__class_Otimes @ SY3525 @ SY3526 @ SV281 ) @ SV281 )
= ( c_HOL_Otimes__class_Otimes @ SY3523 @ ( c_HOL_Otimes__class_Otimes @ SY3524 @ ( c_HOL_Otimes__class_Otimes @ SY3525 @ SY3526 @ SV281 ) @ SV281 ) @ SV281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(3176,plain,
! [SV282: $i] :
( ( ! [SY3527: $i,SY3528: $i,SY3529: $i,SY3530: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV282 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY3527 @ SY3528 @ SV282 ) @ ( c_HOL_Otimes__class_Otimes @ SY3529 @ SY3530 @ SV282 ) @ SV282 )
= ( c_HOL_Otimes__class_Otimes @ SY3529 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY3527 @ SY3528 @ SV282 ) @ SY3530 @ SV282 ) @ SV282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(3177,plain,
! [SV283: $i] :
( ( ! [SY3531: $i,SY3532: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_HOL_Ominus__class_Ominus @ SY3531 @ SY3532 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV283 ) @ SY3532 ) @ SY3531 @ tc_nat ) )
| ~ ( c_lessequals @ SY3532 @ SY3531 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(3178,plain,
! [SV284: $i] :
( ( ! [SY3533: $i,SY3534: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV284 @ SY3533 @ tc_nat ) @ SY3534 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV284 @ SY3534 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(3179,plain,
! [SV285: $i] :
( ( ! [SY3535: $i,SY3536: $i,SY3537: $i] :
( ( c_Type_Otype_Otype__rec @ SV285 @ SY3535 @ ( c_Type_Otype_OAtom @ SY3536 ) @ SY3537 )
= ( hAPP @ SV285 @ SY3536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(3180,plain,
! [SV286: $i] :
( ( ! [SY3538: $i,SY3539: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV286 @ SY3538 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3539 @ SY3538 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ SV286 @ SY3539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(3181,plain,
! [SV287: $i] :
( ( ! [SY3540: $i] :
( ( c_List_Olist_ONil @ SV287 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3540 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(3182,plain,
! [SV288: $i] :
( ( ! [SY3541: $i,SY3542: $i] :
( ~ ( class_Orderings_Opreorder @ SV288 )
| ( c_HOL_Oord__class_Oless @ SY3541 @ SY3542 @ SV288 )
| ( c_lessequals @ SY3542 @ SY3541 @ SV288 )
| ~ ( c_lessequals @ SY3541 @ SY3542 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(3183,plain,
! [SV289: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV289 @ SV289 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(3184,plain,
! [SV290: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV290 @ SV290 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(3185,plain,
! [SV291: $i] :
( ( ! [SY3543: $i] :
( ~ ( class_Orderings_Oorder @ SV291 )
| ~ ( c_HOL_Oord__class_Oless @ SY3543 @ SY3543 @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(3186,plain,
! [SV292: $i] :
( ( ! [SY3544: $i] :
( ~ ( class_Orderings_Olinorder @ SV292 )
| ~ ( c_HOL_Oord__class_Oless @ SY3544 @ SY3544 @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(3187,plain,
! [SV293: $i] :
( ( ! [SY3545: $i] :
( ~ ( class_Orderings_Opreorder @ SV293 )
| ~ ( c_HOL_Oord__class_Oless @ SY3545 @ SY3545 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(3188,plain,
! [SV294: $i] :
( ( ! [SY3546: $i] :
( ~ ( c_lessequals @ SV294 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3546 ) @ SV294 ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3546 ) @ SV294 ) @ SV294 @ tc_nat )
= SY3546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(3189,plain,
! [SV295: $i] :
( ( ! [SY3547: $i] :
( ~ ( class_Orderings_Olinorder @ SV295 )
| ( ( c_Orderings_Oord__class_Omin @ SY3547 @ SY3547 @ SV295 )
= SY3547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(3190,plain,
! [SV296: $i] :
( ( ! [SY3548: $i] : ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV296 ) ) @ SY3548 ) @ ( c_Lambda_Osubst @ SV296 @ SY3548 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(3191,plain,
! [SV297: $i] :
( ( ! [SY3549: $i,SY3550: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV297 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV297 ) @ SY3549 ) @ SY3550 ) @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SY3550 @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SY3549 @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(3192,plain,
! [SV298: $i] :
( ( ! [SY3551: $i] : ( c_lessequals @ SV298 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV298 ) @ SY3551 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(3193,plain,
! [SV299: $i] :
( ( ! [SY3552: $i] : ( c_lessequals @ SV299 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3552 ) @ SV299 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(3194,plain,
! [SV300: $i] :
( ( ! [SY3553: $i] : ( c_lessequals @ SV300 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV300 ) @ SY3553 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(3195,plain,
! [SV301: $i] :
( ( ! [SY3554: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV301 @ SY3554 @ tc_nat ) ) @ SY3554 )
= ( c_Orderings_Oord__class_Omax @ SV301 @ SY3554 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(3196,plain,
! [SV302: $i] :
( ( ! [SY3555: $i,SY3556: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV302 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SY3555 @ SY3556 @ SV302 ) @ SV302 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV302 ) @ SY3555 ) @ ( c_List_Olistsum @ SY3556 @ SV302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(3197,plain,
! [SV303: $i] :
( ( ! [SY3557: $i,SY3558: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV303 )
| ( c_HOL_Oord__class_Oless @ SY3557 @ SY3558 @ SV303 )
| ( c_HOL_Oord__class_Oless @ SY3558 @ SY3557 @ SV303 )
| ( SY3558 = SY3557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(3198,plain,
! [SV304: $i] :
( ( ! [SY3559: $i,SY3560: $i] :
( ~ ( class_Orderings_Olinorder @ SV304 )
| ( SY3559 = SY3560 )
| ( c_HOL_Oord__class_Oless @ SY3560 @ SY3559 @ SV304 )
| ( c_HOL_Oord__class_Oless @ SY3559 @ SY3560 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(3199,plain,
! [SV305: $i] :
( ( ! [SY3561: $i] :
( ( SV305 = SY3561 )
| ~ ( c_lessequals @ SY3561 @ SV305 @ tc_nat )
| ~ ( c_lessequals @ SV305 @ SY3561 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(3200,plain,
! [SV306: $i] :
( ( ! [SY3562: $i] :
( ( c_HOL_Oord__class_Oless @ SV306 @ SY3562 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY3562 @ SV306 @ tc_nat )
| ( SY3562 = SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(3201,plain,
! [SV307: $i] :
( ( ! [SY3563: $i,SY3564: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV307 @ SY3563 ) @ SY3564 ) )
| ( c_HOL_Oord__class_Oless @ SY3563 @ SY3564 @ tc_nat )
| ( SY3564 = SY3563 )
| ( c_HOL_Oord__class_Oless @ SY3564 @ SY3563 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(3202,plain,
! [SV308: $i] :
( ( ! [SY3565: $i,SY3566: $i,SY3567: $i,SY3568: $i] :
( ( SV308 = SY3565 )
| ~ ( c_Type_Otyping @ SY3566 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3567 ) @ SY3568 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY3565 )
| ~ ( c_Type_Otyping @ SY3566 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3567 ) @ SY3568 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(3203,plain,
! [SV309: $i] :
( ( ! [SY3569: $i] :
( ( c_HOL_Oord__class_Oless @ SV309 @ SY3569 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY3569 @ SV309 @ tc_nat )
| ( SY3569 = SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(3204,plain,
! [SV310: $i] :
( ( ! [SY3570: $i,SY3571: $i] :
( ~ ( class_Orderings_Oorder @ SV310 )
| ( SY3570 = SY3571 )
| ~ ( c_lessequals @ SY3571 @ SY3570 @ SV310 )
| ~ ( c_lessequals @ SY3570 @ SY3571 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(3205,plain,
! [SV311: $i] :
( ( ! [SY3572: $i,SY3573: $i] :
( ~ ( class_Orderings_Olinorder @ SV311 )
| ( c_HOL_Oord__class_Oless @ SY3572 @ SY3573 @ SV311 )
| ( c_HOL_Oord__class_Oless @ SY3573 @ SY3572 @ SV311 )
| ( SY3573 = SY3572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(3206,plain,
! [SV312: $i] :
( ( ! [SY3574: $i,SY3575: $i] :
( ~ ( class_Orderings_Oorder @ SV312 )
| ( SY3574 = SY3575 )
| ~ ( c_lessequals @ SY3575 @ SY3574 @ SV312 )
| ~ ( c_lessequals @ SY3574 @ SY3575 @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(3207,plain,
! [SV313: $i] :
( ( ! [SY3576: $i,SY3577: $i] :
( ~ ( class_Orderings_Oorder @ SV313 )
| ( SY3576 = SY3577 )
| ~ ( c_lessequals @ SY3576 @ SY3577 @ SV313 )
| ~ ( c_lessequals @ SY3577 @ SY3576 @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(3208,plain,
! [SV314: $i] :
( ( ! [SY3578: $i,SY3579: $i,SY3580: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV314 @ SY3578 @ SY3579 ) @ ( c_List_Oreplicate @ SY3580 @ SY3578 @ SY3579 ) @ SY3579 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY3580 @ SY3578 @ SY3579 ) @ ( c_List_Oreplicate @ SV314 @ SY3578 @ SY3579 ) @ SY3579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(3209,plain,
! [SV315: $i] :
( ( ! [SY3581: $i,SY3582: $i] :
( ~ ( class_Orderings_Olinorder @ SV315 )
| ( c_HOL_Oord__class_Oless @ SY3581 @ SY3582 @ SV315 )
| ( SY3582 = SY3581 )
| ( c_HOL_Oord__class_Oless @ SY3582 @ SY3581 @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(3210,plain,
! [SV316: $i] :
( ( ! [SY3583: $i,SY3584: $i] :
( ~ ( class_Orderings_Olinorder @ SV316 )
| ( SY3583 = SY3584 )
| ( c_HOL_Oord__class_Oless @ SY3583 @ SY3584 @ SV316 )
| ( c_HOL_Oord__class_Oless @ SY3584 @ SY3583 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(3211,plain,
! [SV317: $i] :
( ( ! [SY3585: $i,SY3586: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV317 )
| ( c_lessequals @ SY3585 @ SY3586 @ SV317 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY3585 @ SY3586 @ SV317 ) @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(3212,plain,
! [SV318: $i] :
( ( ! [SY3587: $i,SY3588: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV318 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY3587 @ SY3588 @ SV318 ) @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV318 )
| ~ ( c_lessequals @ SY3587 @ SY3588 @ SV318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(3213,plain,
! [SV319: $i] :
( ( ! [SY3589: $i] :
( ~ ( class_Orderings_Olinorder @ SV319 )
| ( ( c_Orderings_Oord__class_Omax @ SY3589 @ SY3589 @ SV319 )
= SY3589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(3214,plain,
! [SV320: $i] :
( ( ! [SY3590: $i,SY3591: $i,SY3592: $i,SY3593: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SY3590 ) @ SY3591 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SY3592 ) @ SY3593 ) @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SY3591 @ SY3593 @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SY3590 @ SY3592 @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(3215,plain,
! [SV321: $i] :
( ( ! [SY3594: $i,SY3595: $i,SY3596: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SY3594 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3595 ) @ SY3596 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3594 @ SY3596 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV321 @ SY3595 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(3216,plain,
! [SV322: $i] :
( ( ! [SY3597: $i] :
( ( c_lessequals @ SV322 @ SY3597 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV322 @ SY3597 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(3217,plain,
! [SV323: $i] :
( ( ! [SY3598: $i] :
( ( c_lessequals @ SV323 @ SY3598 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV323 @ SY3598 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(3218,plain,
! [SV324: $i] :
( ( ! [SY3599: $i,SY3600: $i] :
( ~ ( class_Orderings_Oorder @ SV324 )
| ( c_lessequals @ SY3599 @ SY3600 @ SV324 )
| ~ ( c_HOL_Oord__class_Oless @ SY3599 @ SY3600 @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(3219,plain,
! [SV325: $i] :
( ( ! [SY3601: $i,SY3602: $i] :
( ~ ( class_Orderings_Opreorder @ SV325 )
| ( c_lessequals @ SY3601 @ SY3602 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SY3601 @ SY3602 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(3220,plain,
! [SV326: $i] :
( ( ! [SY3603: $i,SY3604: $i,SY3605: $i] :
( ~ ( class_Orderings_Olinorder @ SV326 )
| ( c_HOL_Oord__class_Oless @ SY3603 @ SY3604 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ SY3603 @ ( c_Orderings_Oord__class_Omin @ SY3604 @ SY3605 @ SV326 ) @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(3221,plain,
! [SV327: $i] :
( ( ! [SY3606: $i,SY3607: $i,SY3608: $i] :
( ~ ( class_Orderings_Olinorder @ SV327 )
| ( c_HOL_Oord__class_Oless @ SY3606 @ SY3607 @ SV327 )
| ~ ( c_HOL_Oord__class_Oless @ SY3606 @ ( c_Orderings_Oord__class_Omin @ SY3608 @ SY3607 @ SV327 ) @ SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(3222,plain,
! [SV328: $i] :
( ( ! [SY3609: $i,SY3610: $i,SY3611: $i] :
( ~ ( class_Orderings_Olinorder @ SV328 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY3609 @ SY3610 @ SV328 ) @ SY3611 @ SV328 )
| ~ ( c_HOL_Oord__class_Oless @ SY3609 @ SY3611 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(3223,plain,
! [SV329: $i] :
( ( ! [SY3612: $i,SY3613: $i,SY3614: $i] :
( ~ ( class_Orderings_Olinorder @ SV329 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY3612 @ SY3613 @ SV329 ) @ SY3614 @ SV329 )
| ~ ( c_HOL_Oord__class_Oless @ SY3613 @ SY3614 @ SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(3224,plain,
! [SV330: $i] :
( ( ! [SY3615: $i,SY3616: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV330 @ SY3615 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3616 @ SY3615 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV330 @ SY3616 @ tc_nat ) )
| ~ ( c_lessequals @ SY3615 @ SY3616 @ tc_nat )
| ~ ( c_lessequals @ SY3615 @ SV330 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(3225,plain,
! [SV331: $i] :
( ( ! [SY3617: $i,SY3618: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV331 @ SY3617 @ tc_nat ) @ SY3618 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV331 @ SY3618 @ tc_nat ) @ SY3617 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(3226,plain,
! [SV332: $i] :
( ( ! [SY3619: $i,SY3620: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV332 ) @ SY3619 ) @ SY3620 ) @ SV332 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SY3620 @ SV332 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SY3619 @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(3227,plain,
! [SV333: $i] :
( ( ! [SY3621: $i,SY3622: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV333 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV333 ) @ SY3621 ) @ SY3622 ) @ SV333 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SY3622 @ SV333 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SY3621 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(3228,plain,
! [SV334: $i] :
( ( ! [SY3623: $i,SY3624: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV334 @ SY3623 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3624 @ SY3623 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3623 @ SV334 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV334 @ SY3624 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(3229,plain,
! [SV335: $i] :
( ( ! [SY3625: $i,SY3626: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV335 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3625 @ SY3626 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
| ~ ( c_lessequals @ SY3626 @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SY3625 @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(3230,plain,
! [SV336: $i] :
( ( ! [SY3627: $i,SY3628: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV336 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3627 @ SY3628 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SY3628 @ SV336 )
| ~ ( c_lessequals @ SY3627 @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(3231,plain,
! [SV337: $i] :
( ( ! [SY3629: $i,SY3630: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV337 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3629 @ SY3630 @ SV337 ) @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
| ~ ( c_lessequals @ SY3630 @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SY3629 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(3232,plain,
! [SV338: $i] :
( ( ! [SY3631: $i,SY3632: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV338 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3631 @ SY3632 @ SV338 ) @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SY3632 @ SV338 )
| ~ ( c_lessequals @ SY3631 @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(3233,plain,
! [SV339: $i] :
( ( ! [SY3633: $i,SY3634: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV339 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3633 @ SY3634 @ SV339 ) @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
| ~ ( c_lessequals @ SY3634 @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SY3633 @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(3234,plain,
! [SV340: $i] :
( ( ! [SY3635: $i,SY3636: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV340 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3635 @ SY3636 @ SV340 ) @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SY3636 @ SV340 )
| ~ ( c_lessequals @ SY3635 @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(3235,plain,
! [SV341: $i] :
( ( ! [SY3637: $i,SY3638: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV341 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3637 @ SY3638 @ SV341 ) @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
| ~ ( c_lessequals @ SY3637 @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SY3638 @ SV341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(3236,plain,
! [SV342: $i] :
( ( ! [SY3639: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV342 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3639 @ SY3639 @ SV342 ) @ ( c_HOL_Ozero__class_Ozero @ SV342 ) @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(3237,plain,
! [SV343: $i] :
( ( ! [SY3640: $i,SY3641: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV343 ) @ SY3640 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV343 ) @ SY3641 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3640 @ SY3641 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(3238,plain,
! [SV344: $i] :
( ( ! [SY3642: $i,SY3643: $i] :
( ( c_HOL_Oord__class_Oless @ SV344 @ SY3642 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY3643 ) @ SV344 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY3643 ) @ SY3642 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(3239,plain,
! [SV345: $i] :
( ( ! [SY3644: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV345 ) @ SY3644 @ tc_nat )
| ( ( c_Suc @ SV345 )
= SY3644 )
| ~ ( c_HOL_Oord__class_Oless @ SV345 @ SY3644 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(3240,plain,
! [SV346: $i] :
( ( ! [SY3645: $i] :
( ~ ( c_lessequals @ SV346 @ SY3645 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SY3645 ) @ SV346 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(3241,plain,
! [SV347: $i] :
( ( ! [SY3646: $i] :
( ( c_lessequals @ ( c_Suc @ SV347 ) @ SY3646 @ tc_nat )
| ( c_lessequals @ SY3646 @ SV347 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(3242,plain,
! [SV348: $i] :
( ( ! [SY3647: $i,SY3648: $i,SY3649: $i] :
( ( c_List_Olist_OCons @ SV348 @ ( c_List_Oappend @ SY3647 @ SY3648 @ SY3649 ) @ SY3649 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV348 @ SY3647 @ SY3649 ) @ SY3648 @ SY3649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(3243,plain,
! [SV349: $i] :
( ( ! [SY3650: $i,SY3651: $i,SY3652: $i] :
( ( c_List_Olist_OCons @ SV349 @ ( c_List_Oappend @ SY3650 @ SY3651 @ SY3652 ) @ SY3652 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV349 @ SY3650 @ SY3652 ) @ SY3651 @ SY3652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(3244,plain,
! [SV350: $i] :
( ( ! [SY3653: $i,SY3654: $i,SY3655: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV350 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ ( c_Orderings_Oord__class_Omin @ SY3653 @ SY3654 @ SV350 ) ) @ SY3655 )
= ( c_Orderings_Oord__class_Omin @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SY3653 ) @ SY3655 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SY3654 ) @ SY3655 ) @ SV350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(3245,plain,
! [SV351: $i] :
( ( ! [SY3656: $i,SY3657: $i] :
( ( c_lessequals @ SV351 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3656 ) @ SV351 ) @ SY3657 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3657 @ SY3656 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(3246,plain,
! [SV352: $i] :
( ( ! [SY3658: $i,SY3659: $i,SY3660: $i,SY3661: $i,SY3662: $i,SY3663: $i,SY3664: $i,SY3665: $i] :
( ( ( hAPP @ ( hAPP @ SV352 @ ( hAPP @ ( hAPP @ SY3658 @ SY3659 ) @ SY3660 ) ) @ SY3661 )
= ( hAPP @ ( hAPP @ SY3658 @ ( hAPP @ ( hAPP @ SV352 @ SY3659 ) @ SY3661 ) ) @ ( hAPP @ ( hAPP @ SV352 @ SY3660 ) @ SY3661 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3662 @ SY3658 @ SV352 @ SY3663 @ SY3664 @ SY3665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(3247,plain,
! [SV353: $i] :
( ( ! [SY3666: $i,SY3667: $i,SY3668: $i,SY3669: $i,SY3670: $i,SY3671: $i,SY3672: $i,SY3673: $i] :
( ( ( hAPP @ ( hAPP @ SV353 @ SY3666 ) @ ( hAPP @ ( hAPP @ SY3667 @ SY3668 ) @ SY3669 ) )
= ( hAPP @ ( hAPP @ SY3667 @ ( hAPP @ ( hAPP @ SV353 @ SY3666 ) @ SY3668 ) ) @ ( hAPP @ ( hAPP @ SV353 @ SY3666 ) @ SY3669 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3667 @ SV353 @ SY3670 @ SY3671 @ SY3672 @ SY3673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(3248,plain,
! [SV354: $i] :
( ( ! [SY3674: $i,SY3675: $i,SY3676: $i,SY3677: $i,SY3678: $i,SY3679: $i,SY3680: $i] :
( ( ( hAPP @ ( hAPP @ SV354 @ SY3674 ) @ SY3675 )
= ( hAPP @ ( hAPP @ SV354 @ SY3675 ) @ SY3674 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3676 @ SV354 @ SY3677 @ SY3678 @ SY3679 @ SY3680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(3249,plain,
! [SV355: $i] :
( ( ! [SY3681: $i,SY3682: $i,SY3683: $i,SY3684: $i,SY3685: $i,SY3686: $i,SY3687: $i,SY3688: $i] :
( ( ( hAPP @ ( hAPP @ SV355 @ SY3681 ) @ ( hAPP @ ( hAPP @ SV355 @ SY3682 ) @ SY3683 ) )
= ( hAPP @ ( hAPP @ SV355 @ ( hAPP @ ( hAPP @ SV355 @ SY3681 ) @ SY3682 ) ) @ SY3683 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3684 @ SV355 @ SY3685 @ SY3686 @ SY3687 @ SY3688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(3250,plain,
! [SV356: $i] :
( ( ! [SY3689: $i,SY3690: $i,SY3691: $i,SY3692: $i,SY3693: $i,SY3694: $i] :
( ( ( hAPP @ ( hAPP @ SV356 @ SY3689 ) @ SY3690 )
= SY3690 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3691 @ SV356 @ SY3692 @ SY3693 @ SY3689 @ SY3694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(3251,plain,
! [SV357: $i] :
( ( ! [SY3695: $i,SY3696: $i,SY3697: $i,SY3698: $i,SY3699: $i,SY3700: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SY3695 ) @ SY3696 )
= SY3695 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3697 @ SV357 @ SY3698 @ SY3695 @ SY3699 @ SY3700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(3252,plain,
! [SV358: $i] :
( ( ! [SY3701: $i,SY3702: $i,SY3703: $i,SY3704: $i,SY3705: $i,SY3706: $i,SY3707: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SY3701 ) @ SY3702 )
= ( hAPP @ ( hAPP @ SV358 @ SY3702 ) @ SY3701 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV358 @ SY3703 @ SY3704 @ SY3705 @ SY3706 @ SY3707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(3253,plain,
! [SV359: $i] :
( ( ! [SY3708: $i,SY3709: $i,SY3710: $i,SY3711: $i,SY3712: $i,SY3713: $i,SY3714: $i,SY3715: $i] :
( ( ( hAPP @ ( hAPP @ SV359 @ SY3708 ) @ ( hAPP @ ( hAPP @ SV359 @ SY3709 ) @ SY3710 ) )
= ( hAPP @ ( hAPP @ SV359 @ ( hAPP @ ( hAPP @ SV359 @ SY3708 ) @ SY3709 ) ) @ SY3710 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV359 @ SY3711 @ SY3712 @ SY3713 @ SY3714 @ SY3715 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(3254,plain,
! [SV360: $i] :
( ( ! [SY3716: $i,SY3717: $i,SY3718: $i,SY3719: $i,SY3720: $i,SY3721: $i] :
( ( ( hAPP @ ( hAPP @ SV360 @ SY3716 ) @ SY3717 )
= SY3717 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV360 @ SY3718 @ SY3719 @ SY3716 @ SY3720 @ SY3721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(3255,plain,
! [SV361: $i] :
( ( ! [SY3722: $i,SY3723: $i,SY3724: $i,SY3725: $i,SY3726: $i,SY3727: $i,SY3728: $i,SY3729: $i] :
( ( ( hAPP @ ( hAPP @ SV361 @ SY3722 ) @ ( hAPP @ ( hAPP @ SV361 @ SY3723 ) @ SY3724 ) )
= ( hAPP @ ( hAPP @ SV361 @ ( hAPP @ ( hAPP @ SV361 @ SY3722 ) @ SY3723 ) ) @ SY3724 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV361 @ SY3725 @ SY3726 @ SY3727 @ SY3728 @ SY3729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(3256,plain,
! [SV362: $i] :
( ( ! [SY3730: $i,SY3731: $i,SY3732: $i,SY3733: $i,SY3734: $i,SY3735: $i,SY3736: $i] :
( ( ( hAPP @ ( hAPP @ SV362 @ SY3730 ) @ SY3731 )
= ( hAPP @ ( hAPP @ SV362 @ SY3731 ) @ SY3730 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV362 @ SY3732 @ SY3733 @ SY3734 @ SY3735 @ SY3736 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(3257,plain,
! [SV363: $i] :
( ( ! [SY3737: $i,SY3738: $i,SY3739: $i,SY3740: $i,SY3741: $i,SY3742: $i,SY3743: $i,SY3744: $i] :
( ( ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SY3737 ) @ SY3738 ) ) @ SY3739 )
= ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SY3737 ) @ SY3739 ) ) @ SY3738 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV363 @ SY3740 @ SY3741 @ SY3742 @ SY3743 @ SY3744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(3258,plain,
! [SV364: $i] :
( ( ! [SY3745: $i,SY3746: $i,SY3747: $i,SY3748: $i,SY3749: $i,SY3750: $i,SY3751: $i,SY3752: $i] :
( ( ( hAPP @ ( hAPP @ SV364 @ SY3745 ) @ ( hAPP @ ( hAPP @ SV364 @ SY3746 ) @ SY3747 ) )
= ( hAPP @ ( hAPP @ SV364 @ SY3746 ) @ ( hAPP @ ( hAPP @ SV364 @ SY3745 ) @ SY3747 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV364 @ SY3748 @ SY3749 @ SY3750 @ SY3751 @ SY3752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(3259,plain,
! [SV365: $i] :
( ( ! [SY3753: $i,SY3754: $i,SY3755: $i,SY3756: $i,SY3757: $i,SY3758: $i,SY3759: $i,SY3760: $i] :
( ( ( hAPP @ ( hAPP @ SV365 @ ( hAPP @ ( hAPP @ SV365 @ SY3753 ) @ SY3754 ) ) @ SY3755 )
= ( hAPP @ ( hAPP @ SV365 @ SY3753 ) @ ( hAPP @ ( hAPP @ SV365 @ SY3754 ) @ SY3755 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV365 @ SY3756 @ SY3757 @ SY3758 @ SY3759 @ SY3760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(3260,plain,
! [SV366: $i] :
( ( ! [SY3761: $i,SY3762: $i,SY3763: $i,SY3764: $i,SY3765: $i,SY3766: $i,SY3767: $i,SY3768: $i,SY3769: $i] :
( ( ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SY3761 ) @ SY3762 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SY3763 ) @ SY3764 ) )
= ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SY3761 ) @ SY3763 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SY3762 ) @ SY3764 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV366 @ SY3765 @ SY3766 @ SY3767 @ SY3768 @ SY3769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(3261,plain,
! [SV367: $i] :
( ( ! [SY3770: $i,SY3771: $i,SY3772: $i,SY3773: $i,SY3774: $i,SY3775: $i,SY3776: $i,SY3777: $i] :
( ( ( hAPP @ ( hAPP @ SV367 @ SY3770 ) @ ( hAPP @ ( hAPP @ SV367 @ SY3771 ) @ SY3772 ) )
= ( hAPP @ ( hAPP @ SV367 @ SY3771 ) @ ( hAPP @ ( hAPP @ SV367 @ SY3770 ) @ SY3772 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3773 @ SV367 @ SY3774 @ SY3775 @ SY3776 @ SY3777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(3262,plain,
! [SV368: $i] :
( ( ! [SY3778: $i,SY3779: $i,SY3780: $i,SY3781: $i,SY3782: $i,SY3783: $i,SY3784: $i,SY3785: $i] :
( ( ( hAPP @ ( hAPP @ SV368 @ SY3778 ) @ ( hAPP @ ( hAPP @ SV368 @ SY3779 ) @ SY3780 ) )
= ( hAPP @ ( hAPP @ SV368 @ ( hAPP @ ( hAPP @ SV368 @ SY3778 ) @ SY3779 ) ) @ SY3780 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3781 @ SV368 @ SY3782 @ SY3783 @ SY3784 @ SY3785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(3263,plain,
! [SV369: $i] :
( ( ! [SY3786: $i,SY3787: $i,SY3788: $i,SY3789: $i,SY3790: $i,SY3791: $i,SY3792: $i,SY3793: $i] :
( ( ( hAPP @ ( hAPP @ SV369 @ ( hAPP @ ( hAPP @ SV369 @ SY3786 ) @ SY3787 ) ) @ SY3788 )
= ( hAPP @ ( hAPP @ SV369 @ SY3786 ) @ ( hAPP @ ( hAPP @ SV369 @ SY3787 ) @ SY3788 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3789 @ SV369 @ SY3790 @ SY3791 @ SY3792 @ SY3793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(3264,plain,
! [SV370: $i] :
( ( ! [SY3794: $i,SY3795: $i,SY3796: $i,SY3797: $i,SY3798: $i,SY3799: $i,SY3800: $i,SY3801: $i] :
( ( ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SY3794 ) @ SY3795 ) ) @ SY3796 )
= ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SY3794 ) @ SY3796 ) ) @ SY3795 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3797 @ SV370 @ SY3798 @ SY3799 @ SY3800 @ SY3801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(3265,plain,
! [SV371: $i] :
( ( ! [SY3802: $i,SY3803: $i,SY3804: $i,SY3805: $i,SY3806: $i,SY3807: $i,SY3808: $i,SY3809: $i,SY3810: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SY3802 ) @ SY3803 ) ) @ ( hAPP @ ( hAPP @ SV371 @ SY3804 ) @ SY3805 ) )
= ( hAPP @ ( hAPP @ SV371 @ SY3804 ) @ ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SY3802 ) @ SY3803 ) ) @ SY3805 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3806 @ SV371 @ SY3807 @ SY3808 @ SY3809 @ SY3810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(3266,plain,
! [SV372: $i] :
( ( ! [SY3811: $i,SY3812: $i,SY3813: $i,SY3814: $i,SY3815: $i,SY3816: $i,SY3817: $i,SY3818: $i,SY3819: $i] :
( ( ( hAPP @ ( hAPP @ SV372 @ ( hAPP @ ( hAPP @ SV372 @ SY3811 ) @ SY3812 ) ) @ ( hAPP @ ( hAPP @ SV372 @ SY3813 ) @ SY3814 ) )
= ( hAPP @ ( hAPP @ SV372 @ SY3811 ) @ ( hAPP @ ( hAPP @ SV372 @ SY3812 ) @ ( hAPP @ ( hAPP @ SV372 @ SY3813 ) @ SY3814 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3815 @ SV372 @ SY3816 @ SY3817 @ SY3818 @ SY3819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(3267,plain,
! [SV373: $i] :
( ( ! [SY3820: $i,SY3821: $i,SY3822: $i,SY3823: $i,SY3824: $i,SY3825: $i,SY3826: $i,SY3827: $i,SY3828: $i] :
( ( ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SY3820 ) @ SY3821 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SY3822 ) @ SY3823 ) )
= ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SY3820 ) @ SY3822 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SY3821 ) @ SY3823 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3824 @ SV373 @ SY3825 @ SY3826 @ SY3827 @ SY3828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(3268,plain,
! [SV374: $i] :
( ( ! [SY3829: $i,SY3830: $i,SY3831: $i,SY3832: $i,SY3833: $i,SY3834: $i] :
( ( ( hAPP @ ( hAPP @ SV374 @ SY3829 ) @ SY3830 )
= SY3829 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3831 @ SV374 @ SY3832 @ SY3833 @ SY3830 @ SY3834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(3269,plain,
! [SV375: $i] :
( ( ! [SY3835: $i,SY3836: $i,SY3837: $i,SY3838: $i,SY3839: $i,SY3840: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SY3835 ) @ SY3836 )
= SY3836 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3837 @ SV375 @ SY3838 @ SY3839 @ SY3835 @ SY3840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(3270,plain,
! [SV376: $i] :
( ( ! [SY3841: $i,SY3842: $i,SY3843: $i,SY3844: $i,SY3845: $i,SY3846: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ SY3841 ) @ SY3842 )
= SY3842 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3843 @ SV376 @ SY3844 @ SY3842 @ SY3845 @ SY3846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(3271,plain,
! [SV377: $i] :
( ( ! [SY3847: $i,SY3848: $i,SY3849: $i,SY3850: $i,SY3851: $i,SY3852: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SY3847 ) @ SY3848 )
= SY3847 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3849 @ SV377 @ SY3850 @ SY3847 @ SY3851 @ SY3852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(3272,plain,
! [SV378: $i] :
( ( ! [SY3853: $i,SY3854: $i,SY3855: $i,SY3856: $i,SY3857: $i,SY3858: $i,SY3859: $i,SY3860: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ ( hAPP @ ( hAPP @ SY3853 @ SY3854 ) @ SY3855 ) ) @ SY3856 )
= ( hAPP @ ( hAPP @ SY3853 @ ( hAPP @ ( hAPP @ SV378 @ SY3854 ) @ SY3856 ) ) @ ( hAPP @ ( hAPP @ SV378 @ SY3855 ) @ SY3856 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3853 @ SV378 @ SY3857 @ SY3858 @ SY3859 @ SY3860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(3273,plain,
! [SV379: $i] :
( ( ! [SY3861: $i,SY3862: $i,SY3863: $i,SY3864: $i,SY3865: $i,SY3866: $i,SY3867: $i] :
( ( ( hAPP @ ( hAPP @ SV379 @ SY3861 ) @ SY3862 )
= ( hAPP @ ( hAPP @ SV379 @ SY3862 ) @ SY3861 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3863 @ SV379 @ SY3864 @ SY3865 @ SY3866 @ SY3867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(3274,plain,
! [SV380: $i] :
( ( ! [SY3868: $i,SY3869: $i,SY3870: $i,SY3871: $i,SY3872: $i,SY3873: $i] :
( ( ( hAPP @ ( hAPP @ SV380 @ SY3868 ) @ SY3869 )
= SY3868 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV380 @ SY3870 @ SY3871 @ SY3869 @ SY3872 @ SY3873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(3275,plain,
! [SV381: $i] :
( ( ! [SY3874: $i,SY3875: $i,SY3876: $i,SY3877: $i,SY3878: $i,SY3879: $i] :
( ( ( hAPP @ ( hAPP @ SV381 @ SY3874 ) @ SY3875 )
= SY3875 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV381 @ SY3876 @ SY3877 @ SY3874 @ SY3878 @ SY3879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(3276,plain,
! [SV382: $i] :
( ( ! [SY3880: $i,SY3881: $i,SY3882: $i,SY3883: $i,SY3884: $i,SY3885: $i] :
( ( ( hAPP @ ( hAPP @ SV382 @ SY3880 ) @ SY3880 )
= ( hAPP @ ( hAPP @ SY3881 @ ( hAPP @ ( hAPP @ SV382 @ SY3882 ) @ SY3882 ) ) @ SY3880 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV382 @ SY3881 @ SY3883 @ SY3884 @ SY3882 @ SY3885 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(3277,plain,
! [SV383: $i] :
( ( ! [SY3886: $i,SY3887: $i,SY3888: $i,SY3889: $i,SY3890: $i,SY3891: $i,SY3892: $i] :
( ( ( hAPP @ ( hAPP @ SV383 @ SY3886 ) @ ( hAPP @ ( hAPP @ SY3887 @ SY3888 ) @ SY3886 ) )
= ( hAPP @ ( hAPP @ SY3887 @ ( hAPP @ ( hAPP @ SV383 @ SY3888 ) @ SY3889 ) ) @ SY3886 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV383 @ SY3887 @ SY3890 @ SY3891 @ SY3889 @ SY3892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(3278,plain,
! [SV384: $i] :
( ( ! [SY3893: $i,SY3894: $i,SY3895: $i,SY3896: $i,SY3897: $i,SY3898: $i,SY3899: $i] :
( ( ( hAPP @ ( hAPP @ SV384 @ ( hAPP @ ( hAPP @ SY3893 @ SY3894 ) @ SY3895 ) ) @ SY3895 )
= ( hAPP @ ( hAPP @ SY3893 @ ( hAPP @ ( hAPP @ SV384 @ SY3894 ) @ SY3896 ) ) @ SY3895 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV384 @ SY3893 @ SY3897 @ SY3898 @ SY3896 @ SY3899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(3279,plain,
! [SV385: $i] :
( ( ! [SY3900: $i,SY3901: $i,SY3902: $i,SY3903: $i,SY3904: $i,SY3905: $i,SY3906: $i,SY3907: $i] :
( ( ( hAPP @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ SY3900 @ SY3901 ) @ SY3902 ) ) @ ( hAPP @ ( hAPP @ SY3900 @ SY3903 ) @ SY3902 ) )
= ( hAPP @ ( hAPP @ SY3900 @ ( hAPP @ ( hAPP @ SV385 @ SY3901 ) @ SY3903 ) ) @ SY3902 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV385 @ SY3900 @ SY3904 @ SY3905 @ SY3906 @ SY3907 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(3280,plain,
! [SV386: $i] :
( ( ! [SY3908: $i,SY3909: $i,SY3910: $i] :
( ~ ( hBOOL @ ( hAPP @ SV386 @ ( c_Type_Otype_Otype__case @ SY3908 @ SY3909 @ ( c_Type_Otype_OAtom @ SY3910 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV386 @ ( hAPP @ SY3908 @ SY3910 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(3281,plain,
! [SV387: $i] :
( ( ! [SY3911: $i,SY3912: $i,SY3913: $i] :
( ~ ( hBOOL @ ( hAPP @ SV387 @ ( c_Type_Otype_Otype__case @ SY3911 @ SY3912 @ ( c_Type_Otype_OAtom @ SY3913 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV387 @ ( hAPP @ SY3911 @ SY3913 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(3282,plain,
! [SV388: $i] :
( ( ! [SY3914: $i,SY3915: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV388 ) @ SY3914 @ tc_nat ) @ ( c_Suc @ SY3915 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV388 @ SY3914 @ tc_nat ) @ SY3915 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(3283,plain,
! [SV389: $i] :
( ( ! [SY3916: $i,SY3917: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV389 ) @ SY3916 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV389 ) @ SY3917 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3916 @ SY3917 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(3284,plain,
! [SV390: $i] :
( ( ! [SY3918: $i,SY3919: $i] :
( ( c_lessequals @ SV390 @ SY3918 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY3919 ) @ SV390 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY3919 ) @ SY3918 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(3285,plain,
! [SV391: $i] :
( ( ! [SY3920: $i,SY3921: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV391 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV391 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV391 ) @ ( c_HOL_Otimes__class_Otimes @ SY3920 @ SY3920 @ SV391 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY3921 @ SY3921 @ SV391 ) ) @ SV391 )
| ( SY3920
= ( c_HOL_Ozero__class_Ozero @ SV391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(3286,plain,
! [SV392: $i] :
( ( ! [SY3922: $i,SY3923: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV392 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV392 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV392 ) @ ( c_HOL_Otimes__class_Otimes @ SY3922 @ SY3922 @ SV392 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY3923 @ SY3923 @ SV392 ) ) @ SV392 )
| ( SY3923
= ( c_HOL_Ozero__class_Ozero @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(3287,plain,
! [SV393: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV393 ) )
| ~ ( c_InductTermi_OIT @ SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(3288,plain,
! [SV394: $i] :
( ( ! [SY3924: $i,SY3925: $i,SY3926: $i,SY3927: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV394 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SY3924 ) @ SY3925 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SY3926 ) @ SY3927 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SY3924 ) @ SY3926 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SY3925 ) @ SY3927 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(3289,plain,
! [SV395: $i] :
( ( ! [SY3928: $i,SY3929: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV395 ) @ SY3928 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV395 ) @ SY3929 ) )
| ~ ( c_Lambda_Obeta @ SY3928 @ SY3929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(3290,plain,
! [SV396: $i] :
( ( ! [SY3930: $i,SY3931: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV396 ) @ SY3930 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3931 ) @ SY3930 ) )
| ~ ( c_Lambda_Obeta @ SV396 @ SY3931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(3291,plain,
! [SV397: $i] :
( ( ! [SY3932: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV397 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3932 @ SV397 ) @ ( c_HOL_Ozero__class_Ozero @ SV397 ) @ SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(3292,plain,
! [SV398: $i] :
( ( ! [SY3933: $i,SY3934: $i] :
( ~ ( class_Orderings_Olinorder @ SV398 )
| ( ( c_Orderings_Oord__class_Omax @ SY3933 @ SY3934 @ SV398 )
= ( c_Orderings_Oord__class_Omax @ SY3934 @ SY3933 @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(3293,plain,
! [SV399: $i] :
( ( c_lessequals @ ( c_Suc @ SV399 ) @ ( c_Suc @ SV399 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(3294,plain,
! [SV400: $i] :
( ( ! [SY3935: $i,SY3936: $i,SY3937: $i] :
( ( c_List_Odrop @ SV400 @ ( c_List_Oreplicate @ SY3935 @ SY3936 @ SY3937 ) @ SY3937 )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ SY3935 @ SV400 @ tc_nat ) @ SY3936 @ SY3937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(3295,plain,
! [SV401: $i] :
( ( ! [SY3938: $i,SY3939: $i,SY3940: $i] :
( ~ ( class_Orderings_Olinorder @ SV401 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SY3938 @ SY3939 @ SV401 ) @ ( c_Orderings_Oord__class_Omin @ SY3938 @ SY3940 @ SV401 ) @ SV401 ) @ ( c_Orderings_Oord__class_Omin @ SY3938 @ ( c_Orderings_Oord__class_Omax @ SY3939 @ SY3940 @ SV401 ) @ SV401 ) @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(3296,plain,
! [SV402: $i] :
( ( ! [SY3941: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV402 @ SY3941 )
= ( c_List_Olist_ONil @ SY3941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(3297,plain,
! [SV403: $i] :
( ( ( c_nat_Onat__size @ ( c_Suc @ SV403 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_nat_Onat__size @ SV403 ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(3298,plain,
! [SV404: $i] :
( ( ! [SY3942: $i,SY3943: $i] :
( ~ ( class_Orderings_Olinorder @ SV404 )
| ( ( c_Orderings_Oord__class_Omax @ SY3942 @ ( c_Orderings_Oord__class_Omin @ SY3942 @ SY3943 @ SV404 ) @ SV404 )
= SY3942 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(3299,plain,
! [SV405: $i] :
( ( c_lessequals @ SV405 @ ( c_HOL_Otimes__class_Otimes @ SV405 @ SV405 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(3300,plain,
! [SV406: $i] :
( ( ! [SY3944: $i,SY3945: $i,SY3946: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV406 )
| ( c_HOL_Oord__class_Oless @ SY3944 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SY3944 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3944 @ SY3945 @ SV406 ) @ ( c_HOL_Otimes__class_Otimes @ SY3944 @ SY3946 @ SV406 ) @ SV406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(3301,plain,
! [SV407: $i] :
( ( ! [SY3947: $i,SY3948: $i,SY3949: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV407 )
| ( c_HOL_Oord__class_Oless @ SY3947 @ SY3948 @ SV407 )
| ( c_HOL_Oord__class_Oless @ SY3948 @ SY3947 @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3949 @ SY3948 @ SV407 ) @ ( c_HOL_Otimes__class_Otimes @ SY3949 @ SY3947 @ SV407 ) @ SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(3302,plain,
! [SV408: $i] :
( ( ! [SY3950: $i,SY3951: $i,SY3952: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV408 )
| ( c_HOL_Oord__class_Oless @ SY3950 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SY3950 @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3951 @ SY3950 @ SV408 ) @ ( c_HOL_Otimes__class_Otimes @ SY3952 @ SY3950 @ SV408 ) @ SV408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(3303,plain,
! [SV409: $i] :
( ( ! [SY3953: $i,SY3954: $i,SY3955: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV409 )
| ( c_HOL_Oord__class_Oless @ SY3953 @ SY3954 @ SV409 )
| ( c_HOL_Oord__class_Oless @ SY3954 @ SY3953 @ SV409 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3954 @ SY3955 @ SV409 ) @ ( c_HOL_Otimes__class_Otimes @ SY3953 @ SY3955 @ SV409 ) @ SV409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(3304,plain,
! [SV410: $i] :
( ( ! [SY3956: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV410 @ ( c_HOL_Ominus__class_Ominus @ SV410 @ SY3956 @ tc_nat ) @ tc_nat )
= SY3956 )
| ~ ( c_lessequals @ SY3956 @ SV410 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(3305,plain,
! [SV411: $i] :
( ( ! [SY3957: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV411 ) @ SY3957 )
= ( c_Lambda_OdB_OVar @ SV411 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ SY3957 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(3306,plain,
! [SV412: $i] :
( ( ! [SY3958: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV412 ) @ SY3958 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(3307,plain,
! [SV413: $i] :
( ( ! [SY3959: $i,SY3960: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV413 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SY3959 @ SY3960 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV413 ) @ SY3960 ) @ ( c_Suc @ SY3959 ) @ tc_nat ) )
| ~ ( c_lessequals @ SY3960 @ SY3959 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(3308,plain,
! [SV414: $i] :
( ( ! [SY3961: $i,SY3962: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV414 )
| ( c_HOL_Oord__class_Oless @ SY3961 @ SY3962 @ SV414 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY3961 @ SY3962 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(3309,plain,
! [SV415: $i] :
( ( ! [SY3963: $i,SY3964: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV415 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY3963 @ SY3964 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 )
| ~ ( c_HOL_Oord__class_Oless @ SY3963 @ SY3964 @ SV415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(3310,plain,
! [SV416: $i] :
( ( ! [SY3965: $i,SY3966: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV416 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3965 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3966 @ SV416 ) @ SV416 )
| ~ ( c_HOL_Oord__class_Oless @ SY3965 @ SY3966 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(3311,plain,
! [SV417: $i] :
( ( ! [SY3967: $i,SY3968: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV417 )
| ( c_HOL_Oord__class_Oless @ SY3967 @ SY3968 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3967 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3968 @ SV417 ) @ SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(3312,plain,
! [SV418: $i] :
( ( c_HOL_Oord__class_Oless @ SV418 @ ( c_Suc @ SV418 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(3313,plain,
! [SV419: $i] :
( ( c_HOL_Oord__class_Oless @ SV419 @ ( c_Suc @ SV419 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(3314,plain,
! [SV420: $i] :
( ( ! [SY3969: $i,SY3970: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV420 ) @ SY3969 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3970 @ SY3969 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV420 @ SY3970 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(3315,plain,
! [SV421: $i] :
( ( ! [SY3971: $i,SY3972: $i,SY3973: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SY3971 ) @ SY3972 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SY3973 ) @ SY3972 ) @ SV421 )
| ~ ( c_lessequals @ SY3971 @ SY3973 @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(3316,plain,
! [SV422: $i] :
( ( ! [SY3974: $i,SY3975: $i,SY3976: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
| ( c_lessequals @ SY3974 @ SY3975 @ SV422 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SY3974 ) @ SY3976 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SY3975 ) @ SY3976 ) @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(3317,plain,
! [SV423: $i] :
( ( ! [SY3977: $i,SY3978: $i,SY3979: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV423 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SY3977 ) @ SY3978 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SY3977 ) @ SY3979 ) @ SV423 )
| ~ ( c_lessequals @ SY3978 @ SY3979 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(3318,plain,
! [SV424: $i] :
( ( ! [SY3980: $i,SY3981: $i,SY3982: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
| ( c_lessequals @ SY3980 @ SY3981 @ SV424 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SY3982 ) @ SY3980 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SY3982 ) @ SY3981 ) @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(3319,plain,
! [SV425: $i] :
( ( ! [SY3983: $i,SY3984: $i,SY3985: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV425 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SY3983 ) @ SY3984 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SY3985 ) @ SY3984 ) @ SV425 )
| ~ ( c_lessequals @ SY3983 @ SY3985 @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(3320,plain,
! [SV426: $i] :
( ( ! [SY3986: $i,SY3987: $i,SY3988: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV426 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SY3986 ) @ SY3987 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SY3986 ) @ SY3988 ) @ SV426 )
| ~ ( c_lessequals @ SY3987 @ SY3988 @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(3321,plain,
! [SV427: $i] :
( ( ! [SY3989: $i,SY3990: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV427 ) @ SY3989 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3990 ) @ SY3989 ) @ tc_nat )
| ~ ( c_lessequals @ SV427 @ SY3990 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(3322,plain,
! [SV428: $i] :
( ( ! [SY3991: $i,SY3992: $i] :
( ( c_lessequals @ SV428 @ SY3991 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3992 ) @ SV428 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3992 ) @ SY3991 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(3323,plain,
! [SV429: $i] :
( ( ! [SY3993: $i,SY3994: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV429 ) @ SY3993 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV429 ) @ SY3994 ) @ tc_nat )
| ~ ( c_lessequals @ SY3993 @ SY3994 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(3324,plain,
! [SV430: $i] :
( ( ! [SY3995: $i] :
( ~ ( c_lessequals @ SV430 @ SY3995 @ tc_nat )
| ( SY3995
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3995 @ SV430 @ tc_nat ) ) @ SV430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(3325,plain,
! [SV431: $i] :
( ( ! [SY3996: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV431 ) @ ( c_HOL_Ominus__class_Ominus @ SY3996 @ SV431 @ tc_nat ) )
= SY3996 )
| ~ ( c_lessequals @ SV431 @ SY3996 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(3326,plain,
! [SV432: $i] :
( ( ! [SY3997: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV432 @ SY3997 @ tc_nat ) ) @ SY3997 )
= SV432 )
| ~ ( c_lessequals @ SY3997 @ SV432 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(3327,plain,
! [SV433: $i] :
( ( ! [SY3998: $i,SY3999: $i,SY4000: $i,SY4001: $i,SY4002: $i,SY4003: $i,SY4004: $i] :
( ( ( hAPP @ ( hAPP @ SV433 @ SY3998 ) @ ( hAPP @ ( hAPP @ SY3999 @ SY3998 ) @ SY4000 ) )
= ( hAPP @ ( hAPP @ SY3999 @ SY3998 ) @ ( c_Suc @ SY4000 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4001 @ SV433 @ SY3999 @ SY4002 @ SY4003 @ SY4004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(3328,plain,
! [SV434: $i] :
( ( ! [SY4005: $i,SY4006: $i,SY4007: $i,SY4008: $i,SY4009: $i,SY4010: $i,SY4011: $i] :
( ( ( hAPP @ ( hAPP @ SV434 @ ( hAPP @ ( hAPP @ SY4005 @ SY4006 ) @ SY4007 ) ) @ SY4006 )
= ( hAPP @ ( hAPP @ SY4005 @ SY4006 ) @ ( c_Suc @ SY4007 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4008 @ SV434 @ SY4005 @ SY4009 @ SY4010 @ SY4011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(3329,plain,
! [SV435: $i] :
( ( ! [SY4012: $i,SY4013: $i,SY4014: $i,SY4015: $i,SY4016: $i,SY4017: $i,SY4018: $i] :
( ( ( hAPP @ ( hAPP @ SV435 @ SY4012 ) @ ( c_Suc @ SY4013 ) )
= ( hAPP @ ( hAPP @ SY4014 @ SY4012 ) @ ( hAPP @ ( hAPP @ SV435 @ SY4012 ) @ SY4013 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4015 @ SY4014 @ SV435 @ SY4016 @ SY4017 @ SY4018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(3330,plain,
! [SV436: $i] :
( ( ! [SY4019: $i,SY4020: $i,SY4021: $i,SY4022: $i,SY4023: $i,SY4024: $i,SY4025: $i] :
( ( ( hAPP @ ( hAPP @ SV436 @ SY4019 ) @ ( c_Suc @ SY4020 ) )
= ( hAPP @ ( hAPP @ SY4021 @ SY4019 ) @ ( hAPP @ ( hAPP @ SV436 @ SY4019 ) @ SY4020 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4022 @ SY4021 @ SV436 @ SY4023 @ SY4024 @ SY4025 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(3331,plain,
! [SV437: $i] :
( ( ! [SY4026: $i,SY4027: $i] :
( ( c_HOL_Oord__class_Oless @ SV437 @ SY4026 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4027 @ SV437 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4027 @ SY4026 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(3332,plain,
! [SV438: $i] :
( ( ! [SY4028: $i,SY4029: $i] :
( ( c_HOL_Oord__class_Oless @ SV438 @ SY4028 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV438 @ SY4029 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4028 @ SY4029 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(3333,plain,
! [SV439: $i] :
( ( ! [SY4030: $i,SY4031: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV439 ) @ ( c_HOL_Ominus__class_Ominus @ SY4030 @ SY4031 @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV439 ) @ SY4030 ) @ SY4031 @ tc_nat ) )
| ~ ( c_lessequals @ SY4031 @ SY4030 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(3334,plain,
! [SV440: $i] :
( ( ! [SY4032: $i,SY4033: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV440 @ SY4032 @ tc_nat ) ) @ SY4033 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV440 ) @ SY4033 ) @ SY4032 @ tc_nat ) )
| ~ ( c_lessequals @ SY4032 @ SV440 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(3335,plain,
! [SV441: $i] :
( ( ! [SY4034: $i,SY4035: $i,SY4036: $i] :
( ( c_List_Odrop @ SV441 @ ( c_List_Odrop @ SY4034 @ SY4035 @ SY4036 ) @ SY4036 )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV441 ) @ SY4034 ) @ SY4035 @ SY4036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(3336,plain,
! [SV442: $i] :
( ( ! [SY4037: $i,SY4038: $i,SY4039: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV442 )
| ( c_lessequals @ SY4037 @ SY4038 @ SV442 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV442 ) @ SY4038 @ SV442 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY4037 @ ( c_Suc @ SY4039 ) @ SV442 ) @ ( c_Power_Opower__class_Opower @ SY4038 @ ( c_Suc @ SY4039 ) @ SV442 ) @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(3337,plain,
! [SV443: $i] :
( ( ! [SY4040: $i,SY4041: $i,SY4042: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV443 ) @ SY4040 ) @ SY4041 @ SY4042 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV443 @ SY4041 @ SY4042 ) @ ( c_List_Oreplicate @ SY4040 @ SY4041 @ SY4042 ) @ SY4042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(3338,plain,
! [SV444: $i] :
( ( ! [SY4043: $i,SY4044: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV444 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4043 @ ( c_HOL_Otimes__class_Otimes @ SY4043 @ SY4044 @ SV444 ) @ SV444 )
= ( c_HOL_Otimes__class_Otimes @ SY4043 @ SY4044 @ SV444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(3339,plain,
! [SV445: $i] :
( ( ! [SY4045: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV445 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV445 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4045 @ SV445 ) @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4045 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(3340,plain,
! [SV446: $i] :
( ( ! [SY4046: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV446 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4046 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4046 @ SV446 ) @ SV446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(3341,plain,
! [SV447: $i] :
( ( ! [SY4047: $i,SY4048: $i,SY4049: $i,SY4050: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4047 @ SY4048 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SY4049 @ SY4050 @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SY4048 @ SV447 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SY4047 @ SV447 )
| ~ ( c_lessequals @ SY4048 @ SY4050 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SY4047 @ SY4049 @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(3342,plain,
! [SV448: $i] :
( ( ! [SY4051: $i,SY4052: $i,SY4053: $i,SY4054: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4051 @ SY4052 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SY4053 @ SY4054 @ SV448 ) @ SV448 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SY4052 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SY4051 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ SY4052 @ SY4054 @ SV448 )
| ~ ( c_lessequals @ SY4051 @ SY4053 @ SV448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(3343,plain,
! [SV449: $i] :
( ( ! [SY4055: $i,SY4056: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV449 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4055 @ ( c_Power_Opower__class_Opower @ SY4055 @ SY4056 @ SV449 ) @ SV449 )
= ( c_Power_Opower__class_Opower @ SY4055 @ ( c_Suc @ SY4056 ) @ SV449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(3344,plain,
! [SV450: $i] :
( ( ! [SY4057: $i,SY4058: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV450 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY4057 @ SY4058 @ SV450 ) @ SY4057 @ SV450 )
= ( c_Power_Opower__class_Opower @ SY4057 @ ( c_Suc @ SY4058 ) @ SV450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(3345,plain,
! [SV451: $i] :
( ( ! [SY4059: $i,SY4060: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV451 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SY4059 @ SV451 )
| ( c_lessequals @ SY4059 @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4060 @ SY4059 @ SV451 ) @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(3346,plain,
! [SV452: $i] :
( ( ! [SY4061: $i,SY4062: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV452 )
| ( c_lessequals @ SY4061 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
| ( c_lessequals @ SY4062 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4061 @ SY4062 @ SV452 ) @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(3347,plain,
! [SV453: $i] :
( ( ! [SY4063: $i,SY4064: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV453 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SY4063 @ SV453 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SY4064 @ SV453 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4064 @ SY4063 @ SV453 ) @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(3348,plain,
! [SV454: $i] :
( ( ! [SY4065: $i,SY4066: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV454 )
| ( c_lessequals @ SY4065 @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SY4065 @ SV454 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4065 @ SY4066 @ SV454 ) @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(3349,plain,
! [SV455: $i] :
( ( ! [SY4067: $i,SY4068: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV455 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4067 @ SY4068 @ SV455 ) @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SY4067 @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SY4068 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(3350,plain,
! [SV456: $i] :
( ( ! [SY4069: $i,SY4070: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV456 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4069 @ SY4070 @ SV456 ) @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SY4070 @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SY4069 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(3351,plain,
! [SV457: $i] :
( ( ! [SY4071: $i,SY4072: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV457 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4071 @ SY4072 @ SV457 ) @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SY4072 @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SY4071 @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(3352,plain,
! [SV458: $i] :
( ( ! [SY4073: $i] :
( ( c_lessequals @ SV458 @ SY4073 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV458 ) @ SY4073 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(3353,plain,
! [SV459: $i] :
( ( ! [SY4074: $i] :
( ( c_lessequals @ SV459 @ ( c_Suc @ SY4074 ) @ tc_nat )
| ~ ( c_lessequals @ SV459 @ SY4074 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(3354,plain,
! [SV460: $i] :
( ( ! [SY4075: $i,SY4076: $i,SY4077: $i] :
( ( c_Type_Otypings @ SV460 @ SY4075 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY4076 @ SV460 @ SY4077 @ SY4075 ) )
| ~ ( c_Type_Otyping @ SV460 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4077 @ SY4075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY4076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(3355,plain,
! [SV461: $i] :
( ( ! [SY4078: $i] :
( ( c_HOL_Oord__class_Oless @ SV461 @ ( c_HOL_Otimes__class_Otimes @ SY4078 @ SV461 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY4078 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV461 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(3356,plain,
! [SV462: $i] :
( ( ! [SY4079: $i] :
( ( c_HOL_Oord__class_Oless @ SV462 @ ( c_HOL_Otimes__class_Otimes @ SV462 @ SY4079 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY4079 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV462 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(3357,plain,
! [SV463: $i] :
( ( ~ ( c_lessequals @ ( c_Suc @ SV463 ) @ SV463 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(3358,plain,
! [SV464: $i] :
( ( ! [SY4080: $i,SY4081: $i] :
( ( c_HOL_Oord__class_Oless @ SV464 @ SY4080 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SY4081 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4080 @ SY4081 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4081 @ SY4080 @ tc_nat )
| ~ ( c_lessequals @ SY4081 @ SV464 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2379]) ).
thf(3359,plain,
! [SV465: $i] :
( ( ! [SY4082: $i,SY4083: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV465 @ SY4082 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4083 @ SY4082 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV465 @ SY4083 @ tc_nat )
| ~ ( c_lessequals @ SY4082 @ SY4083 @ tc_nat )
| ~ ( c_lessequals @ SY4082 @ SV465 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2380]) ).
thf(3360,plain,
! [SV466: $i] :
( ( ! [SY4084: $i,SY4085: $i,SY4086: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV466 )
| ( c_HOL_Oord__class_Oless @ SY4084 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ SY4085 ) @ SY4086 ) @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ SY4084 @ SY4086 @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SY4085 @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(3361,plain,
! [SV467: $i] :
( ( ! [SY4087: $i,SY4088: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV467 ) @ SY4087 @ SY4088 )
= ( c_Lambda_OdB_OVar @ SV467 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV467 @ SY4088 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(3362,plain,
! [SV468: $i] :
( ( ! [SY4089: $i,SY4090: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV468 @ ( c_Lambda_OdB_OVar @ SY4089 ) @ SY4090 ) )
| ~ ( c_InductTermi_OIT @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(3363,plain,
! [SV469: $i] :
( ( ! [SY4091: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV469 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV469 ) @ SY4091 ) @ SY4091 ) @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SY4091 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(3364,plain,
! [SV470: $i] :
( ( ! [SY4092: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV470 )
| ( c_lessequals @ SY4092 @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV470 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV470 ) @ SY4092 ) @ SY4092 ) @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(3365,plain,
! [SV471: $i] :
( ( ! [SY4093: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV471 ) @ SY4093 ) @ SV471 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(3366,plain,
! [SV472: $i] :
( ( ! [SY4094: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV472 ) @ SY4094 ) @ SY4094 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(3367,plain,
! [SV473: $i] :
( ( ! [SY4095: $i,SY4096: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ SV473 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SY4095 @ SY4096 @ tc_nat ) @ SV473 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4095 @ SV473 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4096 @ SV473 ) @ SV473 ) )
| ~ ( c_lessequals @ SY4096 @ SY4095 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(3368,plain,
! [SV474: $i] :
( ( ! [SY4097: $i,SY4098: $i,SY4099: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV474 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4097 @ SY4098 @ SV474 ) @ ( c_HOL_Otimes__class_Otimes @ SY4099 @ SY4098 @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SY4098 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SY4099 @ SY4097 @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(3369,plain,
! [SV475: $i] :
( ( ! [SY4100: $i,SY4101: $i,SY4102: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV475 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4100 @ SY4101 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SY4100 @ SY4102 @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SY4100 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SY4102 @ SY4101 @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(3370,plain,
! [SV476: $i] :
( ( ! [SY4103: $i,SY4104: $i,SY4105: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ SV476 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4103 @ SY4104 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SY4105 @ SY4104 @ SV476 ) @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SY4104 @ SV476 )
| ~ ( c_lessequals @ SY4103 @ SY4105 @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(3371,plain,
! [SV477: $i] :
( ( ! [SY4106: $i,SY4107: $i,SY4108: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ SV477 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4106 @ SY4107 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SY4106 @ SY4108 @ SV477 ) @ SV477 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV477 ) @ SY4106 @ SV477 )
| ~ ( c_lessequals @ SY4107 @ SY4108 @ SV477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(3372,plain,
! [SV478: $i] :
( ( ! [SY4109: $i,SY4110: $i,SY4111: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ SV478 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4109 @ SY4110 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SY4109 @ SY4111 @ SV478 ) @ SV478 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV478 ) @ SY4109 @ SV478 )
| ~ ( c_lessequals @ SY4110 @ SY4111 @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(3373,plain,
! [SV479: $i] :
( ( ! [SY4112: $i,SY4113: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV479 ) @ ( c_List_Olist_OCons @ SY4112 @ SY4113 @ SV479 ) @ SV479 )
= ( c_List_Olist_OCons @ SY4112 @ SY4113 @ SV479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(3374,plain,
! [SV480: $i] :
( ( ! [SY4114: $i,SY4115: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV480 ) @ SY4114 ) @ SY4115 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV480 @ ( c_HOL_Ominus__class_Ominus @ SY4115 @ SY4114 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(3375,plain,
! [SV481: $i] :
( ( ! [SY4116: $i,SY4117: $i] :
( ( c_HOL_Oord__class_Oless @ SV481 @ ( c_HOL_Ominus__class_Ominus @ SY4116 @ SY4117 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SY4117 ) @ SY4116 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(3376,plain,
! [SV482: $i] :
( ( ! [SY4118: $i,SY4119: $i,SY4120: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV482 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SY4118 ) @ SY4119 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SY4120 ) @ SY4119 ) @ SV482 )
| ~ ( c_HOL_Oord__class_Oless @ SY4118 @ SY4120 @ SV482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(3377,plain,
! [SV483: $i] :
( ( ! [SY4121: $i,SY4122: $i,SY4123: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV483 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SY4121 ) @ SY4122 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SY4123 ) @ SY4122 ) @ SV483 )
| ~ ( c_HOL_Oord__class_Oless @ SY4121 @ SY4123 @ SV483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(3378,plain,
! [SV484: $i] :
( ( ! [SY4124: $i,SY4125: $i,SY4126: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV484 )
| ( c_HOL_Oord__class_Oless @ SY4124 @ SY4125 @ SV484 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SY4124 ) @ SY4126 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SY4125 ) @ SY4126 ) @ SV484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(3379,plain,
! [SV485: $i] :
( ( ! [SY4127: $i,SY4128: $i,SY4129: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV485 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SY4127 ) @ SY4128 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SY4127 ) @ SY4129 ) @ SV485 )
| ~ ( c_HOL_Oord__class_Oless @ SY4128 @ SY4129 @ SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(3380,plain,
! [SV486: $i] :
( ( ! [SY4130: $i,SY4131: $i,SY4132: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV486 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SY4130 ) @ SY4131 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SY4130 ) @ SY4132 ) @ SV486 )
| ~ ( c_HOL_Oord__class_Oless @ SY4131 @ SY4132 @ SV486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(3381,plain,
! [SV487: $i] :
( ( ! [SY4133: $i,SY4134: $i,SY4135: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV487 )
| ( c_HOL_Oord__class_Oless @ SY4133 @ SY4134 @ SV487 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SY4135 ) @ SY4133 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SY4135 ) @ SY4134 ) @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(3382,plain,
! [SV488: $i] :
( ( ! [SY4136: $i,SY4137: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV488 ) @ SY4136 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4137 ) @ SY4136 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV488 @ SY4137 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(3383,plain,
! [SV489: $i] :
( ( ! [SY4138: $i,SY4139: $i] :
( ( c_HOL_Oord__class_Oless @ SV489 @ SY4138 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4139 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4139 ) @ SY4138 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(3384,plain,
! [SV490: $i] :
( ( ! [SY4140: $i,SY4141: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV490 ) @ SY4140 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV490 ) @ SY4141 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4140 @ SY4141 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(3385,plain,
! [SV491: $i] :
( ( ! [SY4142: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV491 @ SY4142 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY4142 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV491 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(3386,plain,
! [SV492: $i] :
( ( ! [SY4143: $i,SY4144: $i,SY4145: $i] :
( ~ ( class_Orderings_Oorder @ SV492 )
| ( c_lessequals @ SY4143 @ SY4144 @ SV492 )
| ~ ( c_lessequals @ SY4143 @ SY4145 @ SV492 )
| ~ ( c_lessequals @ SY4145 @ SY4144 @ SV492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(3387,plain,
! [SV493: $i] :
( ( ! [SY4146: $i,SY4147: $i,SY4148: $i] :
( ~ ( class_Orderings_Oorder @ SV493 )
| ( c_HOL_Oord__class_Oless @ SY4146 @ SY4147 @ SV493 )
| ~ ( c_lessequals @ SY4146 @ SY4148 @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SY4148 @ SY4147 @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(3388,plain,
! [SV494: $i] :
( ( ! [SY4149: $i,SY4150: $i,SY4151: $i] :
( ~ ( class_Orderings_Oorder @ SV494 )
| ( c_HOL_Oord__class_Oless @ SY4149 @ SY4150 @ SV494 )
| ~ ( c_HOL_Oord__class_Oless @ SY4149 @ SY4151 @ SV494 )
| ~ ( c_lessequals @ SY4151 @ SY4150 @ SV494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(3389,plain,
! [SV495: $i] :
( ( ! [SY4152: $i,SY4153: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV495 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SY4152 ) @ SY4153 ) @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
| ~ ( c_lessequals @ SY4153 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
| ~ ( c_lessequals @ SY4152 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(3390,plain,
! [SV496: $i] :
( ( ! [SY4154: $i,SY4155: $i,SY4156: $i] :
( ~ ( class_Orderings_Opreorder @ SV496 )
| ( c_lessequals @ SY4154 @ SY4155 @ SV496 )
| ~ ( c_lessequals @ SY4156 @ SY4155 @ SV496 )
| ~ ( c_lessequals @ SY4154 @ SY4156 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(3391,plain,
! [SV497: $i] :
( ( c_lessequals @ SV497 @ SV497 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(3392,plain,
! [SV498: $i] :
( ( ! [SY4157: $i,SY4158: $i] :
( ( c_lessequals @ SV498 @ SY4157 @ tc_nat )
| ~ ( c_lessequals @ SY4158 @ SY4157 @ tc_nat )
| ~ ( c_lessequals @ SV498 @ SY4158 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(3393,plain,
! [SV499: $i] :
( ( c_lessequals @ SV499 @ SV499 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(3394,plain,
! [SV500: $i] :
( ( ! [SY4159: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_Suc @ SV500 ) @ ( c_Suc @ SY4159 ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omin @ SV500 @ SY4159 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(3395,plain,
! [SV501: $i] :
( ( ! [SY4160: $i] :
( ( SV501
= ( c_Suc @ SY4160 ) )
| ( c_lessequals @ SV501 @ SY4160 @ tc_nat )
| ~ ( c_lessequals @ SV501 @ ( c_Suc @ SY4160 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(3396,plain,
! [SV502: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV502 @ SV502 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV502 @ ( c_Suc @ SV502 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(3397,plain,
! [SV503: $i] :
( ( ! [SY4161: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV503 @ SY4161 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4161 @ ( c_Suc @ SV503 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(3398,plain,
! [SV504: $i] :
( ( ! [SY4162: $i] :
( ( c_HOL_Oord__class_Oless @ SV504 @ ( c_Suc @ SY4162 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY4162 @ SV504 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(3399,plain,
! [SV505: $i] :
( ( ! [SY4163: $i,SY4164: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SY4163 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4164 @ SY4163 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV505 @ SY4164 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4163 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(3400,plain,
! [SV506: $i] :
( ( ! [SY4165: $i,SY4166: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SY4165 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SY4166 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4165 @ SY4166 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV506 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(3401,plain,
! [SV507: $i] :
( ( ! [SY4167: $i,SY4168: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SY4167 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SY4168 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV507 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4167 @ SY4168 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(3402,plain,
! [SV508: $i] :
( ( ! [SY4169: $i,SY4170: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV508 @ SY4169 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4170 @ SY4169 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4169 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV508 @ SY4170 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(3403,plain,
! [SV509: $i] :
( ( ! [SY4171: $i,SY4172: $i] :
( ( c_HOL_Oord__class_Oless @ SV509 @ SY4171 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4172 @ SV509 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4172 @ SY4171 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4172 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(3404,plain,
! [SV510: $i] :
( ( ! [SY4173: $i,SY4174: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SY4173 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SY4174 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4173 @ SY4174 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV510 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(3405,plain,
! [SV511: $i] :
( ( ! [SY4175: $i,SY4176: $i,SY4177: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV511 )
| ( c_HOL_Oord__class_Oless @ SY4175 @ SY4176 @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4177 @ SY4176 @ SV511 ) @ ( c_HOL_Otimes__class_Otimes @ SY4177 @ SY4175 @ SV511 ) @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ SY4177 @ ( c_HOL_Ozero__class_Ozero @ SV511 ) @ SV511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(3406,plain,
! [SV512: $i] :
( ( ! [SY4178: $i,SY4179: $i,SY4180: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV512 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4178 @ SY4179 @ SV512 ) @ ( c_HOL_Otimes__class_Otimes @ SY4178 @ SY4180 @ SV512 ) @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SY4180 @ SY4179 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SY4178 @ ( c_HOL_Ozero__class_Ozero @ SV512 ) @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(3407,plain,
! [SV513: $i] :
( ( ! [SY4181: $i,SY4182: $i,SY4183: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV513 )
| ( c_HOL_Oord__class_Oless @ SY4181 @ SY4182 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4183 @ SY4181 @ SV513 ) @ ( c_HOL_Otimes__class_Otimes @ SY4183 @ SY4182 @ SV513 ) @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV513 ) @ SY4183 @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2439]) ).
thf(3408,plain,
! [SV514: $i] :
( ( ! [SY4184: $i,SY4185: $i,SY4186: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV514 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4184 @ SY4185 @ SV514 ) @ ( c_HOL_Otimes__class_Otimes @ SY4184 @ SY4186 @ SV514 ) @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ SY4185 @ SY4186 @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SY4184 @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(3409,plain,
! [SV515: $i] :
( ( ! [SY4187: $i,SY4188: $i,SY4189: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV515 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4187 @ SY4188 @ SV515 ) @ ( c_HOL_Otimes__class_Otimes @ SY4187 @ SY4189 @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SY4187 @ ( c_HOL_Ozero__class_Ozero @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SY4189 @ SY4188 @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2441]) ).
thf(3410,plain,
! [SV516: $i] :
( ( ! [SY4190: $i,SY4191: $i,SY4192: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV516 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4190 @ SY4191 @ SV516 ) @ ( c_HOL_Otimes__class_Otimes @ SY4190 @ SY4192 @ SV516 ) @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV516 ) @ SY4190 @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ SY4191 @ SY4192 @ SV516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(3411,plain,
! [SV517: $i] :
( ( ! [SY4193: $i,SY4194: $i,SY4195: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV517 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4193 @ SY4194 @ SV517 ) @ ( c_HOL_Otimes__class_Otimes @ SY4193 @ SY4195 @ SV517 ) @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ SY4194 @ SY4195 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SY4193 @ SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(3412,plain,
! [SV518: $i] :
( ( ! [SY4196: $i,SY4197: $i,SY4198: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV518 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4196 @ SY4197 @ SV518 ) @ ( c_HOL_Otimes__class_Otimes @ SY4196 @ SY4198 @ SV518 ) @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SY4198 @ SY4197 @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SY4196 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(3413,plain,
! [SV519: $i] :
( ( ! [SY4199: $i,SY4200: $i,SY4201: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV519 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4199 @ SY4200 @ SV519 ) @ ( c_HOL_Otimes__class_Otimes @ SY4201 @ SY4200 @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SY4200 @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SY4201 @ SY4199 @ SV519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(3414,plain,
! [SV520: $i] :
( ( ! [SY4202: $i,SY4203: $i,SY4204: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV520 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4202 @ SY4203 @ SV520 ) @ ( c_HOL_Otimes__class_Otimes @ SY4204 @ SY4203 @ SV520 ) @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SY4203 @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ SY4202 @ SY4204 @ SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(3415,plain,
! [SV521: $i] :
( ( ! [SY4205: $i,SY4206: $i,SY4207: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV521 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4205 @ SY4206 @ SV521 ) @ ( c_HOL_Otimes__class_Otimes @ SY4207 @ SY4206 @ SV521 ) @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ SY4205 @ SY4207 @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV521 ) @ SY4206 @ SV521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2447]) ).
thf(3416,plain,
! [SV522: $i] :
( ( ! [SY4208: $i,SY4209: $i,SY4210: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV522 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4208 @ SY4209 @ SV522 ) @ ( c_HOL_Otimes__class_Otimes @ SY4210 @ SY4209 @ SV522 ) @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SY4210 @ SY4208 @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SY4209 @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(3417,plain,
! [SV523: $i] :
( ( ! [SY4211: $i,SY4212: $i,SY4213: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV523 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4211 @ SY4212 @ SV523 ) @ ( c_HOL_Otimes__class_Otimes @ SY4211 @ SY4213 @ SV523 ) @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SY4211 @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ SY4212 @ SY4213 @ SV523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(3418,plain,
! [SV524: $i] :
( ( ! [SY4214: $i,SY4215: $i] :
( ( c_List_Olist_OCons @ SV524 @ SY4214 @ SY4215 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY4215 ) @ ( c_List_Olist_OCons @ SV524 @ SY4214 @ SY4215 ) @ SY4215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(3419,plain,
! [SV525: $i] :
( ( ! [SY4216: $i,SY4217: $i,SY4218: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV525 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ ( c_Orderings_Oord__class_Omax @ SY4216 @ SY4217 @ SV525 ) ) @ SY4218 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ SY4216 ) @ SY4218 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ SY4217 ) @ SY4218 ) @ SV525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(3420,plain,
! [SV526: $i] :
( ( ! [SY4219: $i] :
( ( c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV526 ) @ ( c_Lambda_OdB_OVar @ SY4219 ) ) )
| ~ ( c_InductTermi_OIT @ SV526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(3421,plain,
! [SV527: $i] :
( ( ! [SY4220: $i,SY4221: $i,SY4222: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV527 @ SY4220 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4221 @ SY4222 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4220 @ SY4222 @ tc_nat )
| ~ ( c_lessequals @ SV527 @ SY4221 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(3422,plain,
! [SV528: $i] :
( ( c_lessequals @ SV528 @ ( c_HOL_Otimes__class_Otimes @ SV528 @ ( c_HOL_Otimes__class_Otimes @ SV528 @ SV528 @ tc_nat ) @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(3423,plain,
! [SV529: $i] :
( ( ! [SY4223: $i,SY4224: $i,SY4225: $i,SY4226: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV529 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4223 @ SY4224 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SY4225 @ SY4226 @ SV529 ) @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SY4224 @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SY4225 @ SV529 )
| ~ ( c_lessequals @ SY4224 @ SY4226 @ SV529 )
| ~ ( c_lessequals @ SY4223 @ SY4225 @ SV529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(3424,plain,
! [SV530: $i] :
( ( ! [SY4227: $i,SY4228: $i,SY4229: $i,SY4230: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV530 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4227 @ SY4228 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SY4229 @ SY4230 @ SV530 ) @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SY4228 @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SY4227 @ SV530 )
| ~ ( c_lessequals @ SY4228 @ SY4230 @ SV530 )
| ~ ( c_lessequals @ SY4227 @ SY4229 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(3425,plain,
! [SV531: $i] :
( ( ! [SY4231: $i,SY4232: $i,SY4233: $i] :
( ~ ( class_Orderings_Olinorder @ SV531 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SY4231 @ SY4232 @ SV531 ) @ SY4233 @ SV531 )
= ( c_Orderings_Oord__class_Omax @ SY4231 @ ( c_Orderings_Oord__class_Omax @ SY4232 @ SY4233 @ SV531 ) @ SV531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(3426,plain,
! [SV532: $i] :
( ( ! [SY4234: $i,SY4235: $i,SY4236: $i] :
( ~ ( class_Orderings_Olinorder @ SV532 )
| ( ( c_Orderings_Oord__class_Omax @ SY4234 @ ( c_Orderings_Oord__class_Omax @ SY4235 @ SY4236 @ SV532 ) @ SV532 )
= ( c_Orderings_Oord__class_Omax @ SY4235 @ ( c_Orderings_Oord__class_Omax @ SY4234 @ SY4236 @ SV532 ) @ SV532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(3427,plain,
! [SV533: $i] :
( ( ( c_List_Olist_ONil @ SV533 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV533 ) @ ( c_List_Olist_ONil @ SV533 ) @ SV533 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(3428,plain,
! [SV534: $i] :
( ( ! [SY4237: $i,SY4238: $i,SY4239: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV534 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV534 ) @ ( c_HOL_Otimes__class_Otimes @ SY4237 @ SY4238 @ SV534 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4239 @ SY4238 @ SV534 ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV534 ) @ SY4237 ) @ SY4239 ) @ SY4238 @ SV534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(3429,plain,
! [SV535: $i] :
( ( ! [SY4240: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV535 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV535 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4240 @ SV535 ) @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(3430,plain,
! [SV536: $i] :
( ( ! [SY4241: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV536 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4241 @ SV536 ) @ SV536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(3431,plain,
! [SV537: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV537 ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV537 ) ) @ SV537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(3432,plain,
! [SV538: $i] :
( ( ! [SY4242: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV538 ) @ ( c_Lambda_OdB_OAbs @ SY4242 ) )
| ~ ( c_Lambda_Obeta @ SV538 @ SY4242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(3433,plain,
! [SV539: $i] :
( ( ! [SY4243: $i,SY4244: $i] :
( ~ ( class_Orderings_Olinorder @ SV539 )
| ( ( c_Orderings_Oord__class_Omax @ SY4243 @ ( c_Orderings_Oord__class_Omax @ SY4243 @ SY4244 @ SV539 ) @ SV539 )
= ( c_Orderings_Oord__class_Omax @ SY4243 @ SY4244 @ SV539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(3434,plain,
! [SV540: $i] :
( ( ! [SY4245: $i,SY4246: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV540 @ SY4245 @ SY4246 ) @ ( c_List_Olist_OCons @ SY4245 @ ( c_List_Olist_ONil @ SY4246 ) @ SY4246 ) @ SY4246 )
= ( c_List_Olist_OCons @ SY4245 @ ( c_List_Oreplicate @ SV540 @ SY4245 @ SY4246 ) @ SY4246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(3435,plain,
! [SV541: $i] :
( ( ! [SY4247: $i,SY4248: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV541 )
| ( c_lessequals @ SY4247 @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV541 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SY4247 @ SV541 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ ( c_HOL_Otimes__class_Otimes @ SY4247 @ SY4248 @ SV541 ) @ SV541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(3436,plain,
! [SV542: $i] :
( ( ! [SY4249: $i,SY4250: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV542 )
| ( c_lessequals @ SY4249 @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV542 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SY4250 @ SV542 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ ( c_HOL_Otimes__class_Otimes @ SY4250 @ SY4249 @ SV542 ) @ SV542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(3437,plain,
! [SV543: $i] :
( ( ! [SY4251: $i,SY4252: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV543 )
| ( c_lessequals @ SY4251 @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV543 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SY4252 @ SV543 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ ( c_HOL_Otimes__class_Otimes @ SY4251 @ SY4252 @ SV543 ) @ SV543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(3438,plain,
! [SV544: $i] :
( ( ! [SY4253: $i,SY4254: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV544 )
| ( c_lessequals @ SY4253 @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV544 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SY4253 @ SV544 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ ( c_HOL_Otimes__class_Otimes @ SY4254 @ SY4253 @ SV544 ) @ SV544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(3439,plain,
! [SV545: $i] :
( ( ! [SY4255: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV545 ) @ SY4255 ) @ SY4255 @ tc_nat )
= SV545 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(3440,plain,
! [SV546: $i] :
( ( ! [SY4256: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV546 ) @ SY4256 ) @ SV546 @ tc_nat )
= SY4256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(3441,plain,
! [SV547: $i] :
( ( ! [SY4257: $i,SY4258: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV547 )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV547 ) @ SY4257 ) @ SY4258 ) @ SY4258 @ SV547 )
= SY4257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(3442,plain,
! [SV548: $i] :
( ( ! [SY4259: $i,SY4260: $i,SY4261: $i,SY4262: $i,SY4263: $i] :
( ( c_List_Ofoldl @ SV548 @ SY4259 @ ( c_List_Oappend @ SY4260 @ SY4261 @ SY4262 ) @ SY4263 @ SY4262 )
= ( c_List_Ofoldl @ SV548 @ ( c_List_Ofoldl @ SV548 @ SY4259 @ SY4260 @ SY4263 @ SY4262 ) @ SY4261 @ SY4263 @ SY4262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(3443,plain,
! [SV549: $i] :
( ( ! [SY4264: $i,SY4265: $i,SY4266: $i] :
( ( c_Type_Otype_Otype__case @ SV549 @ SY4264 @ ( c_Type_Otype_OAtom @ SY4265 ) @ SY4266 )
= ( hAPP @ SV549 @ SY4265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(3444,plain,
! [SV550: $i] :
( ( ! [SY4267: $i,SY4268: $i,SY4269: $i,SY4270: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV550 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SY4267 ) @ SY4268 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SY4269 ) @ SY4270 ) @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SY4268 @ SY4270 @ SV550 )
| ~ ( c_lessequals @ SY4267 @ SY4269 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(3445,plain,
! [SV551: $i] :
( ( ! [SY4271: $i,SY4272: $i,SY4273: $i,SY4274: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV551 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SY4271 ) @ SY4272 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SY4273 ) @ SY4274 ) @ SV551 )
| ~ ( c_lessequals @ SY4272 @ SY4274 @ SV551 )
| ~ ( c_HOL_Oord__class_Oless @ SY4271 @ SY4273 @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(3446,plain,
! [SV552: $i] :
( ( ! [SY4275: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV552 ) @ ( c_Suc @ SY4275 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV552 @ SY4275 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(3447,plain,
! [SV553: $i] :
( ( ! [SY4276: $i] :
( ( c_HOL_Oord__class_Oless @ SV553 @ SY4276 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV553 ) @ ( c_Suc @ SY4276 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(3448,plain,
! [SV554: $i] :
( ( ! [SY4277: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV554 ) @ ( c_Suc @ SY4277 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV554 @ SY4277 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(3449,plain,
! [SV555: $i] :
( ( ! [SY4278: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV555 ) @ SY4278 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4278 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(3450,plain,
! [SV556: $i] :
( ( ! [SY4279: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV556 ) @ SY4279 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV556 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(3451,plain,
! [SV557: $i] :
( ( ! [SY4280: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV557 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV557 ) @ SY4280 @ SV557 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV557 ) @ SY4280 ) @ SY4280 ) @ SV557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(3452,plain,
! [SV558: $i] :
( ( ! [SY4281: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV558 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV558 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV558 ) @ SY4281 ) @ SY4281 ) @ SV558 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV558 ) @ SY4281 @ SV558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(3453,plain,
! [SV559: $i] :
( ( ! [SY4282: $i,SY4283: $i] :
( ( SV559
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV559 @ SY4282 @ SY4283 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV559 @ SY4282 @ SY4283 ) ) )
| ~ ( c_Type_Otyping @ SY4282 @ ( c_Lambda_OdB_OAbs @ SY4283 ) @ SV559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(3454,plain,
! [SV560: $i] :
( ( ! [SY4284: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV560 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV560 ) @ SY4284 @ SV560 )
= ( c_HOL_Ozero__class_Ozero @ SV560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(3455,plain,
! [SV561: $i] :
( ( ! [SY4285: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ SV561 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SY4285 @ SV561 )
= ( c_HOL_Ozero__class_Ozero @ SV561 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(3456,plain,
! [SV562: $i] :
( ( ! [SY4286: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ SV562 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4286 @ ( c_HOL_Ozero__class_Ozero @ SV562 ) @ SV562 )
= ( c_HOL_Ozero__class_Ozero @ SV562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(3457,plain,
! [SV563: $i] :
( ( ! [SY4287: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV563 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV563 ) @ SY4287 @ SV563 )
= ( c_HOL_Ozero__class_Ozero @ SV563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(3458,plain,
! [SV564: $i] :
( ( ! [SY4288: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV564 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4288 @ ( c_HOL_Ozero__class_Ozero @ SV564 ) @ SV564 )
= ( c_HOL_Ozero__class_Ozero @ SV564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(3459,plain,
! [SV565: $i] :
( ( ! [SY4289: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV565 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4289 @ ( c_HOL_Ozero__class_Ozero @ SV565 ) @ SV565 )
= ( c_HOL_Ozero__class_Ozero @ SV565 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(3460,plain,
! [SV566: $i] :
( ( ! [SY4290: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV566 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV566 ) @ SY4290 @ SV566 )
= ( c_HOL_Ozero__class_Ozero @ SV566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(3461,plain,
! [SV567: $i] :
( ( ! [SY4291: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV567 )
| ~ ( class_Int_Onumber__ring @ SV567 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4291 @ SY4291 @ SV567 )
= ( c_HOL_Ozero__class_Ozero @ SV567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(3462,plain,
! [SV568: $i] :
( ( ! [SY4292: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV568 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4292 @ SY4292 @ SV568 )
= ( c_HOL_Ozero__class_Ozero @ SV568 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(3463,plain,
! [SV569: $i] :
( ( ! [SY4293: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV569 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4293 @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SV569 )
= SY4293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(3464,plain,
! [SV570: $i] :
( ( ! [SY4294: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV570 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4294 @ SY4294 @ SV570 )
= ( c_HOL_Ozero__class_Ozero @ SV570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(3465,plain,
! [SV571: $i] :
( ( ! [SY4295: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV571 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4295 @ SY4295 @ SV571 )
= ( c_HOL_Ozero__class_Ozero @ SV571 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(3466,plain,
! [SV572: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV572 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV572 ) @ ( c_HOL_Ozero__class_Ozero @ SV572 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV572 ) )
= ( c_HOL_Ozero__class_Ozero @ SV572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(3467,plain,
! [SV573: $i] :
( ( ! [SY4296: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV573 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV573 ) @ ( c_HOL_Ozero__class_Ozero @ SV573 ) ) @ SY4296 )
= SY4296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(3468,plain,
! [SV574: $i] :
( ( ! [SY4297: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV574 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV574 ) @ ( c_HOL_Ozero__class_Ozero @ SV574 ) ) @ SY4297 )
= SY4297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2513]) ).
thf(3469,plain,
! [SV575: $i] :
( ( ! [SY4298: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV575 )
| ~ ( class_Int_Onumber__ring @ SV575 )
| ( SY4298
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SY4298 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(3470,plain,
! [SV576: $i] :
( ( ! [SY4299: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV576 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SY4299 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) )
= SY4299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(3471,plain,
! [SV577: $i] :
( ( ! [SY4300: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV577 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV577 ) @ ( c_HOL_Ozero__class_Ozero @ SV577 ) ) @ SY4300 )
= SY4300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(3472,plain,
! [SV578: $i] :
( ( ! [SY4301: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV578 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV578 ) @ SY4301 ) @ ( c_HOL_Ozero__class_Ozero @ SV578 ) )
= SY4301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(3473,plain,
! [SV579: $i] :
( ( ! [SY4302: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV579 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV579 ) @ SY4302 ) @ ( c_HOL_Ozero__class_Ozero @ SV579 ) )
= SY4302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2518]) ).
thf(3474,plain,
! [SV580: $i] :
( ( ! [SY4303: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV580 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV580 ) @ ( c_HOL_Ozero__class_Ozero @ SV580 ) ) @ SY4303 )
= SY4303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(3475,plain,
! [SV581: $i] :
( ( ! [SY4304: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV581 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SY4304 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2521]) ).
thf(3476,plain,
! [SV582: $i] :
( ( ! [SY4305: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV582 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4305 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(3477,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)],[2523]) ).
thf(3478,plain,
! [SV583: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV583 @ tc_nat )
| ( SV583
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(3479,plain,
! [SV584: $i] :
( ( ! [SY4306: $i] :
( ~ ( class_Orderings_Oorder @ SV584 )
| ( c_lessequals @ SY4306 @ SY4306 @ SV584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(3480,plain,
! [SV585: $i] :
( ( ! [SY4307: $i] :
( ~ ( class_Orderings_Opreorder @ SV585 )
| ( c_lessequals @ SY4307 @ SY4307 @ SV585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(3481,plain,
! [SV586: $i] :
( ( ! [SY4308: $i,SY4309: $i,SY4310: $i] :
( ~ ( class_Orderings_Opreorder @ SV586 )
| ( c_HOL_Oord__class_Oless @ SY4308 @ SY4309 @ SV586 )
| ~ ( c_HOL_Oord__class_Oless @ SY4310 @ SY4309 @ SV586 )
| ~ ( c_lessequals @ SY4308 @ SY4310 @ SV586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(3482,plain,
! [SV587: $i] :
( ( ! [SY4311: $i,SY4312: $i,SY4313: $i] :
( ~ ( class_Orderings_Opreorder @ SV587 )
| ( c_HOL_Oord__class_Oless @ SY4311 @ SY4312 @ SV587 )
| ~ ( c_lessequals @ SY4313 @ SY4312 @ SV587 )
| ~ ( c_HOL_Oord__class_Oless @ SY4311 @ SY4313 @ SV587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(3483,plain,
! [SV588: $i] :
( ( ! [SY4314: $i,SY4315: $i,SY4316: $i,SY4317: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV588 )
| ( c_lessequals @ SY4314 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SY4315 ) @ SY4316 ) @ SV588 )
| ~ ( c_lessequals @ SY4317 @ SY4316 @ SV588 )
| ~ ( c_lessequals @ SY4314 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SY4315 ) @ SY4317 ) @ SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(3484,plain,
! [SV589: $i] :
( ( ! [SY4318: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV589 ) @ SY4318 @ SV589 )
= SY4318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(3485,plain,
! [SV590: $i] :
( ( ! [SY4319: $i,SY4320: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV590 @ SY4319 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4320 @ SY4319 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV590 @ SY4320 @ tc_nat ) @ SY4319 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(3486,plain,
! [SV591: $i] :
( ( ! [SY4321: $i,SY4322: $i] :
( ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4321 @ SY4322 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ominus__class_Ominus @ SY4321 @ SY4322 @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(3487,plain,
! [SV592: $i] :
( ( ! [SY4323: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV592 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4323 @ SY4323 @ SV592 )
= SY4323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(3488,plain,
! [SV593: $i] :
( ( ! [SY4324: $i,SY4325: $i] :
( ~ ( hBOOL @ ( hAPP @ SV593 @ SY4324 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4324 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV593 @ SY4325 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV593 @ SY4325 ) )
| ( hBOOL @ ( hAPP @ SV593 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(3489,plain,
! [SV594: $i] :
( ( ! [SY4326: $i,SY4327: $i,SY4328: $i,SY4329: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4326 @ SY4327 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SY4328 @ SY4329 @ SV594 ) @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SY4327 @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SY4326 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SY4327 @ SY4329 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SY4326 @ SY4328 @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(3490,plain,
! [SV595: $i] :
( ( ! [SY4330: $i] :
( ( SV595 = SY4330 )
| ~ ( c_HOL_Oord__class_Oless @ SV595 @ ( c_Suc @ SY4330 ) @ tc_nat )
| ~ ( c_lessequals @ SY4330 @ SV595 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(3491,plain,
! [SV596: $i] :
( ( ! [SY4331: $i,SY4332: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV596 @ SY4331 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4332 @ SY4331 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV596 @ SY4332 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(3492,plain,
! [SV597: $i] :
( ( ! [SY4333: $i,SY4334: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV597 @ SY4333 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV597 @ SY4334 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4333 @ SY4334 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(3493,plain,
! [SV598: $i] :
( ( ! [SY4335: $i,SY4336: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV598 @ SY4335 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV598 @ SY4336 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4335 @ SY4336 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(3494,plain,
! [SV599: $i] :
( ( ! [SY4337: $i,SY4338: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV599 @ SY4337 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4338 @ SY4337 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV599 @ SY4338 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(3495,plain,
! [SV600: $i] :
( ( ! [SY4339: $i,SY4340: $i,SY4341: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV600 @ SY4339 @ SY4340 ) @ ( c_List_Olist_OCons @ SY4339 @ SY4341 @ SY4340 ) @ SY4340 )
= ( c_List_Olist_OCons @ SY4339 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV600 @ SY4339 @ SY4340 ) @ SY4341 @ SY4340 ) @ SY4340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(3496,plain,
! [SV601: $i] :
( ( ! [SY4342: $i] :
( ( c_HOL_Oord__class_Oless @ SV601 @ SY4342 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4342 @ SV601 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(3497,plain,
! [SV602: $i] :
( ( ! [SY4343: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV602 @ SY4343 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4343 @ SV602 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(3498,plain,
! [SV603: $i] :
( ( ! [SY4344: $i] :
( ( c_HOL_Oord__class_Oless @ SV603 @ SY4344 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV603 ) @ SY4344 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(3499,plain,
! [SV604: $i] :
( ( ! [SY4345: $i] :
( ( c_HOL_Oord__class_Oless @ SV604 @ ( c_Suc @ SY4345 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV604 @ SY4345 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(3500,plain,
! [SV605: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV605 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV605 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV605 ) @ ( c_HOL_Ozero__class_Ozero @ SV605 ) @ SV605 ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV605 ) @ ( c_HOL_Ozero__class_Ozero @ SV605 ) @ SV605 ) )
= ( c_HOL_Ozero__class_Ozero @ SV605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(3501,plain,
! [SV606: $i] :
( ( ! [SY4346: $i,SY4347: $i,SY4348: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV606 )
| ( c_HOL_Oord__class_Oless @ SY4346 @ ( c_HOL_Ozero__class_Ozero @ SV606 ) @ SV606 )
| ( c_HOL_Oord__class_Oless @ SY4347 @ SY4348 @ SV606 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4347 @ SY4346 @ SV606 ) @ ( c_HOL_Otimes__class_Otimes @ SY4348 @ SY4346 @ SV606 ) @ SV606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(3502,plain,
! [SV607: $i] :
( ( ! [SY4349: $i,SY4350: $i,SY4351: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV607 )
| ( c_HOL_Oord__class_Oless @ SY4349 @ SY4350 @ SV607 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV607 ) @ SY4351 @ SV607 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4350 @ SY4351 @ SV607 ) @ ( c_HOL_Otimes__class_Otimes @ SY4349 @ SY4351 @ SV607 ) @ SV607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(3503,plain,
! [SV608: $i] :
( ( ! [SY4352: $i,SY4353: $i,SY4354: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV608 )
| ( c_HOL_Oord__class_Oless @ SY4352 @ ( c_HOL_Ozero__class_Ozero @ SV608 ) @ SV608 )
| ( c_HOL_Oord__class_Oless @ SY4353 @ SY4354 @ SV608 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4352 @ SY4353 @ SV608 ) @ ( c_HOL_Otimes__class_Otimes @ SY4352 @ SY4354 @ SV608 ) @ SV608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(3504,plain,
! [SV609: $i] :
( ( ! [SY4355: $i,SY4356: $i,SY4357: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV609 )
| ( c_HOL_Oord__class_Oless @ SY4355 @ SY4356 @ SV609 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV609 ) @ SY4357 @ SV609 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4357 @ SY4356 @ SV609 ) @ ( c_HOL_Otimes__class_Otimes @ SY4357 @ SY4355 @ SV609 ) @ SV609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(3505,plain,
! [SV610: $i] :
( ( ! [SY4358: $i,SY4359: $i,SY4360: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV610 ) @ SY4358 ) @ SY4359 @ SY4360 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV610 @ SY4359 @ SY4360 ) ) @ ( c_Lambda_Osubst @ SY4358 @ SY4359 @ SY4360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(3506,plain,
! [SV611: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV611 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV611 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV611 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(3507,plain,
! [SV612: $i] :
( ( ! [SY4361: $i,SY4362: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV612 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4361 ) @ SY4362 ) @ SV612 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV612 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4361 @ SV612 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4362 @ SV612 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2563]) ).
thf(3508,plain,
! [SV613: $i] :
( ( ! [SY4363: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV613 @ SY4363 @ tc_nat ) @ SV613 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV613 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4363 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(3509,plain,
! [SV614: $i] :
( ( ! [SY4364: $i,SY4365: $i,SY4366: $i] :
( ~ ( class_Orderings_Olinorder @ SV614 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY4364 @ ( c_Orderings_Oord__class_Omin @ SY4365 @ SY4366 @ SV614 ) @ SV614 ) @ ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SY4364 @ SY4365 @ SV614 ) @ ( c_Orderings_Oord__class_Omax @ SY4364 @ SY4366 @ SV614 ) @ SV614 ) @ SV614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(3510,plain,
! [SV615: $i] :
( ( ! [SY4367: $i,SY4368: $i,SY4369: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV615 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SY4367 @ SY4368 @ SV615 ) @ SY4369 @ SV615 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY4367 @ SY4369 @ SV615 ) @ ( c_Power_Opower__class_Opower @ SY4368 @ SY4369 @ SV615 ) @ SV615 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(3511,plain,
! [SV616: $i] :
( ( ! [SY4370: $i,SY4371: $i,SY4372: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV616 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SY4370 @ SY4371 @ SV616 ) @ SY4372 @ SV616 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY4370 @ SY4372 @ SV616 ) @ ( c_Power_Opower__class_Opower @ SY4371 @ SY4372 @ SV616 ) @ SV616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(3512,plain,
! [SV617: $i] :
( ( ! [SY4373: $i,SY4374: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV617 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SY4373 @ SY4374 @ SV617 ) @ SV617 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ ( c_List_Olistsum @ SY4373 @ SV617 ) ) @ ( c_List_Olistsum @ SY4374 @ SV617 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(3513,plain,
! [SV618: $i] :
( ( ! [SY4375: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV618 ) @ ( c_HOL_Ominus__class_Ominus @ SY4375 @ SV618 @ tc_nat ) )
= SY4375 )
| ( c_HOL_Oord__class_Oless @ SY4375 @ SV618 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(3514,plain,
! [SV619: $i] :
( ( ! [SY4376: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV619 @ ( c_Suc @ SY4376 ) @ tc_nat ) @ SV619 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV619 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(3515,plain,
! [SV620: $i] :
( ( ! [SY4377: $i,SY4378: $i,SY4379: $i] :
( ~ ( class_Orderings_Olinorder @ SV620 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SY4377 @ SY4378 @ SV620 ) @ SY4379 @ SV620 )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SY4377 @ SY4379 @ SV620 ) @ ( c_Orderings_Oord__class_Omax @ SY4378 @ SY4379 @ SV620 ) @ SV620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(3516,plain,
! [SV621: $i] :
( ( ! [SY4380: $i,SY4381: $i,SY4382: $i] :
( ~ ( class_Orderings_Olinorder @ SV621 )
| ( ( c_Orderings_Oord__class_Omax @ SY4380 @ ( c_Orderings_Oord__class_Omin @ SY4381 @ SY4382 @ SV621 ) @ SV621 )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SY4380 @ SY4381 @ SV621 ) @ ( c_Orderings_Oord__class_Omax @ SY4380 @ SY4382 @ SV621 ) @ SV621 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(3517,plain,
! [SV622: $i] :
( ( ! [SY4383: $i,SY4384: $i,SY4385: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV622 )
| ( ( c_Power_Opower__class_Opower @ SY4383 @ ( c_HOL_Otimes__class_Otimes @ SY4384 @ SY4385 @ tc_nat ) @ SV622 )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SY4383 @ SY4384 @ SV622 ) @ SY4385 @ SV622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(3518,plain,
! [SV623: $i] :
( ( ! [SY4386: $i,SY4387: $i] :
( ~ ( class_Orderings_Oorder @ SV623 )
| ( c_HOL_Oord__class_Oless @ SY4386 @ SY4387 @ SV623 )
| ( SY4387 = SY4386 )
| ~ ( c_lessequals @ SY4386 @ SY4387 @ SV623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(3519,plain,
! [SV624: $i] :
( ( ! [SY4388: $i,SY4389: $i] :
( ~ ( class_Orderings_Oorder @ SV624 )
| ( c_HOL_Oord__class_Oless @ SY4388 @ SY4389 @ SV624 )
| ~ ( c_lessequals @ SY4388 @ SY4389 @ SV624 )
| ( SY4389 = SY4388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(3520,plain,
! [SV625: $i] :
( ( ! [SY4390: $i] :
( ( c_HOL_Oord__class_Oless @ SV625 @ SY4390 @ tc_nat )
| ( SV625 = SY4390 )
| ~ ( c_lessequals @ SV625 @ SY4390 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(3521,plain,
! [SV626: $i] :
( ( ! [SY4391: $i] :
( ( SV626 = SY4391 )
| ( c_HOL_Oord__class_Oless @ SV626 @ SY4391 @ tc_nat )
| ~ ( c_lessequals @ SV626 @ SY4391 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(3522,plain,
! [SV627: $i] :
( ( ! [SY4392: $i] :
( ( c_HOL_Oord__class_Oless @ SV627 @ SY4392 @ tc_nat )
| ( SV627 = SY4392 )
| ~ ( c_lessequals @ SV627 @ SY4392 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(3523,plain,
! [SV628: $i] :
( ( ! [SY4393: $i,SY4394: $i] :
( ~ ( class_Orderings_Oorder @ SV628 )
| ( SY4393 = SY4394 )
| ( c_HOL_Oord__class_Oless @ SY4393 @ SY4394 @ SV628 )
| ~ ( c_lessequals @ SY4393 @ SY4394 @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(3524,plain,
! [SV629: $i] :
( ( ! [SY4395: $i,SY4396: $i] :
( ~ ( class_Orderings_Oorder @ SV629 )
| ( c_HOL_Oord__class_Oless @ SY4395 @ SY4396 @ SV629 )
| ( SY4395 = SY4396 )
| ~ ( c_lessequals @ SY4395 @ SY4396 @ SV629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(3525,plain,
! [SV630: $i] :
( ( ! [SY4397: $i,SY4398: $i] :
( ~ ( class_Orderings_Oorder @ SV630 )
| ( c_HOL_Oord__class_Oless @ SY4397 @ SY4398 @ SV630 )
| ( SY4397 = SY4398 )
| ~ ( c_lessequals @ SY4397 @ SY4398 @ SV630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(3526,plain,
! [SV631: $i] :
( ( ! [SY4399: $i,SY4400: $i] :
( ~ ( class_Orderings_Oorder @ SV631 )
| ( c_HOL_Oord__class_Oless @ SY4399 @ SY4400 @ SV631 )
| ~ ( c_lessequals @ SY4399 @ SY4400 @ SV631 )
| ( SY4399 = SY4400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(3527,plain,
! [SV632: $i] :
( ( ! [SY4401: $i,SY4402: $i] :
( ~ ( class_Orderings_Olinorder @ SV632 )
| ( SY4401 = SY4402 )
| ~ ( c_lessequals @ SY4401 @ SY4402 @ SV632 )
| ( c_HOL_Oord__class_Oless @ SY4401 @ SY4402 @ SV632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(3528,plain,
! [SV633: $i] :
( ( ! [SY4403: $i,SY4404: $i] :
( ~ ( class_Orderings_Olinorder @ SV633 )
| ( SY4403 = SY4404 )
| ( c_HOL_Oord__class_Oless @ SY4403 @ SY4404 @ SV633 )
| ~ ( c_lessequals @ SY4403 @ SY4404 @ SV633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(3529,plain,
! [SV634: $i] :
( ( ! [SY4405: $i,SY4406: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV634 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ ( c_HOL_Otimes__class_Otimes @ SY4405 @ SY4406 @ SV634 ) @ SV634 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SY4406 @ SV634 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SY4405 @ SV634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(3530,plain,
! [SV635: $i] :
( ( ! [SY4407: $i,SY4408: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV635 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ ( c_HOL_Otimes__class_Otimes @ SY4407 @ SY4408 @ SV635 ) @ SV635 )
| ~ ( c_lessequals @ SY4408 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 )
| ~ ( c_lessequals @ SY4407 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(3531,plain,
! [SV636: $i] :
( ( ! [SY4409: $i,SY4410: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV636 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ ( c_HOL_Otimes__class_Otimes @ SY4409 @ SY4410 @ SV636 ) @ SV636 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SY4410 @ SV636 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SY4409 @ SV636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(3532,plain,
! [SV637: $i] :
( ( ! [SY4411: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV637 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV637 ) @ ( c_HOL_Otimes__class_Otimes @ SY4411 @ SY4411 @ SV637 ) @ SV637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(3533,plain,
! [SV638: $i] :
( ( ! [SY4412: $i,SY4413: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV638 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ ( c_HOL_Otimes__class_Otimes @ SY4412 @ SY4413 @ SV638 ) @ SV638 )
| ~ ( c_lessequals @ SY4413 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 )
| ~ ( c_lessequals @ SY4412 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(3534,plain,
! [SV639: $i] :
( ( ! [SY4414: $i,SY4415: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV639 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ ( c_HOL_Otimes__class_Otimes @ SY4414 @ SY4415 @ SV639 ) @ SV639 )
| ~ ( c_lessequals @ SY4415 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 )
| ~ ( c_lessequals @ SY4414 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(3535,plain,
! [SV640: $i] :
( ( ! [SY4416: $i,SY4417: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV640 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ ( c_HOL_Otimes__class_Otimes @ SY4416 @ SY4417 @ SV640 ) @ SV640 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SY4417 @ SV640 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SY4416 @ SV640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(3536,plain,
! [SV641: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV641 ) @ ( c_List_Olist_ONil @ SV641 ) @ SV641 )
= ( c_List_Olist_ONil @ SV641 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(3537,plain,
! [SV642: $i] :
( ( ! [SY4418: $i] :
( ( c_lessequals @ SV642 @ SY4418 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV642 ) @ ( c_Suc @ SY4418 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(3538,plain,
! [SV643: $i] :
( ( ! [SY4419: $i] :
( ( c_lessequals @ ( c_Suc @ SV643 ) @ ( c_Suc @ SY4419 ) @ tc_nat )
| ~ ( c_lessequals @ SV643 @ SY4419 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(3539,plain,
! [SV644: $i] :
( ( ! [SY4420: $i,SY4421: $i,SY4422: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV644 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY4420 @ SY4421 @ SV644 ) @ SY4422 @ SV644 )
= ( c_HOL_Otimes__class_Otimes @ SY4420 @ ( c_HOL_Otimes__class_Otimes @ SY4421 @ SY4422 @ SV644 ) @ SV644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(3540,plain,
! [SV645: $i] :
( ( ! [SY4423: $i,SY4424: $i,SY4425: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV645 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY4423 @ SY4424 @ SV645 ) @ SY4425 @ SV645 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY4423 @ SY4425 @ SV645 ) @ SY4424 @ SV645 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(3541,plain,
! [SV646: $i] :
( ( ! [SY4426: $i,SY4427: $i,SY4428: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV646 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY4426 @ SY4427 @ SV646 ) @ SY4428 @ SV646 )
= ( c_HOL_Otimes__class_Otimes @ SY4426 @ ( c_HOL_Otimes__class_Otimes @ SY4427 @ SY4428 @ SV646 ) @ SV646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(3542,plain,
! [SV647: $i] :
( ( ! [SY4429: $i,SY4430: $i,SY4431: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV647 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4429 @ ( c_HOL_Otimes__class_Otimes @ SY4430 @ SY4431 @ SV647 ) @ SV647 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY4429 @ SY4430 @ SV647 ) @ SY4431 @ SV647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(3543,plain,
! [SV648: $i] :
( ( ! [SY4432: $i,SY4433: $i,SY4434: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV648 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4432 @ ( c_HOL_Otimes__class_Otimes @ SY4433 @ SY4434 @ SV648 ) @ SV648 )
= ( c_HOL_Otimes__class_Otimes @ SY4433 @ ( c_HOL_Otimes__class_Otimes @ SY4432 @ SY4434 @ SV648 ) @ SV648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3544,plain,
! [SV649: $i] :
( ( ! [SY4435: $i,SY4436: $i,SY4437: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV649 @ SY4435 @ SY4436 ) @ SY4437 @ SY4436 )
= ( c_List_Oappend @ SV649 @ ( c_List_Oappend @ SY4435 @ SY4437 @ SY4436 ) @ SY4436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(3545,plain,
! [SV650: $i] :
( ( ! [SY4438: $i,SY4439: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV650 @ SY4438 @ tc_nat ) @ SY4439 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV650 @ ( c_HOL_Otimes__class_Otimes @ SY4438 @ SY4439 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(3546,plain,
! [SV651: $i] :
( ( ! [SY4440: $i,SY4441: $i,SY4442: $i] :
( ( c_List_Oappend @ SV651 @ ( c_List_Oappend @ SY4440 @ SY4441 @ SY4442 ) @ SY4442 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV651 @ SY4440 @ SY4442 ) @ SY4441 @ SY4442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3547,plain,
! [SV652: $i] :
( ( ! [SY4443: $i,SY4444: $i,SY4445: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV652 @ SY4443 @ SY4444 ) @ SY4445 @ SY4444 )
= ( c_List_Oappend @ SV652 @ ( c_List_Oappend @ SY4443 @ SY4445 @ SY4444 ) @ SY4444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(3548,plain,
! [SV653: $i] :
( ( ! [SY4446: $i,SY4447: $i,SY4448: $i] :
( ( c_List_Oappend @ SV653 @ ( c_List_Oappend @ SY4446 @ SY4447 @ SY4448 ) @ SY4448 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV653 @ SY4446 @ SY4448 ) @ SY4447 @ SY4448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(3549,plain,
! [SV654: $i] :
( ( ! [SY4449: $i,SY4450: $i,SY4451: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV654 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4449 @ ( c_HOL_Otimes__class_Otimes @ SY4450 @ SY4451 @ SV654 ) @ SV654 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY4449 @ SY4450 @ SV654 ) @ SY4451 @ SV654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3550,plain,
! [SV655: $i] :
( ( ! [SY4452: $i,SY4453: $i,SY4454: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV655 )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV655 ) @ SY4452 ) @ SY4453 ) @ SY4454 @ SV655 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV655 ) @ ( c_HOL_Otimes__class_Otimes @ SY4452 @ SY4454 @ SV655 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4453 @ SY4454 @ SV655 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(3551,plain,
! [SV656: $i] :
( ( ! [SY4455: $i,SY4456: $i,SY4457: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV656 )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV656 ) @ SY4455 ) @ SY4456 ) @ SY4457 @ SV656 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV656 ) @ ( c_HOL_Otimes__class_Otimes @ SY4455 @ SY4457 @ SV656 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4456 @ SY4457 @ SV656 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(3552,plain,
! [SV657: $i] :
( ( ! [SY4458: $i,SY4459: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV657 ) @ SY4458 ) @ SY4459 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV657 @ SY4459 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4458 @ SY4459 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3553,plain,
! [SV658: $i] :
( ( ! [SY4460: $i,SY4461: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4460 ) @ SY4461 ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV658 @ SY4460 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV658 @ SY4461 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(3554,plain,
! [SV659: $i] :
( ( ! [SY4462: $i,SY4463: $i,SY4464: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV659 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4462 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV659 ) @ SY4463 ) @ SY4464 ) @ SV659 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV659 ) @ ( c_HOL_Otimes__class_Otimes @ SY4462 @ SY4463 @ SV659 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4462 @ SY4464 @ SV659 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3555,plain,
! [SV660: $i] :
( ( ! [SY4465: $i,SY4466: $i] :
( ~ ( class_Orderings_Oorder @ SV660 )
| ~ ( c_HOL_Oord__class_Oless @ SY4465 @ SY4466 @ SV660 )
| ~ ( c_HOL_Oord__class_Oless @ SY4466 @ SY4465 @ SV660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3556,plain,
! [SV661: $i] :
( ( ! [SY4467: $i,SY4468: $i] :
( ~ ( class_Orderings_Olinorder @ SV661 )
| ~ ( c_HOL_Oord__class_Oless @ SY4467 @ SY4468 @ SV661 )
| ~ ( c_HOL_Oord__class_Oless @ SY4468 @ SY4467 @ SV661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(3557,plain,
! [SV662: $i] :
( ( ! [SY4469: $i] :
( ( c_lessequals @ SV662 @ SY4469 @ tc_nat )
| ( c_lessequals @ SY4469 @ SV662 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(3558,plain,
! [SV663: $i] :
( ( ! [SY4470: $i,SY4471: $i] :
( ~ ( class_Orderings_Olinorder @ SV663 )
| ( c_lessequals @ SY4470 @ SY4471 @ SV663 )
| ( c_lessequals @ SY4471 @ SY4470 @ SV663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(3559,plain,
! [SV664: $i] :
( ( ! [SY4472: $i,SY4473: $i] :
( ~ ( class_Orderings_Opreorder @ SV664 )
| ~ ( c_HOL_Oord__class_Oless @ SY4472 @ SY4473 @ SV664 )
| ~ ( c_HOL_Oord__class_Oless @ SY4473 @ SY4472 @ SV664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(3560,plain,
! [SV665: $i] :
( ( ! [SY4474: $i,SY4475: $i] :
( ~ ( class_Orderings_Opreorder @ SV665 )
| ~ ( c_HOL_Oord__class_Oless @ SY4474 @ SY4475 @ SV665 )
| ~ ( c_HOL_Oord__class_Oless @ SY4475 @ SY4474 @ SV665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(3561,plain,
! [SV666: $i] :
( ( ! [SY4476: $i,SY4477: $i] :
( ( c_Nat_Onat_Onat__rec @ SV666 @ SY4476 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4477 )
= SV666 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3562,plain,
! [SV667: $i] :
( ( ! [SY4478: $i] :
( ( hBOOL @ ( hAPP @ SV667 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV667 @ SY4478 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV667 @ SY4478 ) )
| ( hBOOL @ ( hAPP @ SV667 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3563,plain,
! [SV668: $i] :
( ( ( SV668
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV668 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(3564,plain,
! [SV669: $i] :
( ( ! [SY4479: $i] :
( ( hBOOL @ ( hAPP @ SV669 @ SY4479 ) )
| ( hBOOL @ ( hAPP @ SV669 @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ SV669 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV669 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3565,plain,
! [SV670: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV670 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3566,plain,
! [SV671: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV671 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(3567,plain,
! [SV672: $i] :
( ( ! [SY4480: $i,SY4481: $i] :
( ( c_Nat_Onat_Onat__case @ SV672 @ SY4480 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4481 )
= SV672 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(3568,plain,
! [SV673: $i] :
( ( ! [SY4482: $i,SY4483: $i] :
( ( c_Nat_Onat_Onat__case @ SV673 @ SY4482 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4483 )
= SV673 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(3569,plain,
! [SV674: $i] :
( ( ( c_Orderings_Oord__class_Omin @ SV674 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(3570,plain,
! [SV675: $i] :
( ( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV675 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3571,plain,
! [SV676: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV676 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV676 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(3572,plain,
! [SV677: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV677 @ SV677 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2645]) ).
thf(3573,plain,
! [SV678: $i] :
( ( ! [SY4484: $i] :
( ( hBOOL @ ( hAPP @ SV678 @ SY4484 ) )
| ( hBOOL @ ( hAPP @ SV678 @ ( v_sko__List__Xreplicate__Xinduct__1 @ SV678 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV678 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(3574,plain,
! [SV679: $i] :
( ( ! [SY4485: $i,SY4486: $i] :
( ~ ( hBOOL @ ( hAPP @ SV679 @ ( c_Nat_Onat_Onat__case @ SY4485 @ SY4486 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV679 @ SY4485 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(3575,plain,
! [SV680: $i] :
( ( ! [SY4487: $i] :
( ( hBOOL @ ( hAPP @ SV680 @ SY4487 ) )
| ( hBOOL @ ( hAPP @ SV680 @ ( v_sko__Nat__Xnat__Xinducts__1 @ SV680 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV680 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(3576,plain,
! [SV681: $i] :
( ( ( c_Nitpick_Onat__gcd @ SV681 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV681 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(3577,plain,
! [SV682: $i] :
( ( ( c_String_Ochar_Ochar__size @ SV682 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2655]) ).
thf(3578,plain,
! [SV683: $i] :
( ( ! [SY4488: $i] :
( ( hBOOL @ ( hAPP @ SV683 @ SY4488 ) )
| ( hBOOL @ ( hAPP @ SV683 @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV683 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV683 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(3579,plain,
! [SV684: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV684 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(3580,plain,
! [SV685: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV685 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(3581,plain,
! [SV686: $i] :
( ( ! [SY4489: $i] :
( ( hBOOL @ ( hAPP @ SV686 @ SY4489 ) )
| ( hBOOL @ ( hAPP @ SV686 @ ( v_sko__List__Xupt__Xinduct__1 @ SV686 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV686 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3582,plain,
! [SV687: $i] :
( ( ! [SY4490: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV687 @ SY4490 )
= SV687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3583,plain,
! [SV688: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV688 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3584,plain,
! [SV689: $i] :
( ( ! [SY4491: $i] :
( ( hBOOL @ ( hAPP @ SV689 @ SY4491 ) )
| ~ ( hBOOL @ ( hAPP @ SV689 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV689 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV689 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3585,plain,
! [SV690: $i] :
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV690 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(3586,plain,
! [SV691: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV691 @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3587,plain,
! [SV692: $i] :
( ( ! [SY4492: $i,SY4493: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV692 @ SY4492 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4493 @ SY4492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3588,plain,
! [SV693: $i] :
( ( ( c_Orderings_Oord__class_Omax @ SV693 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV693 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2668]) ).
thf(3589,plain,
! [SV694: $i] :
( ( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV694 @ tc_nat )
= SV694 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(3590,plain,
! [SV695: $i] :
( ( SV695
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV695 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(3591,plain,
! [SV696: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV696 )
= SV696 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(3592,plain,
! [SV697: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV697 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV697 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(3593,plain,
! [SV698: $i] :
( ( ! [SY4494: $i,SY4495: $i,SY4496: $i,SY4497: $i,SY4498: $i,SY4499: $i] :
( ( ( hAPP @ ( hAPP @ SV698 @ SY4494 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SY4495 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4496 @ SY4497 @ SV698 @ SY4498 @ SY4495 @ SY4499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2674]) ).
thf(3594,plain,
! [SV699: $i] :
( ( ! [SY4500: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV699 )
| ( ( c_List_Olistsum @ SY4500 @ SV699 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV699 ) @ SY4500 @ ( c_HOL_Ozero__class_Ozero @ SV699 ) @ SV699 @ SV699 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(3595,plain,
! [SV700: $i] :
( ( ! [SY4501: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV700 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV700 ) @ ( c_HOL_Ozero__class_Ozero @ SV700 ) @ SY4501 @ SV700 @ SV700 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV700 ) @ SY4501 @ ( c_HOL_Ozero__class_Ozero @ SV700 ) @ SV700 @ SV700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(3596,plain,
! [SV701: $i] :
( ( ! [SY4502: $i,SY4503: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV701 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SY4502 @ SY4503 @ SV701 @ SV701 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SY4502 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SY4503 @ ( c_HOL_Ozero__class_Ozero @ SV701 ) @ SV701 @ SV701 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(3597,plain,
! [SV702: $i] :
( ( ! [SY4504: $i,SY4505: $i,SY4506: $i] :
( ( c_Type_Otyping @ SV702 @ SY4504 @ SY4505 )
| ~ ( c_Lambda_Obeta @ SY4506 @ SY4504 )
| ~ ( c_Type_Otyping @ SV702 @ SY4506 @ SY4505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(3598,plain,
! [SV703: $i] :
( ( ! [SY4507: $i,SY4508: $i] :
( ( ( hAPP @ SV703 @ SY4507 )
= SY4508 )
| ~ ( c_Type_Otyping @ SV703 @ ( c_Lambda_OdB_OVar @ SY4507 ) @ SY4508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(3599,plain,
! [SV704: $i] :
( ( ! [SY4509: $i] : ( c_Type_Otyping @ SV704 @ ( c_Lambda_OdB_OVar @ SY4509 ) @ ( hAPP @ SV704 @ SY4509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(3600,plain,
! [SV705: $i] :
( ( ! [SY4510: $i,SY4511: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV705 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV705 @ SY4510 ) @ tc_Type_Otype ) @ SY4510 @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV705 @ SY4510 ) )
| ~ ( c_Type_Otyping @ SV705 @ ( c_Lambda_OdB_OAbs @ SY4510 ) @ SY4511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(3601,plain,
! [SV706: $i] :
( ( ! [SY4512: $i,SY4513: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV706 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SY4512 @ SV706 @ SY4513 ) @ tc_Type_Otype ) @ SY4513 @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SY4512 @ SV706 @ SY4513 ) )
| ~ ( c_Type_Otyping @ SV706 @ ( c_Lambda_OdB_OAbs @ SY4513 ) @ SY4512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(3602,plain,
! [SV707: $i] :
( ( ! [SY4514: $i,SY4515: $i,SY4516: $i] :
( ( c_Type_Otyping @ SV707 @ SY4514 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY4515 @ SV707 @ SY4514 @ SY4516 ) ) @ SY4515 ) )
| ~ ( c_Type_Otyping @ SV707 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4514 ) @ SY4516 ) @ SY4515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3603,plain,
! [SV708: $i] :
( ( ! [SY4517: $i,SY4518: $i,SY4519: $i,SY4520: $i] :
( ( c_Type_Otype_Otype__rec @ SV708 @ SY4517 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4518 ) @ SY4519 ) @ SY4520 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SY4517 @ SY4518 ) @ SY4519 ) @ ( c_Type_Otype_Otype__rec @ SV708 @ SY4517 @ SY4518 @ SY4520 ) ) @ ( c_Type_Otype_Otype__rec @ SV708 @ SY4517 @ SY4519 @ SY4520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(3604,plain,
! [SV709: $i] :
( ( ! [SY4521: $i,SY4522: $i,SY4523: $i,SY4524: $i] :
( ( c_Type_Otype_Otype__case @ SV709 @ SY4521 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4522 ) @ SY4523 ) @ SY4524 )
= ( hAPP @ ( hAPP @ SY4521 @ SY4522 ) @ SY4523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3605,plain,
! [SV710: $i] :
( ( ! [SY4525: $i,SY4526: $i,SY4527: $i,SY4528: $i] :
( ~ ( hBOOL @ ( hAPP @ SV710 @ ( c_Type_Otype_Otype__case @ SY4525 @ SY4526 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4527 ) @ SY4528 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV710 @ ( hAPP @ ( hAPP @ SY4526 @ SY4527 ) @ SY4528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3606,plain,
! [SV711: $i] :
( ( ! [SY4529: $i,SY4530: $i,SY4531: $i,SY4532: $i] :
( ~ ( hBOOL @ ( hAPP @ SV711 @ ( c_Type_Otype_Otype__case @ SY4529 @ SY4530 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4531 ) @ SY4532 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV711 @ ( hAPP @ ( hAPP @ SY4530 @ SY4531 ) @ SY4532 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3607,plain,
! [SV712: $i] :
( ( ! [SY4533: $i,SY4534: $i,SY4535: $i,SY4536: $i,SY4537: $i] :
( ( c_List_Ofoldr @ SV712 @ ( c_List_Olist_OCons @ SY4533 @ SY4534 @ SY4535 ) @ SY4536 @ SY4535 @ SY4537 )
= ( hAPP @ ( hAPP @ SV712 @ SY4533 ) @ ( c_List_Ofoldr @ SV712 @ SY4534 @ SY4536 @ SY4535 @ SY4537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(3608,plain,
! [SV713: $i] :
( ( ! [SY4538: $i,SY4539: $i,SY4540: $i,SY4541: $i,SY4542: $i] :
( ( c_List_Ofoldr @ SV713 @ ( c_List_Oappend @ SY4538 @ SY4539 @ SY4540 ) @ SY4541 @ SY4540 @ SY4542 )
= ( c_List_Ofoldr @ SV713 @ SY4538 @ ( c_List_Ofoldr @ SV713 @ SY4539 @ SY4541 @ SY4540 @ SY4542 ) @ SY4540 @ SY4542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3609,plain,
! [SV714: $i] :
( ( ! [SY4543: $i,SY4544: $i,SY4545: $i] :
( ( c_List_Ofoldr @ SV714 @ ( c_List_Olist_ONil @ SY4543 ) @ SY4544 @ SY4543 @ SY4545 )
= SY4544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(3610,plain,
! [SV715: $i] :
( ( ! [SY4546: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ SV715 @ SY4546 ) )
| ~ ( c_InductTermi_OIT @ SV715 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3611,plain,
! [SV716: $i] :
( ( ! [SY4547: $i,SY4548: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV716 ) @ SY4547 ) @ SY4548 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV716 @ SY4548 ) ) @ ( c_Lambda_Olift @ SY4547 @ SY4548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3612,plain,
! [SV717: $i] :
( ( ! [SY4549: $i,SY4550: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV717 @ SY4549 ) @ SY4550 @ SY4549 )
= SV717 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3613,plain,
! [SV718: $i] :
( ( ! [SY4551: $i,SY4552: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV718 @ SY4551 ) @ ( c_Lambda_Olift @ SY4552 @ SY4551 ) )
| ~ ( c_Lambda_Obeta @ SV718 @ SY4552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(3614,plain,
! [SV719: $i] :
( ( ! [SY4553: $i,SY4554: $i,SY4555: $i,SY4556: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV719 @ SY4553 @ SY4554 @ SY4555 ) @ SY4556 )
= ( hAPP @ SV719 @ SY4556 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4556 @ SY4553 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2702]) ).
thf(3615,plain,
! [SV720: $i] :
( ( ! [SY4557: $i,SY4558: $i,SY4559: $i] :
( ( c_Type_Otyping @ SV720 @ SY4557 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY4558 @ SV720 @ SY4557 @ SY4559 ) @ SY4558 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV720 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4557 @ SY4559 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY4558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(3616,plain,
! [SV721: $i] :
( ( ! [SY4560: $i,SY4561: $i,SY4562: $i,SY4563: $i] :
( ( c_Type_Otyping @ SV721 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4560 @ SY4561 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY4562 )
| ~ ( c_Type_Otypings @ SV721 @ SY4561 @ SY4563 )
| ~ ( c_Type_Otyping @ SV721 @ SY4560 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY4563 @ SY4562 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(3617,plain,
! [SV722: $i] :
( ( ! [SY4564: $i,SY4565: $i,SY4566: $i] :
( ( c_Type_Otyping @ SV722 @ SY4564 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY4565 @ SV722 @ SY4564 @ SY4566 ) @ SY4565 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV722 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4564 @ SY4566 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY4565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(3618,plain,
! [SV723: $i] :
( ( ! [SY4567: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV723 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV723 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV723 )
| ~ ( class_Power_Opower @ SV723 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV723 ) @ SY4567 @ SV723 )
= ( c_HOL_Ozero__class_Ozero @ SV723 ) )
| ( SY4567
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2709]) ).
thf(3619,plain,
! [SV724: $i] :
( ( ! [SY4568: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV724 )
| ~ ( class_Power_Opower @ SV724 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV724 ) @ SY4568 @ SV724 )
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SY4568
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2710]) ).
thf(3620,plain,
! [SV725: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV725 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV725 )
= ( c_HOL_Ozero__class_Ozero @ SV725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2712]) ).
thf(3621,plain,
! [SV726: $i] :
( ( ! [SY4569: $i,SY4570: $i,SY4571: $i,SY4572: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ SV726 @ SY4569 @ SY4570 @ SY4571 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4572 @ SY4571 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV726 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4572 @ SY4571 ) @ ( c_Suc @ SY4569 ) @ SY4570 @ SY4571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(3622,plain,
! [SV727: $i] :
( ( ! [SY4573: $i,SY4574: $i,SY4575: $i,SY4576: $i] :
( ( c_Type_Otyping @ SV727 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4573 ) @ SY4574 ) @ SY4575 )
| ~ ( c_Type_Otyping @ SV727 @ SY4574 @ SY4576 )
| ~ ( c_Type_Otyping @ SV727 @ SY4573 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4576 ) @ SY4575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(3623,plain,
! [SV728: $i] :
( ( ! [SY4577: $i,SY4578: $i,SY4579: $i,SY4580: $i,SY4581: $i] :
( ~ ( c_Type_Otyping @ SV728 @ SY4577 @ SY4578 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV728 @ SY4579 @ SY4578 @ tc_Type_Otype ) @ SY4580 @ SY4581 )
| ( c_Type_Otyping @ SV728 @ ( c_Lambda_Osubst @ SY4580 @ SY4577 @ SY4579 ) @ SY4581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2715]) ).
thf(3624,plain,
! [SV729: $i] :
( ( ! [SY4582: $i,SY4583: $i,SY4584: $i] :
( ( c_Type_Otyping @ SV729 @ ( c_Lambda_OdB_OAbs @ SY4582 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4583 ) @ SY4584 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV729 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4583 @ tc_Type_Otype ) @ SY4582 @ SY4584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(3625,plain,
! [SV730: $i] :
( ( ! [SY4585: $i,SY4586: $i,SY4587: $i,SY4588: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV730 @ SY4585 @ SY4586 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY4587 @ SY4585 ) @ SY4588 )
| ~ ( c_Type_Otyping @ SV730 @ SY4587 @ SY4588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(3626,plain,
! [SV731: $i] :
( ( ! [SY4589: $i,SY4590: $i,SY4591: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV731 @ SY4589 @ SY4590 @ SY4591 ) @ SY4589 )
= SY4590 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(3627,plain,
! [SV732: $i] :
( ( ! [SY4592: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV732 @ SY4592 ) )
| ~ ( class_Orderings_Opreorder @ SY4592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(3628,plain,
! [SV733: $i] :
( ( ! [SY4593: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV733 @ SY4593 ) )
| ~ ( class_Orderings_Oorder @ SY4593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(3629,plain,
! [SV734: $i] :
( ( ! [SY4594: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ SV734 @ SY4594 ) )
| ~ ( class_Orderings_Obot @ SY4594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(3630,plain,
! [SV735: $i] :
( ( ! [SY4595: $i] : ( c_fequal @ SV735 @ SV735 @ SY4595 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(3631,plain,
! [SV736: $i] :
( ( ! [SY4596: $i,SY4597: $i] :
( ( SV736 = SY4596 )
| ~ ( c_fequal @ SV736 @ SY4596 @ SY4597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2764]) ).
thf(3632,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(3633,plain,
! [SV737: $i] :
( ( ! [SY4598: $i,SY4599: $i,SY4600: $i,SY4601: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV737 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4598 @ SY4599 @ SV737 )
!= ( c_HOL_Ominus__class_Ominus @ SY4600 @ SY4601 @ SV737 ) )
| ( c_lessequals @ SY4599 @ SY4598 @ SV737 )
| ~ ( c_lessequals @ SY4601 @ SY4600 @ SV737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(3634,plain,
! [SV738: $i] :
( ( ! [SY4602: $i,SY4603: $i,SY4604: $i,SY4605: $i] :
( ( ( c_List_Olist_OCons @ SV738 @ SY4602 @ SY4603 )
!= ( c_List_Olist_OCons @ SY4604 @ SY4605 @ SY4603 ) )
| ( SV738 = SY4604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3635,plain,
! [SV739: $i] :
( ( ! [SY4606: $i,SY4607: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV739 @ SY4606 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV739 @ SY4607 @ tc_nat ) )
| ( SY4606 = SY4607 )
| ( SV739
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2768]) ).
thf(3636,plain,
! [SV740: $i] :
( ( ! [SY4608: $i,SY4609: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV740 ) @ SY4608 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV740 ) @ SY4609 ) )
| ( SY4608 = SY4609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3637,plain,
! [SV741: $i] :
( ( ! [SY4610: $i,SY4611: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV741 ) @ SY4610 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV741 ) @ SY4611 ) )
| ( SY4610 = SY4611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3638,plain,
! [SV742: $i] :
( ( ! [SY4612: $i,SY4613: $i,SY4614: $i,SY4615: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SY4612 @ tc_nat ) ) @ SY4613 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4614 @ SY4612 @ tc_nat ) ) @ SY4615 ) )
| ~ ( c_lessequals @ SY4614 @ SV742 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV742 @ SY4614 @ tc_nat ) @ SY4612 @ tc_nat ) ) @ SY4613 )
= SY4615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(3639,plain,
! [SV743: $i] :
( ( ! [SY4616: $i,SY4617: $i] :
( ( ( c_List_Oappend @ SV743 @ SY4616 @ SY4617 )
!= SV743 )
| ( SY4616
= ( c_List_Olist_ONil @ SY4617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2772]) ).
thf(3640,plain,
! [SV744: $i] :
( ( ! [SY4618: $i,SY4619: $i,SY4620: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV744 ) @ SY4618 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4619 ) @ SY4620 ) )
| ( SV744 = SY4619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2773]) ).
thf(3641,plain,
! [SV745: $i] :
( ( ! [SY4621: $i,SY4622: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SY4621 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SY4622 @ SY4621 @ tc_nat ) )
| ( SY4621
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV745 = SY4622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2774]) ).
thf(3642,plain,
! [SV746: $i] :
( ( ! [SY4623: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV746 )
!= ( c_Lambda_OdB_OAbs @ SY4623 ) )
| ( SV746 = SY4623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2775]) ).
thf(3643,plain,
! [SV747: $i] :
( ( ! [SY4624: $i,SY4625: $i,SY4626: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV747 ) @ SY4624 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY4625 ) @ SY4626 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY4624 = SY4626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(3644,plain,
! [SV748: $i] :
( ( ! [SY4627: $i,SY4628: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV748 ) @ SY4627 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV748 ) @ SY4628 @ tc_nat ) )
| ( SY4627 = SY4628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(3645,plain,
! [SV749: $i] :
( ( ! [SY4629: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV749 ) @ SY4629 ) )
| ( SY4629
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY4629
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2778]) ).
thf(3646,plain,
! [SV750: $i] :
( ( ! [SY4630: $i,SY4631: $i,SY4632: $i,SY4633: $i,SY4634: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV750 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SY4630 @ SY4631 @ SV750 ) ) @ SY4632 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SY4633 @ SY4631 @ SV750 ) ) @ SY4634 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4630 @ SY4633 @ SV750 ) @ SY4631 @ SV750 ) ) @ SY4632 )
= SY4634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(3647,plain,
! [SV751: $i] :
( ( ! [SY4635: $i,SY4636: $i,SY4637: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV751 ) ) @ SY4635 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4636 ) @ SY4637 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2780]) ).
thf(3648,plain,
! [SV752: $i] :
( ( ! [SY4638: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV752 ) @ SY4638 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY4638
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(3649,plain,
! [SV753: $i] :
( ( ! [SY4639: $i] :
( ( SV753
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV753 ) @ SY4639 ) )
| ( SY4639
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2782]) ).
thf(3650,plain,
! [SV754: $i] :
( ( ! [SY4640: $i,SY4641: $i,SY4642: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV754 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SY4640 ) @ SY4641 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SY4642 ) @ SY4641 ) )
| ( SY4640 = SY4642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2783]) ).
thf(3651,plain,
! [SV755: $i] :
( ( ! [SY4643: $i,SY4644: $i] :
( ( ( c_List_Olist_ONil @ SV755 )
!= ( c_List_Oappend @ SY4643 @ SY4644 @ SV755 ) )
| ( SY4644
= ( c_List_Olist_ONil @ SV755 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(3652,plain,
! [SV756: $i] :
( ( ! [SY4645: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV756 ) @ SY4645 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY4645
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY4645
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2785]) ).
thf(3653,plain,
! [SV757: $i] :
( ( ! [SY4646: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV757 ) @ SY4646 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV757
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY4646
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(3654,plain,
! [SV758: $i] :
( ( ! [SY4647: $i,SY4648: $i,SY4649: $i] :
( ( ( c_List_Oappend @ SV758 @ SY4647 @ SY4648 )
!= ( c_List_Oappend @ SY4649 @ SY4647 @ SY4648 ) )
| ( SV758 = SY4649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(3655,plain,
! [SV759: $i] :
( ( ! [SY4650: $i,SY4651: $i,SY4652: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4650 ) @ SY4651 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SY4652 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SY4651 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3656,plain,
! [SV760: $i] :
( ( ! [SY4653: $i,SY4654: $i,SY4655: $i,SY4656: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV760 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4653 @ SY4654 @ SV760 )
!= ( c_HOL_Ominus__class_Ominus @ SY4655 @ SY4656 @ SV760 ) )
| ( c_HOL_Oord__class_Oless @ SY4655 @ SY4656 @ SV760 )
| ~ ( c_HOL_Oord__class_Oless @ SY4653 @ SY4654 @ SV760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(3657,plain,
! [SV761: $i] :
( ( ! [SY4657: $i,SY4658: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV761 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4657 @ SY4658 @ SV761 )
!= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
| ( SY4657
= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
| ( SY4658
= ( c_HOL_Ozero__class_Ozero @ SV761 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(3658,plain,
! [SV762: $i] :
( ( ! [SY4659: $i,SY4660: $i] :
( SV762
!= ( c_List_Olist_OCons @ SY4659 @ SV762 @ SY4660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2791]) ).
thf(3659,plain,
! [SV763: $i] :
( ( ! [SY4661: $i,SY4662: $i,SY4663: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV763 )
| ( ( c_Power_Opower__class_Opower @ SY4661 @ SY4662 @ SV763 )
!= ( c_Power_Opower__class_Opower @ SY4663 @ SY4662 @ SV763 ) )
| ( SY4661 = SY4663 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4662 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SY4663 @ SV763 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SY4661 @ SV763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2792]) ).
thf(3660,plain,
! [SV764: $i] :
( ( ! [SY4664: $i,SY4665: $i,SY4666: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV764 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SY4664 ) @ SY4665 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SY4664 ) @ SY4666 ) )
| ( SY4665 = SY4666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(3661,plain,
! [SV765: $i] :
( ( ! [SY4667: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV765 ) @ SY4667 ) )
| ( SV765
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV765
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(3662,plain,
! [SV766: $i] :
( ( ! [SY4668: $i,SY4669: $i,SY4670: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV766 ) @ SY4668 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4669 ) @ SY4670 ) )
| ( SY4668 = SY4670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3663,plain,
! [SV767: $i] :
( ( ( c_Suc @ SV767 )
!= SV767 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3664,plain,
! [SV768: $i] :
( ( ! [SY4671: $i] :
( ( c_Lambda_OdB_OVar @ SV768 )
!= ( c_Lambda_OdB_OAbs @ SY4671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(3665,plain,
! [SV769: $i] :
( ( ! [SY4672: $i,SY4673: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV769 ) @ SY4672 )
!= ( c_Lambda_OdB_OAbs @ SY4673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3666,plain,
! [SV770: $i] :
( ( ! [SY4674: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV770 @ SY4674 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV770
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3667,plain,
! [SV771: $i] :
( ( ! [SY4675: $i,SY4676: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV771 ) @ SY4675 )
!= ( c_Type_Otype_OAtom @ SY4676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3668,plain,
! [SV772: $i] :
( ( ! [SY4677: $i,SY4678: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV772 @ SY4677 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4678 @ SY4677 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV772 = SY4678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3669,plain,
! [SV773: $i] :
( ( ! [SY4679: $i,SY4680: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV773 )
| ~ ( class_Int_Onumber__ring @ SV773 )
| ( SY4679
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV773 ) @ SY4679 ) @ SY4680 ) )
| ( SY4680
= ( c_HOL_Ozero__class_Ozero @ SV773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(3670,plain,
! [SV774: $i] :
( ( ! [SY4681: $i,SY4682: $i,SY4683: $i,SY4684: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV774 )
| ~ ( class_Int_Onumber__ring @ SV774 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SY4681 ) @ ( c_HOL_Otimes__class_Otimes @ SY4682 @ SY4683 @ SV774 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SY4681 ) @ ( c_HOL_Otimes__class_Otimes @ SY4682 @ SY4684 @ SV774 ) ) )
| ( SY4683 = SY4684 )
| ( SY4682
= ( c_HOL_Ozero__class_Ozero @ SV774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(3671,plain,
! [SV775: $i] :
( ( ! [SY4685: $i,SY4686: $i,SY4687: $i,SY4688: $i] :
( ( ( c_List_Oreplicate @ SV775 @ SY4685 @ SY4686 )
!= ( c_List_Oreplicate @ SY4687 @ SY4688 @ SY4686 ) )
| ( SV775 = SY4687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2804]) ).
thf(3672,plain,
! [SV776: $i] :
( ( ! [SY4689: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV776 ) @ SY4689 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY4689
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV776
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(3673,plain,
! [SV777: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV777 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3674,plain,
! [SV778: $i] :
( ( ! [SY4690: $i,SY4691: $i,SY4692: $i,SY4693: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV778 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4690 @ SY4691 @ SV778 )
!= ( c_HOL_Ominus__class_Ominus @ SY4692 @ SY4693 @ SV778 ) )
| ( c_HOL_Oord__class_Oless @ SY4690 @ SY4691 @ SV778 )
| ~ ( c_HOL_Oord__class_Oless @ SY4692 @ SY4693 @ SV778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3675,plain,
! [SV779: $i] :
( ( ! [SY4694: $i,SY4695: $i] :
( ~ ( class_Orderings_Olinorder @ SV779 )
| ( ( c_Orderings_Oord__class_Omax @ SY4694 @ SY4695 @ SV779 )
!= SY4695 )
| ( c_lessequals @ SY4694 @ SY4695 @ SV779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(3676,plain,
! [SV780: $i] :
( ( ! [SY4696: $i,SY4697: $i,SY4698: $i,SY4699: $i] :
( ( ( c_List_Oappend @ SV780 @ ( c_List_Olist_OCons @ SY4696 @ ( c_List_Olist_ONil @ SY4697 ) @ SY4697 ) @ SY4697 )
!= ( c_List_Oappend @ SY4698 @ ( c_List_Olist_OCons @ SY4699 @ ( c_List_Olist_ONil @ SY4697 ) @ SY4697 ) @ SY4697 ) )
| ( SY4696 = SY4699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2809]) ).
thf(3677,plain,
! [SV781: $i] :
( ( ! [SY4700: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV781 ) @ SY4700 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV781
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(3678,plain,
! [SV782: $i] :
( ( ! [SY4701: $i,SY4702: $i,SY4703: $i] :
( ( ( c_List_Oappend @ SV782 @ SY4701 @ SY4702 )
!= ( c_List_Oappend @ SV782 @ SY4703 @ SY4702 ) )
| ( SY4701 = SY4703 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(3679,plain,
! [SV783: $i] :
( ( ! [SY4704: $i,SY4705: $i] :
( ( c_Type_Otype_OAtom @ SV783 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4704 ) @ SY4705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3680,plain,
! [SV784: $i] :
( ( ! [SY4706: $i,SY4707: $i,SY4708: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SY4706 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4707 @ SY4708 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SY4708 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4707 @ SY4706 @ tc_nat ) ) )
| ( SY4706 = SY4708 )
| ( SV784 = SY4707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3681,plain,
! [SV785: $i] :
( ( ( c_Suc @ SV785 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(3682,plain,
! [SV786: $i] :
( ( ! [SY4709: $i,SY4710: $i] :
( ( ( c_List_Olist_ONil @ SV786 )
!= ( c_List_Oreplicate @ SY4709 @ SY4710 @ SV786 ) )
| ( SY4709
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(3683,plain,
! [SV787: $i] :
( ( ! [SY4711: $i,SY4712: $i,SY4713: $i,SY4714: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV787 )
| ~ ( class_Int_Onumber__ring @ SV787 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SY4711 @ SY4712 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4713 @ SY4714 @ SV787 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SY4711 @ SY4714 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4713 @ SY4712 @ SV787 ) ) )
| ( SY4712 = SY4714 )
| ( SY4711 = SY4713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3684,plain,
! [SV788: $i] :
( ( ! [SY4715: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV788 @ SY4715 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY4715
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3685,plain,
! [SV789: $i] :
( ( ! [SY4716: $i,SY4717: $i,SY4718: $i,SY4719: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV789 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4716 @ SY4717 @ SV789 )
!= ( c_HOL_Ominus__class_Ominus @ SY4718 @ SY4719 @ SV789 ) )
| ( c_lessequals @ SY4719 @ SY4718 @ SV789 )
| ~ ( c_lessequals @ SY4717 @ SY4716 @ SV789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3686,plain,
! [SV790: $i] :
( ( ! [SY4720: $i,SY4721: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV790 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4720 @ SY4721 @ SV790 )
!= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
| ( SY4721
= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
| ( SY4720
= ( c_HOL_Ozero__class_Ozero @ SV790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(3687,plain,
! [SV791: $i] :
( ( ! [SY4722: $i] :
( ( ( c_Suc @ SV791 )
!= ( c_Suc @ SY4722 ) )
| ( SV791 = SY4722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2820]) ).
thf(3688,plain,
! [SV792: $i] :
( ( ! [SY4723: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV792 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV792 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV792 )
| ~ ( class_Power_Opower @ SV792 )
| ( ( c_Power_Opower__class_Opower @ SY4723 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV792 )
!= ( c_HOL_Ozero__class_Ozero @ SV792 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(3689,plain,
! [SV793: $i] :
( ( ! [SY4724: $i,SY4725: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV793 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV793 ) @ SY4724 ) @ SY4725 )
!= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SY4725 @ SV793 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SY4724 @ SV793 )
| ( SY4724
= ( c_HOL_Ozero__class_Ozero @ SV793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(3690,plain,
! [SV794: $i] :
( ( ! [SY4726: $i,SY4727: $i,SY4728: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV794 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4726 ) @ SY4727 ) )
| ( hBOOL @ ( hAPP @ SV794 @ SY4728 ) )
| ( hBOOL @ ( hAPP @ SV794 @ SY4726 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3691,plain,
! [SV795: $i] :
( ( ! [SY4729: $i,SY4730: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV795 @ SY4729 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SY4730 @ SY4729 @ tc_nat ) )
| ~ ( c_lessequals @ SY4729 @ SY4730 @ tc_nat )
| ~ ( c_lessequals @ SY4729 @ SV795 @ tc_nat )
| ( SV795 = SY4730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(3692,plain,
! [SV796: $i] :
( ( ! [SY4731: $i,SY4732: $i,SY4733: $i,SY4734: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV796 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SY4731 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SY4732 ) @ SY4733 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SY4732 ) @ SY4734 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SY4731 ) @ SY4733 )
= SY4734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(3693,plain,
! [SV797: $i] :
( ( ! [SY4735: $i,SY4736: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV797 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV797 ) @ ( c_HOL_Otimes__class_Otimes @ SY4735 @ SY4735 @ SV797 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4736 @ SY4736 @ SV797 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV797 ) )
| ( SY4736
= ( c_HOL_Ozero__class_Ozero @ SV797 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3694,plain,
! [SV798: $i] :
( ( ! [SY4737: $i,SY4738: $i,SY4739: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV798 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4737 @ SY4737 @ SV798 )
!= ( c_HOL_Ominus__class_Ominus @ SY4738 @ SY4739 @ SV798 ) )
| ( SY4738 = SY4739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3695,plain,
! [SV799: $i] :
( ( ! [SY4740: $i,SY4741: $i,SY4742: $i,SY4743: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV799 @ SY4740 @ tc_nat ) ) @ SY4741 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4742 @ SY4740 @ tc_nat ) ) @ SY4743 ) )
| ~ ( c_lessequals @ SV799 @ SY4742 @ tc_nat )
| ( SY4741
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4742 @ SV799 @ tc_nat ) @ SY4740 @ tc_nat ) ) @ SY4743 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3696,plain,
! [SV800: $i] :
( ( ! [SY4744: $i,SY4745: $i,SY4746: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV800 ) @ SY4744 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4745 ) @ SY4746 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4745 @ SY4744 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV800 @ SY4746 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3697,plain,
! [SV801: $i] :
( ( ! [SY4747: $i,SY4748: $i,SY4749: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV801 ) @ SY4747 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY4748 ) @ SY4749 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV801 = SY4748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3698,plain,
! [SV802: $i] :
( ( ! [SY4750: $i,SY4751: $i] :
( ( ( c_List_Oappend @ SV802 @ SY4750 @ SY4751 )
!= ( c_List_Olist_ONil @ SY4751 ) )
| ( SY4750
= ( c_List_Olist_ONil @ SY4751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(3699,plain,
! [SV803: $i] :
( ( ! [SY4752: $i,SY4753: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV803 @ SY4752 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV803 @ SY4753 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV803 @ tc_nat )
| ( SY4752 = SY4753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3700,plain,
! [SV804: $i] :
( ( ! [SY4754: $i,SY4755: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV804 ) @ SY4754 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4755 ) @ SY4754 ) )
| ( SV804 = SY4755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(3701,plain,
! [SV805: $i] :
( ( ! [SY4756: $i] :
( ( ( c_Lambda_OdB_OVar @ SV805 )
!= ( c_Lambda_OdB_OVar @ SY4756 ) )
| ( SV805 = SY4756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2834]) ).
thf(3702,plain,
! [SV806: $i] :
( ( ! [SY4757: $i,SY4758: $i,SY4759: $i,SY4760: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV806 )
| ~ ( class_Int_Onumber__ring @ SV806 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SY4757 @ SY4758 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4759 @ SY4760 @ SV806 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SY4757 @ SY4760 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4759 @ SY4758 @ SV806 ) ) )
| ( SY4758 = SY4760 )
| ( SY4757 = SY4759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3703,plain,
! [SV807: $i] :
( ( ! [SY4761: $i,SY4762: $i,SY4763: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV807 ) @ SY4761 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4762 ) @ SY4763 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY4761 = SY4763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(3704,plain,
! [SV808: $i] :
( ( ! [SY4764: $i,SY4765: $i,SY4766: $i,SY4767: $i,SY4768: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV808 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SY4764 @ SY4765 @ SV808 ) ) @ SY4766 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SY4767 @ SY4765 @ SV808 ) ) @ SY4768 ) )
| ( SY4766
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4767 @ SY4764 @ SV808 ) @ SY4765 @ SV808 ) ) @ SY4768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(3705,plain,
! [SV809: $i] :
( ( ! [SY4769: $i,SY4770: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV809 @ SY4769 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV809 @ SY4770 @ tc_nat ) )
| ( SV809
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY4769 = SY4770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(3706,plain,
! [SV810: $i] :
( ( ! [SY4771: $i,SY4772: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV810 )
| ~ ( class_Int_Onumber__ring @ SV810 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4771 @ SY4772 @ SV810 )
!= ( c_HOL_Ozero__class_Ozero @ SV810 ) )
| ( SY4771 = SY4772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2839]) ).
thf(3707,plain,
! [SV811: $i] :
( ( ! [SY4773: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV811 @ SY4773 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SV811 @ SY4773 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(3708,plain,
! [SV812: $i] :
( ( ! [SY4774: $i,SY4775: $i,SY4776: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SY4774 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4775 @ SY4776 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SY4776 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4775 @ SY4774 @ tc_nat ) ) )
| ( SY4774 = SY4776 )
| ( SV812 = SY4775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(3709,plain,
! [SV813: $i] :
( ( ! [SY4777: $i] :
( ( c_Lambda_OdB_OAbs @ SV813 )
!= ( c_Lambda_OdB_OVar @ SY4777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3710,plain,
! [SV814: $i] :
( ( ! [SY4778: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV814 @ SY4778 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SY4778 @ SV814 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY4778 = SV814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(3711,plain,
! [SV815: $i] :
( ( ! [SY4779: $i,SY4780: $i] :
( ( ( c_Lambda_OdB_OVar @ SV815 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4779 @ SY4780 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV815 )
= SY4779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3712,plain,
! [SV816: $i] :
( ( ! [SY4781: $i,SY4782: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV816 )
| ( ( c_HOL_Otimes__class_Otimes @ SY4781 @ SY4782 @ SV816 )
!= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
| ( SY4782
= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
| ( SY4781
= ( c_HOL_Ozero__class_Ozero @ SV816 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3713,plain,
! [SV817: $i] :
( ( ! [SY4783: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV817 ) @ SY4783 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV817
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV817
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3714,plain,
! [SV818: $i] :
( ( ! [SY4784: $i,SY4785: $i,SY4786: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV818 ) @ SY4784 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY4785 ) @ SY4786 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3715,plain,
! [SV819: $i] :
( ( ! [SY4787: $i,SY4788: $i,SY4789: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV819 ) @ SY4787 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4788 ) @ SY4789 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV819 = SY4788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3716,plain,
! [SV820: $i] :
( ( ! [SY4790: $i,SY4791: $i,SY4792: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV820 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SY4790 ) @ SY4791 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SY4790 ) @ SY4792 ) )
| ( SY4791 = SY4792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3717,plain,
! [SV821: $i] :
( ( ! [SY4793: $i,SY4794: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV821 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY4793 @ SV821 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY4794 @ SV821 ) )
| ( SY4793 = SY4794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3718,plain,
! [SV822: $i] :
( ( ! [SY4795: $i,SY4796: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV822 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV822 ) @ ( c_HOL_Otimes__class_Otimes @ SY4795 @ SY4795 @ SV822 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY4796 @ SY4796 @ SV822 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV822 ) )
| ( SY4795
= ( c_HOL_Ozero__class_Ozero @ SV822 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(3719,plain,
! [SV823: $i] :
( ( ! [SY4797: $i,SY4798: $i,SY4799: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV823 )
| ( ( c_Power_Opower__class_Opower @ SY4797 @ ( c_Suc @ SY4798 ) @ SV823 )
!= ( c_Power_Opower__class_Opower @ SY4799 @ ( c_Suc @ SY4798 ) @ SV823 ) )
| ( SY4797 = SY4799 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SY4799 @ SV823 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SY4797 @ SV823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3720,plain,
! [SV824: $i] :
( ( ! [SY4800: $i,SY4801: $i] :
( ( ( c_List_Oappend @ SV824 @ SY4800 @ SY4801 )
!= SY4800 )
| ( SV824
= ( c_List_Olist_ONil @ SY4801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(3721,plain,
! [SV825: $i] :
( ( ! [SY4802: $i,SY4803: $i] :
( ( c_Lambda_OdB_OAbs @ SV825 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4802 ) @ SY4803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3722,plain,
! [SV826: $i] :
( ( ! [SY4804: $i,SY4805: $i] :
( ( SV826
!= ( c_List_Oappend @ SY4804 @ SV826 @ SY4805 ) )
| ( SY4804
= ( c_List_Olist_ONil @ SY4805 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(3723,plain,
! [SV827: $i] :
( ( ! [SY4806: $i] :
( ( ( c_Suc @ SV827 )
!= ( c_Suc @ SY4806 ) )
| ( SV827 = SY4806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(3724,plain,
! [SV828: $i] :
( ( ! [SY4807: $i,SY4808: $i] :
( ( c_List_Olist_OCons @ SV828 @ SY4807 @ SY4808 )
!= ( c_List_Olist_ONil @ SY4808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(3725,plain,
! [SV829: $i] :
( ( ! [SY4809: $i,SY4810: $i] :
( ( c_List_Olist_OCons @ SV829 @ SY4809 @ SY4810 )
!= ( c_List_Olist_ONil @ SY4810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(3726,plain,
! [SV830: $i] :
( ( ! [SY4811: $i,SY4812: $i,SY4813: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV830 ) @ SY4811 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4812 ) @ SY4813 ) )
| ( SY4811 = SY4813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3727,plain,
! [SV831: $i] :
( ( SV831
!= ( c_Suc @ SV831 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(3728,plain,
! [SV832: $i] :
( ( ! [SY4814: $i,SY4815: $i,SY4816: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV832 )
| ~ ( class_Int_Onumber__ring @ SV832 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SY4814 ) @ SY4815 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SY4814 ) @ SY4816 ) )
| ( SY4815 = SY4816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3729,plain,
! [SV833: $i] :
( ( ! [SY4817: $i,SY4818: $i] :
( ( ( c_List_Oreplicate @ SV833 @ SY4817 @ SY4818 )
!= ( c_List_Olist_ONil @ SY4818 ) )
| ( SV833
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3730,plain,
! [SV834: $i] :
( ( ! [SY4819: $i,SY4820: $i] :
( ~ ( class_Orderings_Olinorder @ SV834 )
| ( ( c_Orderings_Oord__class_Omin @ SY4819 @ SY4820 @ SV834 )
!= SY4819 )
| ( c_lessequals @ SY4819 @ SY4820 @ SV834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3731,plain,
! [SV835: $i] :
( ( ! [SY4821: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV835 @ SY4821 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY4821
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV835
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3732,plain,
! [SV836: $i] :
( ( ! [SY4822: $i,SY4823: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV836 @ SY4822 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY4823 ) )
| ( SV836
= ( c_Lambda_OdB_OAbs @ SY4823 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(3733,plain,
! [SV837: $i] :
( ( ! [SY4824: $i,SY4825: $i,SY4826: $i,SY4827: $i] :
( ( ( c_List_Oreplicate @ SV837 @ SY4824 @ SY4825 )
!= ( c_List_Oreplicate @ SY4826 @ SY4827 @ SY4825 ) )
| ( SY4824 = SY4827 )
| ( SV837
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3734,plain,
! [SV838: $i] :
( ( ! [SY4828: $i,SY4829: $i,SY4830: $i,SY4831: $i,SY4832: $i,SY4833: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SY4828 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY4829 @ SY4830 @ SY4831 ) )
| ~ ( c_Type_Otyping @ SY4832 @ SY4830 @ SY4828 )
| ~ ( c_InductTermi_OIT @ SY4830 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY4832 @ SY4831 @ SY4828 @ tc_Type_Otype ) @ SY4829 @ SY4833 )
| ~ ( c_InductTermi_OIT @ SY4829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3735,plain,
! [SV839: $i] :
( ( ! [SY4834: $i,SY4835: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV839 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV839 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV839 )
| ~ ( class_Power_Opower @ SV839 )
| ( ( c_Power_Opower__class_Opower @ SY4834 @ SY4835 @ SV839 )
!= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
| ( SY4834
= ( c_HOL_Ozero__class_Ozero @ SV839 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(3736,plain,
! [SV840: $i] :
( ( ! [SY4836: $i,SY4837: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV840 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4836 @ SY4837 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV840 )
= SY4836 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(3737,plain,
! [SV841: $i] :
( ( ! [SY4838: $i,SY4839: $i,SY4840: $i,SY4841: $i] :
( ( ( c_List_Oappend @ SV841 @ ( c_List_Olist_OCons @ SY4838 @ ( c_List_Olist_ONil @ SY4839 ) @ SY4839 ) @ SY4839 )
!= ( c_List_Oappend @ SY4840 @ ( c_List_Olist_OCons @ SY4841 @ ( c_List_Olist_ONil @ SY4839 ) @ SY4839 ) @ SY4839 ) )
| ( SV841 = SY4840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3738,plain,
! [SV842: $i] :
( ( ! [SY4842: $i,SY4843: $i] :
( ( SV842
!= ( c_List_Oappend @ SV842 @ SY4842 @ SY4843 ) )
| ( SY4842
= ( c_List_Olist_ONil @ SY4843 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3739,plain,
! [SV843: $i] :
( ( ! [SY4844: $i,SY4845: $i] :
( ( c_Lambda_OdB_OVar @ SV843 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4844 ) @ SY4845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3740,plain,
! [SV844: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV844 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3741,plain,
! [SV845: $i] :
( ( ! [SY4846: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV845 ) @ SY4846 ) )
| ( SY4846
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV845
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(3742,plain,
! [SV846: $i] :
( ( ! [SY4847: $i,SY4848: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV846 )
| ( ( c_Power_Opower__class_Opower @ SY4847 @ SY4848 @ SV846 )
!= ( c_HOL_Ozero__class_Ozero @ SV846 ) )
| ( SY4847
= ( c_HOL_Ozero__class_Ozero @ SV846 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(3743,plain,
! [SV847: $i] :
( ( ! [SY4849: $i,SY4850: $i] :
( ( c_List_Olist_ONil @ SV847 )
!= ( c_List_Olist_OCons @ SY4849 @ SY4850 @ SV847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3744,plain,
! [SV848: $i] :
( ( ! [SY4851: $i,SY4852: $i,SY4853: $i,SY4854: $i] :
( ( ( c_List_Olist_OCons @ SV848 @ SY4851 @ SY4852 )
!= ( c_List_Olist_OCons @ SY4853 @ SY4854 @ SY4852 ) )
| ( SY4851 = SY4854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3745,plain,
! [SV849: $i] :
( ( ! [SY4855: $i,SY4856: $i] :
( ( ( c_List_Olist_ONil @ SV849 )
!= ( c_List_Oappend @ SY4855 @ SY4856 @ SV849 ) )
| ( SY4855
= ( c_List_Olist_ONil @ SV849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3746,plain,
! [SV850: $i] :
( ( ! [SY4857: $i] :
( ( ( c_Type_Otype_OAtom @ SV850 )
!= ( c_Type_Otype_OAtom @ SY4857 ) )
| ( SV850 = SY4857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3747,plain,
! [SV851: $i] :
( ( ! [SY4858: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV851 ) @ SY4858 ) )
| ( SV851
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY4858
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3748,plain,
! [SV852: $i] :
( ( ! [SY4859: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV852 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV852 ) @ SY4859 ) @ SY4859 )
!= ( c_HOL_Ozero__class_Ozero @ SV852 ) )
| ( SY4859
= ( c_HOL_Ozero__class_Ozero @ SV852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3749,plain,
! [SV853: $i] :
( ( ! [SY4860: $i,SY4861: $i,SY4862: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV853 ) @ SY4860 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY4861 ) @ SY4862 ) )
| ( SV853 = SY4861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(3750,plain,
! [SV854: $i] :
( ( ! [SY4863: $i,SY4864: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV854 ) @ SY4863 )
!= ( c_Lambda_OdB_OVar @ SY4864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3751,plain,
! [SV855: $i] :
( ( ! [SY4865: $i,SY4866: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV855 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV855 ) @ SY4865 ) @ SY4866 )
!= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SY4866 @ SV855 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SY4865 @ SV855 )
| ( SY4866
= ( c_HOL_Ozero__class_Ozero @ SV855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3752,plain,
! [SV856: $i] :
( ( ! [SY4867: $i,SY4868: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV856 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4867 @ SY4868 @ SV856 )
!= ( c_HOL_Ozero__class_Ozero @ SV856 ) )
| ( SY4867 = SY4868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3753,plain,
! [SV857: $i] :
( ( ! [SY4869: $i,SY4870: $i] :
( ( ( c_List_Oappend @ SV857 @ SY4869 @ SY4870 )
!= ( c_List_Olist_ONil @ SY4870 ) )
| ( SV857
= ( c_List_Olist_ONil @ SY4870 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(3754,plain,
! [SV858: $i] :
( ( ! [SY4871: $i,SY4872: $i,SY4873: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV858 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4871 @ SY4872 @ SV858 )
!= ( c_HOL_Ominus__class_Ominus @ SY4873 @ SY4873 @ SV858 ) )
| ( SY4871 = SY4872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(3755,plain,
! [SV859: $i] :
( ( ! [SY4874: $i,SY4875: $i] :
( ( c_List_Olist_OCons @ SV859 @ SY4874 @ SY4875 )
!= SY4874 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3756,plain,
! [SV860: $i] :
( ( ! [SY4876: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV860 ) @ SY4876 )
!= SV860 )
| ( SY4876
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3757,plain,
! [SV861: $i] :
( ( ! [SY4877: $i,SY4878: $i,SY4879: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SY4877 @ SY4878 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SY4877 @ SY4879 @ tc_nat ) ) )
| ( SY4878 = SY4879 )
| ( SY4877
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3758,plain,
! [SV862: $i] :
( ( ( c_Suc @ SV862 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3759,plain,
! [SV863: $i] :
( ( ! [SY4880: $i,SY4881: $i,SY4882: $i,SY4883: $i,SY4884: $i,SY4885: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SY4880 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY4881 @ SY4882 @ SY4883 ) )
| ~ ( c_Type_Otyping @ SY4884 @ SY4882 @ SV863 )
| ~ ( c_InductTermi_OIT @ SY4882 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY4884 @ SY4883 @ SV863 @ tc_Type_Otype ) @ SY4881 @ SY4885 )
| ~ ( c_InductTermi_OIT @ SY4881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(3760,plain,
! [SV864: $i] :
( ( ! [SY4886: $i,SY4887: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV864 )
| ( ( c_HOL_Ominus__class_Ominus @ SY4886 @ SY4887 @ SV864 )
!= ( c_HOL_Ozero__class_Ozero @ SV864 ) )
| ( SY4886 = SY4887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3761,plain,
! [SV865: $i,SV1: $i] :
( ( ! [SY4888: $i,SY4889: $i,SY4890: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1 @ SV865 @ tc_nat ) ) @ SY4888 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4889 @ SV865 @ tc_nat ) ) @ SY4890 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4888 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4889 @ SV1 @ tc_nat ) @ SV865 @ tc_nat ) ) @ SY4890 ) @ tc_nat )
| ~ ( c_lessequals @ SV1 @ SY4889 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2895]) ).
thf(3762,plain,
! [SV866: $i,SV2: $i] :
( ( ! [SY4891: $i,SY4892: $i,SY4893: $i] :
( ( c_HOL_Oord__class_Oless @ SV2 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV866 @ SY4891 @ tc_nat ) @ SY4892 @ tc_nat ) ) @ SY4893 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4891 @ SY4892 @ tc_nat ) ) @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV866 @ SY4892 @ tc_nat ) ) @ SY4893 ) @ tc_nat )
| ~ ( c_lessequals @ SY4891 @ SV866 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2896]) ).
thf(3763,plain,
! [SV867: $i,SV3: $i] :
( ( ! [SY4894: $i,SY4895: $i,SY4896: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV3 @ SV867 @ tc_nat ) ) @ SY4894 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4895 @ SV867 @ tc_nat ) ) @ SY4896 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV3 @ SY4895 @ tc_nat ) @ SV867 @ tc_nat ) ) @ SY4894 ) @ SY4896 @ tc_nat )
| ~ ( c_lessequals @ SY4895 @ SV3 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2897]) ).
thf(3764,plain,
! [SV868: $i,SV4: $i] :
( ( ! [SY4897: $i,SY4898: $i,SY4899: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV868 @ tc_nat ) @ SY4897 @ tc_nat ) ) @ SY4898 ) @ SY4899 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV4 @ SY4897 @ tc_nat ) ) @ SY4898 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV868 @ SY4897 @ tc_nat ) ) @ SY4899 ) @ tc_nat )
| ~ ( c_lessequals @ SV868 @ SV4 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3765,plain,
! [SV869: $i,SV5: $i] :
( ( ! [SY4900: $i,SY4901: $i,SY4902: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV5 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV869 @ SY4900 @ SV5 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4901 @ SV869 @ SV5 ) @ SY4900 @ SV5 ) ) @ SY4902 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SY4901 @ SY4900 @ SV5 ) ) @ SY4902 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3766,plain,
! [SV870: $i,SV6: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV6 ) ) @ SV870 )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV6 ) @ SV870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3767,plain,
! [SV871: $i,SV7: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV7 ) @ ( c_Suc @ SV871 ) )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV7 ) @ SV871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3768,plain,
! [SV872: $i,SV8: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV8 )
| ~ ( class_Power_Opower @ SV8 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ ( c_Suc @ SV872 ) @ SV8 )
= ( c_HOL_Ozero__class_Ozero @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3769,plain,
! [SV873: $i,SV9: $i] :
( ( ! [SY4903: $i,SY4904: $i,SY4905: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SY4903 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SY4904 @ SY4905 @ SV9 ) @ SV9 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SY4903 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SY4904 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SY4903 @ SY4905 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV873 @ SY4904 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3770,plain,
! [SV874: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ SV10 @ SV874 ) )
| ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV10 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3771,plain,
! [SV875: $i,SV11: $i] :
( ( ! [SY4906: $i] :
( ~ ( class_Orderings_Olinorder @ SV11 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV875 @ SY4906 @ SV11 ) @ SV875 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3772,plain,
! [SV876: $i,SV12: $i] :
( ( ! [SY4907: $i] :
( ~ ( class_Orderings_Olinorder @ SV12 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV876 @ SY4907 @ SV12 ) @ SY4907 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3773,plain,
! [SV877: $i,SV13: $i] :
( ( ! [SY4908: $i,SY4909: $i] :
( ~ ( class_Orderings_Olinorder @ SV13 )
| ( c_lessequals @ SV877 @ ( c_Orderings_Oord__class_Omin @ SY4908 @ SY4909 @ SV13 ) @ SV13 )
| ~ ( c_lessequals @ SV877 @ SY4909 @ SV13 )
| ~ ( c_lessequals @ SV877 @ SY4908 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3774,plain,
! [SV878: $i,SV14: $i] :
( ( ! [SY4910: $i,SY4911: $i] :
( ~ ( class_Orderings_Olinorder @ SV14 )
| ( c_lessequals @ SV878 @ ( c_Orderings_Oord__class_Omin @ SY4910 @ SY4911 @ SV14 ) @ SV14 )
| ~ ( c_lessequals @ SV878 @ SY4911 @ SV14 )
| ~ ( c_lessequals @ SV878 @ SY4910 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3775,plain,
! [SV879: $i,SV15: $i] :
( ( ! [SY4912: $i,SY4913: $i] :
( ~ ( class_Orderings_Olinorder @ SV15 )
| ( c_lessequals @ SV879 @ ( c_Orderings_Oord__class_Omin @ SY4912 @ SY4913 @ SV15 ) @ SV15 )
| ~ ( c_lessequals @ SV879 @ SY4913 @ SV15 )
| ~ ( c_lessequals @ SV879 @ SY4912 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3776,plain,
! [SV880: $i,SV16: $i] :
( ( ! [SY4914: $i,SY4915: $i,SY4916: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV16 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SV880 @ SY4914 @ SV16 ) ) @ SY4915 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SY4916 @ SY4914 @ SV16 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV880 @ SY4916 @ SV16 ) @ SY4914 @ SV16 ) ) @ SY4915 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3777,plain,
! [SV881: $i,SV17: $i] :
( ( ! [SY4917: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV17 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SV881 @ SY4917 @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV881 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3778,plain,
! [SV882: $i,SV18: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV18 @ SV882 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV18 @ SV882 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(3779,plain,
! [SV883: $i,SV19: $i] :
( ( ! [SY4918: $i,SY4919: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV19 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV883 @ SY4918 @ SV19 ) @ SY4919 @ SV19 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV883 @ SY4919 @ SV19 ) @ ( c_HOL_Ominus__class_Ominus @ SY4918 @ SY4919 @ SV19 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3780,plain,
! [SV884: $i,SV20: $i] :
( ( ! [SY4920: $i,SY4921: $i] :
( ~ ( class_Orderings_Olinorder @ SV20 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV884 @ SY4920 @ SV20 ) @ SY4921 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SY4920 @ SY4921 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SV884 @ SY4921 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3781,plain,
! [SV885: $i,SV21: $i] :
( ( ! [SY4922: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV21 @ SV885 @ tc_nat ) ) @ SY4922 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV21 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV885 ) @ SY4922 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV885 @ SV21 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2915]) ).
thf(3782,plain,
! [SV886: $i,SV22: $i] :
( ( ! [SY4923: $i,SY4924: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV22 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV22 )
| ( c_HOL_Oord__class_Oless @ SV886 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SY4923 ) @ SY4924 ) @ SV22 )
| ~ ( c_lessequals @ SV886 @ SY4924 @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SY4923 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3783,plain,
! [SV887: $i,SV23: $i] :
( ( ! [SY4925: $i] :
( ( c_HOL_Oord__class_Oless @ SV23 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV887 ) @ SY4925 ) @ tc_nat )
| ~ ( c_lessequals @ SV23 @ SV887 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4925 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3784,plain,
! [SV888: $i,SV24: $i] :
( ( ! [SY4926: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV24 )
| ( c_lessequals @ SV888 @ SY4926 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV888 @ SV24 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4926 @ SV24 ) @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3785,plain,
! [SV889: $i,SV25: $i] :
( ( ! [SY4927: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV25 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV889 @ SV25 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4927 @ SV25 ) @ SV25 )
| ~ ( c_lessequals @ SV889 @ SY4927 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(3786,plain,
! [SV890: $i,SV26: $i] :
( ( ! [SY4928: $i,SY4929: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV26 @ SV890 @ SY4928 ) @ ( c_Lambda_Osubst @ SY4929 @ SV890 @ SY4928 ) )
| ~ ( c_Lambda_Obeta @ SV26 @ SY4929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(3787,plain,
! [SV891: $i,SV27: $i] :
( ( ! [SY4930: $i,SY4931: $i] :
( ~ ( class_Orderings_Olinorder @ SV27 )
| ( c_HOL_Oord__class_Oless @ SV891 @ ( c_Orderings_Oord__class_Omin @ SY4930 @ SY4931 @ SV27 ) @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SY4931 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SY4930 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3788,plain,
! [SV892: $i,SV28: $i] :
( ( ! [SY4932: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV28 @ SV892 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV28 @ SY4932 @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV28 @ SY4932 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV28 @ SV892 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3789,plain,
! [SV893: $i,SV29: $i] :
( ( ! [SY4933: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV29 @ SV893 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV29 @ SY4933 @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV29 @ SY4933 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV29 @ SV893 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3790,plain,
! [SV894: $i,SV30: $i] :
( ( ! [SY4934: $i,SY4935: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV30 )
| ~ ( class_Int_Onumber__ring @ SV30 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SY4934 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SY4935 @ SV30 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SY4935 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SY4934 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(3791,plain,
! [SV895: $i,SV31: $i] :
( ( ! [SY4936: $i,SY4937: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV31 )
| ~ ( class_Int_Onumber__ring @ SV31 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SY4936 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SY4937 @ SV31 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SY4937 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SY4936 @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2925]) ).
thf(3792,plain,
! [SV896: $i,SV32: $i] :
( ( ( c_Orderings_Oord__class_Omax @ ( c_Suc @ SV32 ) @ ( c_Suc @ SV896 ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omax @ SV32 @ SV896 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2926]) ).
thf(3793,plain,
! [SV33: $i] :
( ( ( SV33
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV33 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2927]) ).
thf(3794,plain,
! [SV897: $i,SV34: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV34 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV897 @ SV34 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV897 ) @ SV897 ) @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3795,plain,
! [SV898: $i,SV35: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV35 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV35 ) @ SV898 ) @ SV898 ) @ SV35 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV898 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2929]) ).
thf(3796,plain,
! [SV899: $i,SV36: $i] :
( ( ! [SY4938: $i] :
( ~ ( class_Orderings_Olinorder @ SV36 )
| ( ( c_Orderings_Oord__class_Omin @ SV899 @ ( c_Orderings_Oord__class_Omin @ SV899 @ SY4938 @ SV36 ) @ SV36 )
= ( c_Orderings_Oord__class_Omin @ SV899 @ SY4938 @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2930]) ).
thf(3797,plain,
! [SV900: $i,SV37: $i] :
( ( ! [SY4939: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV37 ) @ SV900 @ SY4939 )
= ( c_Lambda_OdB_OVar @ SV37 ) )
| ( SV37 = SY4939 )
| ( c_HOL_Oord__class_Oless @ SY4939 @ SV37 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3798,plain,
! [SV901: $i,SV38: $i] :
( ( ! [SY4940: $i,SY4941: $i,SY4942: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV38 @ SV901 @ tc_nat ) ) @ SY4940 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4941 @ SV901 @ tc_nat ) ) @ SY4942 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SY4940 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4941 @ SV38 @ tc_nat ) @ SV901 @ tc_nat ) ) @ SY4942 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV38 @ SY4941 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3799,plain,
! [SV902: $i,SV39: $i] :
( ( ! [SY4943: $i,SY4944: $i,SY4945: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV39 @ SV902 @ tc_nat ) ) @ SY4943 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4944 @ SV902 @ tc_nat ) ) @ SY4945 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SY4944 @ tc_nat ) @ SV902 @ tc_nat ) ) @ SY4943 ) @ SY4945 @ tc_nat ) )
| ~ ( c_lessequals @ SY4944 @ SV39 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3800,plain,
! [SV903: $i,SV40: $i] :
( ( ! [SY4946: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV40 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ ( c_HOL_Ominus__class_Ominus @ SV903 @ SY4946 @ SV40 ) ) @ SY4946 )
= SV903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3801,plain,
! [SV904: $i,SV41: $i] :
( ( ! [SY4947: $i] :
( ~ ( hBOOL @ ( hAPP @ SV41 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV904 ) @ SY4947 ) @ SV904 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV41 @ SY4947 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3802,plain,
! [SV905: $i,SV42: $i] :
( ( ! [SY4948: $i] :
( ~ ( hBOOL @ ( hAPP @ SV42 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV905 ) @ SY4948 ) @ SV905 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV42 @ SY4948 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3803,plain,
! [SV906: $i,SV43: $i] :
( ( ! [SY4949: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV43 @ SV906 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4949 @ SV906 @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV906 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3804,plain,
! [SV907: $i,SV44: $i] :
( ( ! [SY4950: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV44 @ SV907 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV44 @ SY4950 @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV44 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(3805,plain,
! [SV908: $i,SV45: $i] :
( ( ! [SY4951: $i,SY4952: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV45 )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV908 @ SY4951 @ SV45 ) @ SY4952 @ SV45 )
= ( c_Power_Opower__class_Opower @ SV908 @ ( c_HOL_Otimes__class_Otimes @ SY4951 @ SY4952 @ tc_nat ) @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2939]) ).
thf(3806,plain,
! [SV909: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ SV46 @ SV909 ) )
| ~ ( hBOOL @ ( hAPP @ SV46 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ SV46 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV46 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3807,plain,
! [SV910: $i,SV47: $i] :
( ( ! [SY4953: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV47 )
| ( ( c_Power_Opower__class_Opower @ SV910 @ ( c_Suc @ SY4953 ) @ SV47 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV910 @ SY4953 @ SV47 ) @ SV910 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3808,plain,
! [SV911: $i,SV48: $i] :
( ( ! [SY4954: $i] :
( ~ ( class_Power_Opower @ SV48 )
| ( ( c_Power_Opower__class_Opower @ SV911 @ ( c_Suc @ SY4954 ) @ SV48 )
= ( c_HOL_Otimes__class_Otimes @ SV911 @ ( c_Power_Opower__class_Opower @ SV911 @ SY4954 @ SV48 ) @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3809,plain,
! [SV912: $i,SV49: $i] :
( ( ! [SY4955: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
| ( ( c_Power_Opower__class_Opower @ SV912 @ ( c_Suc @ SY4955 ) @ SV49 )
= ( c_HOL_Otimes__class_Otimes @ SV912 @ ( c_Power_Opower__class_Opower @ SV912 @ SY4955 @ SV49 ) @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3810,plain,
! [SV913: $i,SV50: $i] :
( ( ! [SY4956: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
| ( ( c_Power_Opower__class_Opower @ SV913 @ ( c_Suc @ SY4956 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ SV913 @ ( c_Power_Opower__class_Opower @ SV913 @ SY4956 @ SV50 ) @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3811,plain,
! [SV914: $i,SV51: $i] :
( ( ! [SY4957: $i,SY4958: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV914 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4957 ) @ SY4958 ) @ tc_nat )
| ~ ( c_lessequals @ SV914 @ SY4958 @ tc_nat )
| ~ ( c_lessequals @ SV51 @ SY4957 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3812,plain,
! [SV915: $i,SV52: $i] :
( ( ! [SY4959: $i,SY4960: $i,SY4961: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV52 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV915 ) @ SY4959 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SY4960 ) @ SY4961 ) @ SV52 )
| ~ ( c_lessequals @ SY4959 @ SY4961 @ SV52 )
| ~ ( c_lessequals @ SV915 @ SY4960 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3813,plain,
! [SV916: $i,SV53: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV53 @ ( c_Suc @ SV916 ) @ tc_nat )
| ~ ( c_lessequals @ SV53 @ SV916 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3814,plain,
! [SV917: $i,SV54: $i] :
( ( ( c_lessequals @ SV54 @ SV917 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ ( c_Suc @ SV917 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2948]) ).
thf(3815,plain,
! [SV55: $i] :
( ( ( ~ ( c_lessequals @ SV55 @ SV55 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV55 @ ( c_Suc @ SV55 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2949]) ).
thf(3816,plain,
! [SV918: $i,SV56: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV56 )
| ( ( c_List_Olistsum @ SV918 @ SV56 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ ( c_HOL_Ozero__class_Ozero @ SV56 ) @ SV918 @ SV56 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2950]) ).
thf(3817,plain,
! [SV919: $i,SV57: $i] :
( ( ! [SY4962: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV57 )
| ( ( c_HOL_Otimes__class_Otimes @ SV919 @ SY4962 @ SV57 )
= ( c_HOL_Otimes__class_Otimes @ SY4962 @ SV919 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3818,plain,
! [SV920: $i,SV58: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV58 @ SV920 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV920 @ SV58 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3819,plain,
! [SV59: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV59 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) )
= ( c_HOL_Ozero__class_Ozero @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2953]) ).
thf(3820,plain,
! [SV921: $i,SV60: $i] :
( ( ! [SY4963: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV60 )
| ( ( c_HOL_Otimes__class_Otimes @ SV921 @ SY4963 @ SV60 )
= ( c_HOL_Otimes__class_Otimes @ SY4963 @ SV921 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3821,plain,
! [SV922: $i,SV61: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV61 @ SV922 @ tc_nat ) @ ( c_Suc @ SV61 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3822,plain,
! [SV923: $i,SV62: $i] :
( ( ! [SY4964: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV62 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV923 ) @ SY4964 ) @ SV62 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SY4964 @ SV62 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV923 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3823,plain,
! [SV924: $i,SV63: $i] :
( ( ! [SY4965: $i,SY4966: $i] :
( ~ ( class_Orderings_Opreorder @ SV63 )
| ( c_HOL_Oord__class_Oless @ SV924 @ SY4965 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SY4966 @ SY4965 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ SY4966 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3824,plain,
! [SV925: $i,SV64: $i] :
( ( ! [SY4967: $i,SY4968: $i] :
( ~ ( class_Orderings_Oorder @ SV64 )
| ( c_HOL_Oord__class_Oless @ SV925 @ SY4967 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV925 @ SY4968 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SY4968 @ SY4967 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3825,plain,
! [SV926: $i,SV65: $i] :
( ( ! [SY4969: $i,SY4970: $i] :
( ( c_Type_Otyping @ SV65 @ SV926 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY4969 @ SV65 @ SY4970 @ SV926 ) )
| ~ ( c_Type_Otyping @ SV65 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4970 ) @ SV926 ) @ SY4969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3826,plain,
! [SV927: $i,SV66: $i] :
( ( ! [SY4971: $i] :
( ~ ( class_Orderings_Olinorder @ SV66 )
| ( ( c_Orderings_Oord__class_Omax @ SV927 @ SY4971 @ SV66 )
= SY4971 )
| ~ ( c_lessequals @ SV927 @ SY4971 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3827,plain,
! [SV928: $i,SV67: $i] :
( ( ! [SY4972: $i] :
( ~ ( class_Orderings_Olinorder @ SV67 )
| ( ( c_Orderings_Oord__class_Omax @ SV928 @ SY4972 @ SV67 )
= SV928 )
| ~ ( c_lessequals @ SY4972 @ SV928 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2961]) ).
thf(3828,plain,
! [SV929: $i,SV68: $i] :
( ( ! [SY4973: $i,SY4974: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV929 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SY4973 ) @ SY4974 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV929 ) @ SY4973 ) ) @ SY4974 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2962]) ).
thf(3829,plain,
! [SV930: $i,SV69: $i] :
( ( ! [SY4975: $i,SY4976: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV69 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV930 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SY4975 ) @ SY4976 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SY4975 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV930 ) @ SY4976 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3830,plain,
! [SV931: $i,SV70: $i] :
( ( ! [SY4977: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV70 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV931 ) @ SY4977 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV931 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV70 ) @ SY4977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2964]) ).
thf(3831,plain,
! [SV932: $i,SV71: $i] :
( ( ! [SY4978: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV71 ) @ SV932 ) ) @ SY4978 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV932 ) @ SY4978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3832,plain,
! [SV933: $i,SV72: $i] :
( ( ! [SY4979: $i] :
( ( hBOOL @ ( hAPP @ SV72 @ SV933 ) )
| ( hBOOL @ ( hAPP @ SV72 @ SY4979 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4979 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV72 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV72 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2966]) ).
thf(3833,plain,
! [SV934: $i,SV73: $i] :
( ( c_HOL_Oord__class_Oless @ SV73 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV73 ) @ SV934 ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2967]) ).
thf(3834,plain,
! [SV935: $i,SV74: $i] :
( ( c_HOL_Oord__class_Oless @ SV74 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV935 ) @ SV74 ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2968]) ).
thf(3835,plain,
! [SV936: $i,SV75: $i] :
( ( c_HOL_Oord__class_Oless @ SV75 @ ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV75 ) @ SV936 ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(3836,plain,
! [SV937: $i,SV76: $i] :
( ( ! [SY4980: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV76 ) @ SV937 ) @ SY4980 @ tc_nat )
| ~ ( c_lessequals @ SV76 @ ( c_HOL_Ominus__class_Ominus @ SY4980 @ SV937 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV937 @ SY4980 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3837,plain,
! [SV938: $i,SV77: $i] :
( ( ! [SY4981: $i] :
( ( c_lessequals @ SV77 @ ( c_HOL_Ominus__class_Ominus @ SV938 @ SY4981 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV77 ) @ SY4981 ) @ SV938 @ tc_nat )
| ~ ( c_lessequals @ SY4981 @ SV938 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3838,plain,
! [SV939: $i,SV78: $i] :
( ( ! [SY4982: $i,SY4983: $i] :
( ~ ( class_Orderings_Olinorder @ SV78 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV939 @ SY4982 @ SV78 ) @ SY4983 @ SV78 )
| ~ ( c_lessequals @ SY4982 @ SY4983 @ SV78 )
| ~ ( c_lessequals @ SV939 @ SY4983 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3839,plain,
! [SV940: $i,SV79: $i] :
( ( ! [SY4984: $i,SY4985: $i] :
( ~ ( class_Orderings_Olinorder @ SV79 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV940 @ SY4984 @ SV79 ) @ SY4985 @ SV79 )
| ~ ( c_lessequals @ SY4984 @ SY4985 @ SV79 )
| ~ ( c_lessequals @ SV940 @ SY4985 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2973]) ).
thf(3840,plain,
! [SV941: $i,SV80: $i] :
( ( ! [SY4986: $i,SY4987: $i] :
( ~ ( class_Orderings_Olinorder @ SV80 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV941 @ SY4986 @ SV80 ) @ SY4987 @ SV80 )
| ~ ( c_lessequals @ SY4986 @ SY4987 @ SV80 )
| ~ ( c_lessequals @ SV941 @ SY4987 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2974]) ).
thf(3841,plain,
! [SV942: $i,SV81: $i] :
( ( ! [SY4988: $i] :
( ~ ( class_Orderings_Olinorder @ SV81 )
| ( c_lessequals @ SV942 @ ( c_Orderings_Oord__class_Omax @ SV942 @ SY4988 @ SV81 ) @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3842,plain,
! [SV943: $i,SV82: $i] :
( ( ! [SY4989: $i] :
( ~ ( class_Orderings_Olinorder @ SV82 )
| ( c_lessequals @ SV943 @ ( c_Orderings_Oord__class_Omax @ SY4989 @ SV943 @ SV82 ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2976]) ).
thf(3843,plain,
! [SV944: $i,SV83: $i] :
( ( ( c_List_Oappend @ SV83 @ ( c_List_Olist_ONil @ SV944 ) @ SV944 )
= SV83 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3844,plain,
! [SV945: $i,SV84: $i] :
( ( SV84
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV945 ) @ SV84 @ SV945 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3845,plain,
! [SV946: $i,SV85: $i] :
( ( SV85
= ( c_List_Oappend @ SV85 @ ( c_List_Olist_ONil @ SV946 ) @ SV946 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3846,plain,
! [SV947: $i,SV86: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV86 ) @ SV947 @ SV86 )
= SV947 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2980]) ).
thf(3847,plain,
! [SV948: $i,SV87: $i] :
( ( SV87
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV948 ) @ SV87 @ SV948 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3848,plain,
! [SV949: $i,SV88: $i] :
( ( ~ ( class_Orderings_Obot @ SV88 )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV88 ) @ SV949 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3849,plain,
! [SV950: $i,SV89: $i] :
( ( ! [SY4990: $i,SY4991: $i] :
( ( c_Nat_Onat_Onat__rec @ SV89 @ SV950 @ ( c_Suc @ SY4990 ) @ SY4991 )
= ( hAPP @ ( hAPP @ SV950 @ SY4990 ) @ ( c_Nat_Onat_Onat__rec @ SV89 @ SV950 @ SY4990 @ SY4991 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2983]) ).
thf(3850,plain,
! [SV951: $i,SV90: $i] :
( ( ! [SY4992: $i,SY4993: $i,SY4994: $i,SY4995: $i,SY4996: $i,SY4997: $i,SY4998: $i] :
( ( ( hAPP @ ( hAPP @ SV90 @ ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ SY4992 ) ) @ SY4993 )
= ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ ( c_HOL_Otimes__class_Otimes @ SY4992 @ SY4993 @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4994 @ SY4995 @ SV90 @ SY4996 @ SY4997 @ SY4998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3851,plain,
! [SV952: $i,SV91: $i] :
( ( ! [SY4999: $i,SY5000: $i] :
( ~ ( class_Orderings_Olinorder @ SV91 )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV952 @ SY4999 @ SV91 ) @ SY5000 @ SV91 )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV952 @ SY5000 @ SV91 ) @ ( c_Orderings_Oord__class_Omin @ SY4999 @ SY5000 @ SV91 ) @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3852,plain,
! [SV953: $i,SV92: $i] :
( ( ! [SY5001: $i,SY5002: $i] :
( ~ ( class_Orderings_Olinorder @ SV92 )
| ( ( c_Orderings_Oord__class_Omin @ SV953 @ ( c_Orderings_Oord__class_Omax @ SY5001 @ SY5002 @ SV92 ) @ SV92 )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV953 @ SY5001 @ SV92 ) @ ( c_Orderings_Oord__class_Omin @ SV953 @ SY5002 @ SV92 ) @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2986]) ).
thf(3853,plain,
! [SV954: $i,SV93: $i] :
( ( ! [SY5003: $i,SY5004: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV93 )
| ( c_lessequals @ SV954 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SY5003 ) @ SY5004 ) @ SV93 )
| ~ ( c_lessequals @ SV954 @ SY5004 @ SV93 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SY5003 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3854,plain,
! [SV955: $i,SV94: $i] :
( ( ! [SY5005: $i,SY5006: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV94 )
| ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SY5005 ) @ SY5006 ) @ SV94 )
| ~ ( c_lessequals @ SV955 @ SY5005 @ SV94 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SY5006 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(3855,plain,
! [SV956: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ SV95 @ SV956 ) )
| ~ ( hBOOL @ ( hAPP @ SV95 @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV95 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2989]) ).
thf(3856,plain,
! [SV957: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ SV96 @ SV957 ) )
| ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ SV96 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3857,plain,
! [SV958: $i,SV97: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV97 ) @ SV958 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV97 @ SV958 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2991]) ).
thf(3858,plain,
! [SV959: $i,SV98: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV98 @ SV959 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV98 ) @ SV959 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3859,plain,
! [SV960: $i,SV99: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV99 ) @ SV960 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV99 @ SV960 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3860,plain,
! [SV961: $i,SV100: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV100 @ SV961 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV100 ) @ SV961 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2994]) ).
thf(3861,plain,
! [SV962: $i,SV101: $i] :
( ( ! [SY5007: $i] :
( ( c_HOL_Oord__class_Oless @ SV101 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV962 ) @ SY5007 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV101 @ SV962 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2995]) ).
thf(3862,plain,
! [SV963: $i,SV102: $i] :
( ( ! [SY5008: $i] :
( ( c_HOL_Oord__class_Oless @ SV102 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV963 ) @ SY5008 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV102 @ SY5008 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2996]) ).
thf(3863,plain,
! [SV964: $i,SV103: $i] :
( ( ! [SY5009: $i] :
( ( c_HOL_Oord__class_Oless @ SV103 @ SV964 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV103 ) @ SY5009 ) @ SV964 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2997]) ).
thf(3864,plain,
! [SV965: $i,SV104: $i] :
( ( ! [SY5010: $i] :
( ( c_HOL_Oord__class_Oless @ SV104 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV965 ) @ SY5010 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV104 @ SV965 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3865,plain,
! [SV966: $i,SV105: $i] :
( ( ! [SY5011: $i] :
( ( c_HOL_Oord__class_Oless @ SV105 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV966 ) @ SY5011 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV105 @ SY5011 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2999]) ).
thf(3866,plain,
! [SV967: $i,SV106: $i] :
( ( ! [SY5012: $i,SY5013: $i,SY5014: $i,SY5015: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV106 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV967 @ SY5012 @ SV106 ) ) @ SY5013 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SY5014 @ SY5012 @ SV106 ) ) @ SY5015 ) @ SV106 )
| ~ ( c_lessequals @ SY5013 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY5014 @ SV967 @ SV106 ) @ SY5012 @ SV106 ) ) @ SY5015 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3000]) ).
thf(3867,plain,
! [SV968: $i,SV107: $i] :
( ( ! [SY5016: $i,SY5017: $i,SY5018: $i,SY5019: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV107 )
| ( c_lessequals @ SV968 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY5016 @ SY5017 @ SV107 ) @ SY5018 @ SV107 ) ) @ SY5019 ) @ SV107 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SY5017 @ SY5018 @ SV107 ) ) @ SV968 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SY5016 @ SY5018 @ SV107 ) ) @ SY5019 ) @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3001]) ).
thf(3868,plain,
! [SV969: $i,SV108: $i] :
( ( ! [SY5020: $i,SY5021: $i,SY5022: $i,SY5023: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV108 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV969 @ SY5020 @ SV108 ) ) @ SY5021 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SY5022 @ SY5020 @ SV108 ) ) @ SY5023 ) @ SV108 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV969 @ SY5022 @ SV108 ) @ SY5020 @ SV108 ) ) @ SY5021 ) @ SY5023 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3002]) ).
thf(3869,plain,
! [SV970: $i,SV109: $i] :
( ( ! [SY5024: $i,SY5025: $i,SY5026: $i,SY5027: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV109 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV970 @ SY5024 @ SV109 ) @ SY5025 @ SV109 ) ) @ SY5026 ) @ SY5027 @ SV109 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV970 @ SY5025 @ SV109 ) ) @ SY5026 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SY5024 @ SY5025 @ SV109 ) ) @ SY5027 ) @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3870,plain,
! [SV971: $i,SV110: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV110 ) @ SV971 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV110 @ SV971 @ tc_nat ) ) )
| ~ ( c_lessequals @ SV971 @ SV110 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3004]) ).
thf(3871,plain,
! [SV972: $i,SV111: $i] :
( ( ! [SY5028: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV111 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ ( c_HOL_Otimes__class_Otimes @ SV972 @ SV972 @ SV111 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY5028 @ SY5028 @ SV111 ) ) @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3005]) ).
thf(3872,plain,
! [SV973: $i,SV112: $i] :
( ( ! [SY5029: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV112 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV973 ) @ SY5029 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SY5029 ) @ SV973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3006]) ).
thf(3873,plain,
! [SV974: $i,SV113: $i] :
( ( ! [SY5030: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV974 ) @ SY5030 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SY5030 ) @ SV974 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3007]) ).
thf(3874,plain,
! [SV975: $i,SV114: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV114 ) @ SV975 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV975 ) @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3008]) ).
thf(3875,plain,
! [SV976: $i,SV115: $i] :
( ( ! [SY5031: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV976 ) @ SY5031 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SY5031 ) @ SV976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3876,plain,
! [SV977: $i,SV116: $i] :
( ( ! [SY5032: $i,SY5033: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV116 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV977 ) @ SY5032 ) @ SY5033 @ SV116 @ SV116 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV977 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SY5032 @ SY5033 @ SV116 @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3010]) ).
thf(3877,plain,
! [SV978: $i,SV117: $i] :
( ( ! [SY5034: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV978 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SY5034 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY5034 @ SV117 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY5034 @ SV978 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3011]) ).
thf(3878,plain,
! [SV979: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ SV118 @ SV979 ) )
| ~ ( hBOOL @ ( hAPP @ SV118 @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ SV118 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV118 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3012]) ).
thf(3879,plain,
! [SV980: $i,SV119: $i] :
( ( ! [SY5035: $i,SY5036: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV980 @ SY5035 @ SV119 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SY5036 @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV980 @ SY5036 @ SV119 ) @ ( c_HOL_Otimes__class_Otimes @ SY5035 @ SY5036 @ SV119 ) @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3013]) ).
thf(3880,plain,
! [SV981: $i,SV120: $i] :
( ( ! [SY5037: $i,SY5038: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV981 @ SY5037 @ SV120 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SY5038 @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY5038 @ SV981 @ SV120 ) @ ( c_HOL_Otimes__class_Otimes @ SY5038 @ SY5037 @ SV120 ) @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3881,plain,
! [SV982: $i,SV121: $i] :
( ( ! [SY5039: $i,SY5040: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ SV121 )
| ( c_HOL_Oord__class_Oless @ SV982 @ SY5039 @ SV121 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SY5040 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV982 @ SY5040 @ SV121 ) @ ( c_HOL_Otimes__class_Otimes @ SY5039 @ SY5040 @ SV121 ) @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3015]) ).
thf(3882,plain,
! [SV983: $i,SV122: $i] :
( ( ! [SY5041: $i,SY5042: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ SV122 )
| ( c_HOL_Oord__class_Oless @ SV983 @ SY5041 @ SV122 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SY5042 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY5042 @ SV983 @ SV122 ) @ ( c_HOL_Otimes__class_Otimes @ SY5042 @ SY5041 @ SV122 ) @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3016]) ).
thf(3883,plain,
! [SV984: $i,SV123: $i] :
( ( ! [SY5043: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV123 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV984 @ SY5043 @ SV123 ) @ SV984 @ SV123 )
= ( c_HOL_Otimes__class_Otimes @ SV984 @ ( c_Power_Opower__class_Opower @ SV984 @ SY5043 @ SV123 ) @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3884,plain,
! [SV985: $i,SV124: $i] :
( ( ! [SY5044: $i,SY5045: $i] :
( ~ ( class_Orderings_Olinorder @ SV124 )
| ( c_lessequals @ SV985 @ SY5044 @ SV124 )
| ( c_lessequals @ SV985 @ SY5045 @ SV124 )
| ~ ( c_lessequals @ SV985 @ ( c_Orderings_Oord__class_Omax @ SY5045 @ SY5044 @ SV124 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3885,plain,
! [SV986: $i,SV125: $i] :
( ( ! [SY5046: $i,SY5047: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV986 @ SY5046 @ SV125 ) @ ( c_Power_Opower__class_Opower @ SV986 @ SY5047 @ SV125 ) @ SV125 )
= ( c_Power_Opower__class_Opower @ SV986 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5046 ) @ SY5047 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3019]) ).
thf(3886,plain,
! [SV987: $i,SV126: $i] :
( ( ( c_List_Odrop @ SV126 @ ( c_List_Olist_ONil @ SV987 ) @ SV987 )
= ( c_List_Olist_ONil @ SV987 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3020]) ).
thf(3887,plain,
! [SV988: $i,SV127: $i] :
( ( ( c_lessequals @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV127 @ SV988 ) @ SV988 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV127 @ SV988 ) )
| ( hBOOL @ ( hAPP @ SV127 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3888,plain,
! [SV989: $i,SV128: $i] :
( ( ! [SY5048: $i,SY5049: $i,SY5050: $i,SY5051: $i,SY5052: $i,SY5053: $i,SY5054: $i] :
( ( ( hAPP @ ( hAPP @ SV128 @ ( hAPP @ ( hAPP @ SV989 @ SY5048 ) @ SY5049 ) ) @ ( hAPP @ ( hAPP @ SV989 @ SY5048 ) @ SY5050 ) )
= ( hAPP @ ( hAPP @ SV989 @ SY5048 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5049 ) @ SY5050 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5051 @ SV128 @ SV989 @ SY5052 @ SY5053 @ SY5054 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3022]) ).
thf(3889,plain,
! [SV990: $i,SV129: $i] :
( ( ! [SY5055: $i,SY5056: $i] :
( ~ ( c_lessequals @ SV129 @ SV990 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SY5055 @ tc_nat ) ) @ SY5056 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV129 @ SY5055 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV990 @ SV129 @ tc_nat ) @ SY5055 @ tc_nat ) ) @ SY5056 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3890,plain,
! [SV991: $i,SV131: $i] :
( ( ! [SY5057: $i,SY5058: $i] :
( ~ ( class_Orderings_Olinorder @ SV131 )
| ( c_lessequals @ SV991 @ SY5057 @ SV131 )
| ~ ( c_lessequals @ SV991 @ ( c_Orderings_Oord__class_Omin @ SY5058 @ SY5057 @ SV131 ) @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3891,plain,
! [SV992: $i,SV132: $i] :
( ( ! [SY5059: $i,SY5060: $i] :
( ~ ( class_Orderings_Olinorder @ SV132 )
| ( c_lessequals @ SV992 @ SY5059 @ SV132 )
| ~ ( c_lessequals @ SV992 @ ( c_Orderings_Oord__class_Omin @ SY5059 @ SY5060 @ SV132 ) @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3892,plain,
! [SV993: $i,SV133: $i] :
( ( ! [SY5061: $i,SY5062: $i] :
( ~ ( class_Orderings_Olinorder @ SV133 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV993 @ SY5061 @ SV133 ) @ SY5062 @ SV133 )
| ~ ( c_lessequals @ SY5061 @ SY5062 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3893,plain,
! [SV994: $i,SV134: $i] :
( ( ! [SY5063: $i,SY5064: $i] :
( ~ ( class_Orderings_Olinorder @ SV134 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV994 @ SY5063 @ SV134 ) @ SY5064 @ SV134 )
| ~ ( c_lessequals @ SV994 @ SY5064 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3028]) ).
thf(3894,plain,
! [SV995: $i,SV135: $i] :
( ( ! [SY5065: $i,SY5066: $i] :
( ~ ( class_Orderings_Olinorder @ SV135 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV995 @ SY5065 @ SV135 ) @ SY5066 @ SV135 )
| ~ ( c_lessequals @ SY5065 @ SY5066 @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3895,plain,
! [SV996: $i,SV136: $i] :
( ( ! [SY5067: $i,SY5068: $i] :
( ~ ( class_Orderings_Olinorder @ SV136 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV996 @ SY5067 @ SV136 ) @ SY5068 @ SV136 )
| ~ ( c_lessequals @ SV996 @ SY5068 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3896,plain,
! [SV997: $i,SV137: $i] :
( ( ! [SY5069: $i,SY5070: $i] :
( ~ ( class_Orderings_Olinorder @ SV137 )
| ( c_lessequals @ SV997 @ SY5069 @ SV137 )
| ~ ( c_lessequals @ SV997 @ ( c_Orderings_Oord__class_Omin @ SY5070 @ SY5069 @ SV137 ) @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3897,plain,
! [SV998: $i,SV138: $i] :
( ( ! [SY5071: $i,SY5072: $i] :
( ~ ( class_Orderings_Olinorder @ SV138 )
| ( c_lessequals @ SV998 @ SY5071 @ SV138 )
| ~ ( c_lessequals @ SV998 @ ( c_Orderings_Oord__class_Omin @ SY5071 @ SY5072 @ SV138 ) @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3898,plain,
! [SV999: $i,SV139: $i] :
( ( ! [SY5073: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV139 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV999 @ SY5073 @ SV139 @ SV139 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SY5073 @ SV999 @ SV139 @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3899,plain,
! [SV1000: $i,SV140: $i] :
( ( ! [SY5074: $i,SY5075: $i,SY5076: $i,SY5077: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV140 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SY5074 @ SV140 ) ) @ SY5075 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SY5076 @ SY5074 @ SV140 ) ) @ SY5077 ) @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SY5075 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY5076 @ SV1000 @ SV140 ) @ SY5074 @ SV140 ) ) @ SY5077 ) @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3900,plain,
! [SV1001: $i,SV141: $i] :
( ( ! [SY5078: $i,SY5079: $i,SY5080: $i,SY5081: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV141 )
| ( c_HOL_Oord__class_Oless @ SV1001 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY5078 @ SY5079 @ SV141 ) @ SY5080 @ SV141 ) ) @ SY5081 ) @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SY5079 @ SY5080 @ SV141 ) ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SY5078 @ SY5080 @ SV141 ) ) @ SY5081 ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3035]) ).
thf(3901,plain,
! [SV1002: $i,SV142: $i] :
( ( ! [SY5082: $i,SY5083: $i,SY5084: $i,SY5085: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV142 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SY5082 @ SV142 ) ) @ SY5083 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SY5084 @ SY5082 @ SV142 ) ) @ SY5085 ) @ SV142 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1002 @ SY5084 @ SV142 ) @ SY5082 @ SV142 ) ) @ SY5083 ) @ SY5085 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3036]) ).
thf(3902,plain,
! [SV1003: $i,SV143: $i] :
( ( ! [SY5086: $i,SY5087: $i,SY5088: $i,SY5089: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV143 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1003 @ SY5086 @ SV143 ) @ SY5087 @ SV143 ) ) @ SY5088 ) @ SY5089 @ SV143 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1003 @ SY5087 @ SV143 ) ) @ SY5088 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SY5086 @ SY5087 @ SV143 ) ) @ SY5089 ) @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3037]) ).
thf(3903,plain,
! [SV1004: $i,SV144: $i] :
( ( ! [SY5090: $i,SY5091: $i] :
( ~ ( class_Orderings_Olinorder @ SV144 )
| ( c_lessequals @ SV1004 @ SY5090 @ SV144 )
| ( c_lessequals @ SY5091 @ SY5090 @ SV144 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY5091 @ SV1004 @ SV144 ) @ SY5090 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3904,plain,
! [SV1005: $i,SV145: $i] :
( ( ! [SY5092: $i,SY5093: $i] :
( ~ ( c_lessequals @ SV145 @ SV1005 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV145 @ SY5092 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1005 @ SV145 @ tc_nat ) @ SY5092 @ tc_nat ) ) @ SY5093 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1005 @ SY5092 @ tc_nat ) ) @ SY5093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3905,plain,
! [SV1006: $i,SV146: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV146 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV1006 ) @ SV1006 ) @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3906,plain,
! [SV1007: $i,SV147: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV147 )
| ( c_HOL_Oord__class_Oless @ SV1007 @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1007 ) @ SV1007 ) @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3907,plain,
! [SV1008: $i,SV148: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV148 )
| ( c_HOL_Oord__class_Oless @ SV1008 @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV1008 ) @ SV1008 ) @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3908,plain,
! [SV1009: $i,SV149: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV149 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV1009 ) @ SV1009 ) @ ( c_HOL_Ozero__class_Ozero @ SV149 ) @ SV149 )
| ~ ( c_HOL_Oord__class_Oless @ SV1009 @ ( c_HOL_Ozero__class_Ozero @ SV149 ) @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3043]) ).
thf(3909,plain,
! [SV1010: $i,SV150: $i] :
( ( ! [SY5094: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV150 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1010 @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SY5094 @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ ( c_HOL_Otimes__class_Otimes @ SV1010 @ SY5094 @ SV150 ) @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3044]) ).
thf(3910,plain,
! [SV1011: $i,SV151: $i] :
( ( ! [SY5095: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV151 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1011 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SY5095 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ ( c_HOL_Otimes__class_Otimes @ SY5095 @ SV1011 @ SV151 ) @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3045]) ).
thf(3911,plain,
! [SV1012: $i,SV152: $i] :
( ( ! [SY5096: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV152 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SY5096 @ SV152 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SY5096 @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1012 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3912,plain,
! [SV1013: $i,SV153: $i] :
( ( ! [SY5097: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV153 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV1013 @ SY5097 @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SY5097 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1013 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3047]) ).
thf(3913,plain,
! [SV1014: $i,SV154: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV154 @ SV1014 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1014 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV154 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3914,plain,
! [SV1015: $i,SV155: $i] :
( ( ! [SY5098: $i,SY5099: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV155 )
| ( c_HOL_Oord__class_Oless @ SV1015 @ SY5098 @ SV155 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SY5098 @ SV155 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1015 @ SY5099 @ SV155 ) @ ( c_Power_Opower__class_Opower @ SY5098 @ SY5099 @ SV155 ) @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3049]) ).
thf(3915,plain,
! [SV1016: $i,SV156: $i] :
( ( ! [SY5100: $i,SY5101: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV156 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1016 ) @ SY5100 ) ) @ SY5101 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SY5100 ) @ SY5101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3050]) ).
thf(3916,plain,
! [SV1017: $i,SV157: $i] :
( ( ! [SY5102: $i,SY5103: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1017 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY5102 ) @ SY5103 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SY5102 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1017 ) @ SY5103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3051]) ).
thf(3917,plain,
! [SV1018: $i,SV158: $i] :
( ( ! [SY5104: $i,SY5105: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV158 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1018 ) @ SY5104 ) ) @ SY5105 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1018 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SY5104 ) @ SY5105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3052]) ).
thf(3918,plain,
! [SV1019: $i,SV159: $i] :
( ( ! [SY5106: $i,SY5107: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV159 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1019 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SY5106 ) @ SY5107 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1019 ) @ SY5106 ) ) @ SY5107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3053]) ).
thf(3919,plain,
! [SV1020: $i,SV160: $i] :
( ( ! [SY5108: $i,SY5109: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV160 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV1020 ) @ SY5108 ) ) @ SY5109 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV1020 ) @ SY5109 ) ) @ SY5108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3054]) ).
thf(3920,plain,
! [SV1021: $i,SV161: $i] :
( ( ! [SY5110: $i,SY5111: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV161 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1021 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SY5110 ) @ SY5111 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SY5110 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1021 ) @ SY5111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3055]) ).
thf(3921,plain,
! [SV1022: $i,SV162: $i] :
( ( ! [SY5112: $i,SY5113: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1022 ) @ SY5112 ) ) @ SY5113 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1022 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SY5112 ) @ SY5113 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(3922,plain,
! [SV1023: $i,SV163: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV163 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1023 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1023 ) @ SV163 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(3923,plain,
! [SV1024: $i,SV164: $i] :
( ( ! [SY5114: $i,SY5115: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV164 )
| ( ( c_Power_Opower__class_Opower @ SV1024 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5114 ) @ SY5115 ) @ SV164 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1024 @ SY5114 @ SV164 ) @ ( c_Power_Opower__class_Opower @ SV1024 @ SY5115 @ SV164 ) @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3924,plain,
! [SV1025: $i,SV165: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV165 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1025 @ SV165 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3925,plain,
! [SV1026: $i,SV166: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV166 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV166 @ SV1026 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3060]) ).
thf(3926,plain,
! [SV1027: $i,SV167: $i] :
( ( ! [SY5116: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV167 @ SV1027 @ SY5116 ) @ SY5116 )
= ( c_List_Olist_OCons @ SV167 @ SV1027 @ SY5116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3927,plain,
! [SV1028: $i,SV168: $i] :
( ( ! [SY5117: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ SV168 ) @ SV1028 @ SY5117 )
= ( c_List_Olist_OCons @ SV1028 @ ( c_List_Oreplicate @ SV168 @ SV1028 @ SY5117 ) @ SY5117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3062]) ).
thf(3928,plain,
! [SV1029: $i,SV169: $i] :
( ( ! [SY5118: $i] :
( ( c_lessequals @ SV169 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1029 ) @ SY5118 ) @ tc_nat )
| ~ ( c_lessequals @ SV169 @ SY5118 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3063]) ).
thf(3929,plain,
! [SV1030: $i,SV170: $i] :
( ( ! [SY5119: $i] :
( ( c_lessequals @ SV170 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1030 ) @ SY5119 ) @ tc_nat )
| ~ ( c_lessequals @ SV170 @ SV1030 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3930,plain,
! [SV1031: $i,SV171: $i] :
( ( ! [SY5120: $i] :
( ( c_lessequals @ SV171 @ SV1031 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5120 ) @ SV171 ) @ SV1031 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3065]) ).
thf(3931,plain,
! [SV1032: $i,SV172: $i] :
( ( ! [SY5121: $i] :
( ( c_lessequals @ SV172 @ SV1032 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV172 ) @ SY5121 ) @ SV1032 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3066]) ).
thf(3932,plain,
! [SV1033: $i,SV173: $i] :
( ( ! [SY5122: $i] :
( ( c_lessequals @ SV173 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1033 ) @ SY5122 ) @ tc_nat )
| ~ ( c_lessequals @ SV173 @ SY5122 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3933,plain,
! [SV1034: $i,SV174: $i] :
( ( ! [SY5123: $i] :
( ( c_lessequals @ SV174 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1034 ) @ SY5123 ) @ tc_nat )
| ~ ( c_lessequals @ SV174 @ SV1034 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3934,plain,
! [SV1035: $i,SV175: $i] :
( ( ! [SY5124: $i] :
( ~ ( class_Orderings_Olinorder @ SV175 )
| ( ( c_Orderings_Oord__class_Omin @ SV1035 @ SY5124 @ SV175 )
= SV1035 )
| ~ ( c_lessequals @ SV1035 @ SY5124 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(3935,plain,
! [SV1036: $i,SV176: $i] :
( ( ! [SY5125: $i] :
( ~ ( class_Orderings_Olinorder @ SV176 )
| ( ( c_Orderings_Oord__class_Omin @ SV1036 @ SY5125 @ SV176 )
= SY5125 )
| ~ ( c_lessequals @ SY5125 @ SV1036 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3070]) ).
thf(3936,plain,
! [SV1037: $i,SV177: $i] :
( ( ! [SY5126: $i,SY5127: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV177 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ SV1037 @ SY5126 @ SV177 ) @ SY5127 @ SV177 )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ SV1037 @ SY5127 @ SV177 ) @ ( c_HOL_Ominus__class_Ominus @ SY5126 @ SY5127 @ SV177 ) @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3937,plain,
! [SV1038: $i,SV178: $i] :
( ( ! [SY5128: $i,SY5129: $i] :
( ( c_Type_Otypings @ SV178 @ SV1038 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY5128 @ SV178 @ SY5129 @ SV1038 ) )
| ~ ( c_Type_Otyping @ SV178 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY5129 @ SV1038 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY5128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3072]) ).
thf(3938,plain,
! [SV1039: $i,SV179: $i] :
( ( ! [SY5130: $i] :
( ~ ( class_Orderings_Olinorder @ SV179 )
| ( c_HOL_Oord__class_Oless @ SV1039 @ SY5130 @ SV179 )
| ( c_lessequals @ SY5130 @ SV1039 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3073]) ).
thf(3939,plain,
! [SV1040: $i,SV180: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV180 )
| ~ ( c_lessequals @ SV1040 @ SV1040 @ SV180 )
| ~ ( c_HOL_Oord__class_Oless @ SV1040 @ SV1040 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3940,plain,
! [SV1041: $i,SV181: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV181 )
| ( c_HOL_Oord__class_Oless @ SV1041 @ SV1041 @ SV181 )
| ( c_lessequals @ SV1041 @ SV1041 @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(3941,plain,
! [SV1042: $i,SV182: $i] :
( ( ! [SY5131: $i] :
( ~ ( class_Orderings_Olinorder @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SY5131 @ SV182 )
| ~ ( c_lessequals @ SY5131 @ SV1042 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3942,plain,
! [SV1043: $i,SV183: $i] :
( ( ! [SY5132: $i] :
( ~ ( class_Orderings_Olinorder @ SV183 )
| ( c_lessequals @ SV1043 @ SY5132 @ SV183 )
| ( c_HOL_Oord__class_Oless @ SY5132 @ SV1043 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3077]) ).
thf(3943,plain,
! [SV1044: $i,SV184: $i] :
( ( ! [SY5133: $i] :
( ~ ( class_Orderings_Olinorder @ SV184 )
| ~ ( c_lessequals @ SV1044 @ SY5133 @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ SY5133 @ SV1044 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3078]) ).
thf(3944,plain,
! [SV1045: $i,SV185: $i] :
( ( ! [SY5134: $i] :
( ~ ( class_Orderings_Olinorder @ SV185 )
| ( c_HOL_Oord__class_Oless @ SV1045 @ SY5134 @ SV185 )
| ( c_lessequals @ SY5134 @ SV1045 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3079]) ).
thf(3945,plain,
! [SV1046: $i,SV186: $i] :
( ( ! [SY5135: $i] :
( ~ ( class_Orderings_Opreorder @ SV186 )
| ~ ( c_lessequals @ SV1046 @ SY5135 @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SY5135 @ SV1046 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3080]) ).
thf(3946,plain,
! [SV1047: $i,SV187: $i] :
( ( ( hBOOL @ ( hAPP @ SV187 @ SV1047 ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV187 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV187 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3947,plain,
! [SV1048: $i,SV188: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV188 @ SV188 @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV188 ) @ SV1048 @ SV188 )
= SV1048 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3948,plain,
! [SV1049: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ SV189 @ SV1049 ) )
| ~ ( hBOOL @ ( hAPP @ SV189 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3949,plain,
! [SV1050: $i,SV190: $i] :
( ( ! [SY5136: $i,SY5137: $i] :
( ~ ( class_Orderings_Olinorder @ SV190 )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ SV1050 @ SY5136 @ SV190 ) @ SY5137 @ SV190 )
= ( c_Orderings_Oord__class_Omin @ SV1050 @ ( c_Orderings_Oord__class_Omin @ SY5136 @ SY5137 @ SV190 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3950,plain,
! [SV1051: $i,SV191: $i] :
( ( ! [SY5138: $i,SY5139: $i] :
( ~ ( class_Orderings_Olinorder @ SV191 )
| ( ( c_Orderings_Oord__class_Omin @ SV1051 @ ( c_Orderings_Oord__class_Omin @ SY5138 @ SY5139 @ SV191 ) @ SV191 )
= ( c_Orderings_Oord__class_Omin @ SY5138 @ ( c_Orderings_Oord__class_Omin @ SV1051 @ SY5139 @ SV191 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3951,plain,
! [SV1052: $i,SV192: $i] :
( ( ! [SY5140: $i,SY5141: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV192 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV192 )
| ( c_HOL_Oord__class_Oless @ SV1052 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SY5140 ) @ SY5141 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SY5141 @ SV192 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SY5140 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3086]) ).
thf(3952,plain,
! [SV1053: $i,SV193: $i] :
( ( ! [SY5142: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV193 @ SV1053 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV193 @ SY5142 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY5142 @ SV1053 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3087]) ).
thf(3953,plain,
! [SV1054: $i,SV194: $i] :
( ( ! [SY5143: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV194 @ SV1054 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY5143 @ SV1054 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV194 @ SY5143 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3088]) ).
thf(3954,plain,
! [SV1055: $i,SV195: $i] :
( ( ! [SY5144: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV195 @ SV1055 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY5144 @ SV1055 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV195 @ SY5144 @ tc_nat )
| ~ ( c_lessequals @ SV1055 @ SY5144 @ tc_nat )
| ~ ( c_lessequals @ SV1055 @ SV195 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3955,plain,
! [SV1056: $i,SV196: $i] :
( ( ! [SY5145: $i] :
( ( c_lessequals @ SV196 @ SV1056 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV196 @ SY5145 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1056 @ SY5145 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY5145 @ SV1056 @ tc_nat )
| ~ ( c_lessequals @ SY5145 @ SV196 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3090]) ).
thf(3956,plain,
! [SV1057: $i,SV197: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV197 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV197 ) @ SV1057 ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3091]) ).
thf(3957,plain,
! [SV1058: $i,SV198: $i] :
( ( ! [SY5146: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV198 @ SV1058 @ tc_nat ) @ SY5146 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV198 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1058 ) @ SY5146 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(3958,plain,
! [SV1059: $i,SV199: $i] :
( ( ! [SY5147: $i,SY5148: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV199 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1059 @ SY5147 @ SV199 ) @ ( c_Power_Opower__class_Opower @ SY5148 @ SY5147 @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV1059 @ SV199 )
| ~ ( c_lessequals @ SV1059 @ SY5148 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(3959,plain,
! [SV1060: $i,SV200: $i] :
( ( ! [SY5149: $i] :
( ~ ( class_Orderings_Olinorder @ SV200 )
| ( ( c_Orderings_Oord__class_Omin @ SV1060 @ ( c_Orderings_Oord__class_Omax @ SV1060 @ SY5149 @ SV200 ) @ SV200 )
= SV1060 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3960,plain,
! [SV1061: $i,SV201: $i] :
( ( ! [SY5150: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV201 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1061 @ SV201 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5150 @ SV201 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(3961,plain,
! [SV1062: $i,SV202: $i] :
( ( ! [SY5151: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV202 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV1062 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SY5151 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3962,plain,
! [SV1063: $i,SV203: $i] :
( ( ! [SY5152: $i,SY5153: $i,SY5154: $i,SY5155: $i] :
( ( c_List_Ofoldl @ SV203 @ SV1063 @ ( c_List_Olist_OCons @ SY5152 @ SY5153 @ SY5154 ) @ SY5155 @ SY5154 )
= ( c_List_Ofoldl @ SV203 @ ( hAPP @ ( hAPP @ SV203 @ SV1063 ) @ SY5152 ) @ SY5153 @ SY5155 @ SY5154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3097]) ).
thf(3963,plain,
! [SV1064: $i,SV204: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_Suc @ SV204 ) ) @ SV1064 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV204 ) @ ( c_Suc @ SV1064 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3964,plain,
! [SV1065: $i,SV205: $i] :
( ( ! [SY5156: $i,SY5157: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV205 ) @ ( c_List_Olist_OCons @ SV1065 @ SY5156 @ SY5157 ) @ SY5157 )
= ( c_List_Odrop @ SV205 @ SY5156 @ SY5157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3099]) ).
thf(3965,plain,
! [SV1066: $i,SV206: $i] :
( ( ! [SY5158: $i] :
( ( c_lessequals @ SV206 @ SV1066 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5158 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV206 @ SY5158 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1066 @ SY5158 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3100]) ).
thf(3966,plain,
! [SV1067: $i,SV207: $i] :
( ( ! [SY5159: $i] :
( ( c_lessequals @ SV207 @ SV1067 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5159 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY5159 @ SV207 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5159 @ SV1067 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3101]) ).
thf(3967,plain,
! [SV1068: $i,SV208: $i] :
( ( ! [SY5160: $i] :
( ( c_lessequals @ SV208 @ SV1068 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY5160 @ SV208 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5160 @ SV1068 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5160 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(3968,plain,
! [SV1069: $i,SV209: $i] :
( ( ! [SY5161: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SV1069 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SY5161 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1069 @ SY5161 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV209 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3969,plain,
! [SV1070: $i,SV210: $i] :
( ( ! [SY5162: $i,SY5163: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV210 )
| ( c_lessequals @ SV1070 @ SY5162 @ SV210 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY5163 @ SY5162 @ SV210 ) @ ( c_HOL_Otimes__class_Otimes @ SY5163 @ SV1070 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SY5163 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(3970,plain,
! [SV1071: $i,SV211: $i] :
( ( ! [SY5164: $i,SY5165: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV211 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SY5164 @ SV211 ) @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SY5165 @ SV211 ) @ SV211 )
| ~ ( c_lessequals @ SY5165 @ SY5164 @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3105]) ).
thf(3971,plain,
! [SV1072: $i,SV212: $i] :
( ( ! [SY5166: $i,SY5167: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV212 )
| ( c_lessequals @ SV1072 @ SY5166 @ SV212 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY5167 @ SV1072 @ SV212 ) @ ( c_HOL_Otimes__class_Otimes @ SY5167 @ SY5166 @ SV212 ) @ SV212 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SY5167 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3106]) ).
thf(3972,plain,
! [SV1073: $i,SV213: $i] :
( ( ! [SY5168: $i,SY5169: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV213 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SY5168 @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SY5169 @ SV213 ) @ SV213 )
| ~ ( c_lessequals @ SY5168 @ SY5169 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV1073 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3973,plain,
! [SV1074: $i,SV214: $i] :
( ( ! [SY5170: $i,SY5171: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV214 )
| ( c_lessequals @ SV1074 @ SY5170 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SY5171 @ SV214 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY5171 @ SV1074 @ SV214 ) @ ( c_HOL_Otimes__class_Otimes @ SY5171 @ SY5170 @ SV214 ) @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3108]) ).
thf(3974,plain,
! [SV1075: $i,SV215: $i] :
( ( ! [SY5172: $i,SY5173: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV215 )
| ( c_lessequals @ SV1075 @ SY5172 @ SV215 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SY5173 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1075 @ SY5173 @ SV215 ) @ ( c_HOL_Otimes__class_Otimes @ SY5172 @ SY5173 @ SV215 ) @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3109]) ).
thf(3975,plain,
! [SV1076: $i,SV216: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV216 @ SV1076 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV216 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1076 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3110]) ).
thf(3976,plain,
! [SV1077: $i,SV217: $i] :
( ( ! [SY5174: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV217 ) @ SV1077 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5174 ) @ SV1077 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV217 @ SY5174 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3977,plain,
! [SV1078: $i,SV218: $i] :
( ( ! [SY5175: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV218 ) @ SV1078 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV218 ) @ SY5175 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1078 @ SY5175 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3978,plain,
! [SV1079: $i,SV221: $i] :
( ( ! [SY5176: $i,SY5177: $i] :
( ~ ( class_Orderings_Olinorder @ SV221 )
| ( c_HOL_Oord__class_Oless @ SV1079 @ ( c_Orderings_Oord__class_Omax @ SY5176 @ SY5177 @ SV221 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SV1079 @ SY5176 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3115]) ).
thf(3979,plain,
! [SV1080: $i,SV222: $i] :
( ( ! [SY5178: $i,SY5179: $i] :
( ~ ( class_Orderings_Olinorder @ SV222 )
| ( c_HOL_Oord__class_Oless @ SV1080 @ ( c_Orderings_Oord__class_Omax @ SY5178 @ SY5179 @ SV222 ) @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ SV1080 @ SY5179 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3980,plain,
! [SV1081: $i,SV223: $i] :
( ( ! [SY5180: $i,SY5181: $i] :
( ~ ( class_Orderings_Olinorder @ SV223 )
| ( c_HOL_Oord__class_Oless @ SV1081 @ ( c_Orderings_Oord__class_Omax @ SY5180 @ SY5181 @ SV223 ) @ SV223 )
| ~ ( c_HOL_Oord__class_Oless @ SV1081 @ SY5180 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3981,plain,
! [SV1082: $i,SV224: $i] :
( ( ! [SY5182: $i,SY5183: $i] :
( ~ ( class_Orderings_Olinorder @ SV224 )
| ( c_HOL_Oord__class_Oless @ SV1082 @ ( c_Orderings_Oord__class_Omax @ SY5182 @ SY5183 @ SV224 ) @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ SV1082 @ SY5183 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3982,plain,
! [SV1083: $i,SV225: $i] :
( ( ! [SY5184: $i,SY5185: $i] :
( ~ ( class_Orderings_Olinorder @ SV225 )
| ( c_HOL_Oord__class_Oless @ SV1083 @ SY5184 @ SV225 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SY5185 @ SV225 ) @ SY5184 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3983,plain,
! [SV1084: $i,SV226: $i] :
( ( ! [SY5186: $i,SY5187: $i] :
( ~ ( class_Orderings_Olinorder @ SV226 )
| ( c_HOL_Oord__class_Oless @ SV1084 @ SY5186 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY5187 @ SV1084 @ SV226 ) @ SY5186 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3984,plain,
! [SV227: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV227 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV227 ) @ SV227 )
= ( c_HOL_Ozero__class_Ozero @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3121]) ).
thf(3985,plain,
! [SV1085: $i,SV228: $i] :
( ( ! [SY5188: $i] :
( ~ ( class_Orderings_Olinorder @ SV228 )
| ( ( c_Orderings_Oord__class_Omin @ SV1085 @ SY5188 @ SV228 )
= ( c_Orderings_Oord__class_Omin @ SY5188 @ SV1085 @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3122]) ).
thf(3986,plain,
! [SV1086: $i,SV229: $i] :
( ( ! [SY5189: $i,SY5190: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV229 @ SV1086 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5189 @ SV1086 @ tc_nat ) ) @ SY5190 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV229 ) @ SY5189 ) @ SV1086 @ tc_nat ) ) @ SY5190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(3987,plain,
! [SV1087: $i,SV230: $i] :
( ( ! [SY5191: $i,SY5192: $i,SY5193: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV230 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SV1087 @ SY5191 @ SV230 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SY5192 @ SY5191 @ SV230 ) ) @ SY5193 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ SV1087 ) @ SY5192 ) @ SY5191 @ SV230 ) ) @ SY5193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(3988,plain,
! [SV1088: $i,SV231: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV231 @ SV1088 @ tc_nat ) @ SV231 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3989,plain,
! [SV1089: $i,SV232: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV232 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV232 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3990,plain,
! [SV1090: $i,SV233: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV233 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV233 @ SV1090 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3127]) ).
thf(3991,plain,
! [SV1091: $i,SV234: $i] :
( ( ! [SY5194: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV1091 ) @ SY5194 ) @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SY5194 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV1091 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(3992,plain,
! [SV1092: $i,SV235: $i] :
( ( ! [SY5195: $i,SY5196: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV235 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1092 @ SY5195 @ SV235 ) @ ( c_Power_Opower__class_Opower @ SY5196 @ SY5195 @ SV235 ) @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5195 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV235 ) @ SV1092 @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SY5196 @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(3993,plain,
! [SV1093: $i,SV236: $i] :
( ( ! [SY5197: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV236 )
| ( SV1093
= ( c_HOL_Ozero__class_Ozero @ SV236 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ ( c_HOL_Otimes__class_Otimes @ SV1093 @ SV1093 @ SV236 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY5197 @ SY5197 @ SV236 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV236 ) @ SV236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3994,plain,
! [SV1094: $i,SV237: $i] :
( ( ! [SY5198: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV237 )
| ( SV1094
= ( c_HOL_Ozero__class_Ozero @ SV237 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( c_HOL_Otimes__class_Otimes @ SY5198 @ SY5198 @ SV237 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1094 @ SV1094 @ SV237 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV237 ) @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3131]) ).
thf(3995,plain,
! [SV1095: $i,SV238: $i] :
( ( ! [SY5199: $i,SY5200: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV238 @ SV1095 @ SY5199 ) @ SY5200 @ SY5199 )
= ( c_List_Olist_OCons @ SV238 @ ( c_List_Oappend @ SV1095 @ SY5200 @ SY5199 ) @ SY5199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3996,plain,
! [SV1096: $i,SV239: $i] :
( ( ! [SY5201: $i,SY5202: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV239 @ SV1096 @ SY5201 ) @ SY5202 @ SY5201 )
= ( c_List_Olist_OCons @ SV239 @ ( c_List_Oappend @ SV1096 @ SY5202 @ SY5201 ) @ SY5201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3133]) ).
thf(3997,plain,
! [SV1097: $i,SV240: $i] :
( ( ! [SY5203: $i,SY5204: $i] :
( ~ ( hBOOL @ ( hAPP @ SV240 @ ( c_Nat_Onat_Onat__case @ SV1097 @ SY5203 @ ( c_Suc @ SY5204 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV240 @ ( hAPP @ SY5203 @ SY5204 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3134]) ).
thf(3998,plain,
! [SV1098: $i,SV241: $i] :
( ( ! [SY5205: $i,SY5206: $i] :
( ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_Nat_Onat_Onat__case @ SV1098 @ SY5205 @ ( c_Suc @ SY5206 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV241 @ ( hAPP @ SY5205 @ SY5206 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3135]) ).
thf(3999,plain,
! [SV1099: $i,SV242: $i] :
( ( ! [SY5207: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV242 @ ( c_HOL_Ominus__class_Ominus @ SV1099 @ SY5207 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV242 @ SV1099 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV242 @ SY5207 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3136]) ).
thf(4000,plain,
! [SV1100: $i,SV243: $i] :
( ( ! [SY5208: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV243 @ SV1100 @ tc_nat ) @ SY5208 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV243 @ SY5208 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1100 @ SY5208 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3137]) ).
thf(4001,plain,
! [SV1101: $i,SV244: $i] :
( ( ! [SY5209: $i,SY5210: $i] :
( ~ ( class_Orderings_Olinorder @ SV244 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1101 @ SY5209 @ SV244 ) @ SY5210 @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ SV1101 @ SY5210 @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3138]) ).
thf(4002,plain,
! [SV1102: $i,SV245: $i] :
( ( ! [SY5211: $i,SY5212: $i] :
( ~ ( class_Orderings_Olinorder @ SV245 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1102 @ SY5211 @ SV245 ) @ SY5212 @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ SY5211 @ SY5212 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3139]) ).
thf(4003,plain,
! [SV1103: $i,SV246: $i] :
( ( ! [SY5213: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV246 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ SV1103 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ ( c_HOL_Ozero__class_Ozero @ SV246 ) @ SY5213 @ SV246 @ SV246 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ SV1103 @ SY5213 @ SV246 @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(4004,plain,
! [SV1104: $i,SV247: $i] :
( ( ! [SY5214: $i,SY5215: $i] :
( ~ ( class_Orderings_Olinorder @ SV247 )
| ( c_lessequals @ SV1104 @ SY5214 @ SV247 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY5215 @ SV1104 @ SV247 ) @ SY5214 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3141]) ).
thf(4005,plain,
! [SV1105: $i,SV248: $i] :
( ( ! [SY5216: $i,SY5217: $i] :
( ~ ( class_Orderings_Olinorder @ SV248 )
| ( c_lessequals @ SV1105 @ SY5216 @ SV248 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1105 @ SY5217 @ SV248 ) @ SY5216 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3142]) ).
thf(4006,plain,
! [SV1106: $i,SV249: $i] :
( ( ! [SY5218: $i,SY5219: $i] :
( ~ ( class_Orderings_Olinorder @ SV249 )
| ( c_lessequals @ SV1106 @ ( c_Orderings_Oord__class_Omax @ SY5218 @ SY5219 @ SV249 ) @ SV249 )
| ~ ( c_lessequals @ SV1106 @ SY5219 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(4007,plain,
! [SV1107: $i,SV250: $i] :
( ( ! [SY5220: $i,SY5221: $i] :
( ~ ( class_Orderings_Olinorder @ SV250 )
| ( c_lessequals @ SV1107 @ ( c_Orderings_Oord__class_Omax @ SY5220 @ SY5221 @ SV250 ) @ SV250 )
| ~ ( c_lessequals @ SV1107 @ SY5220 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(4008,plain,
! [SV1108: $i,SV251: $i] :
( ( ! [SY5222: $i,SY5223: $i] :
( ~ ( class_Orderings_Olinorder @ SV251 )
| ( c_lessequals @ SV1108 @ ( c_Orderings_Oord__class_Omax @ SY5222 @ SY5223 @ SV251 ) @ SV251 )
| ~ ( c_lessequals @ SV1108 @ SY5223 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(4009,plain,
! [SV1109: $i,SV252: $i] :
( ( ! [SY5224: $i,SY5225: $i] :
( ~ ( class_Orderings_Olinorder @ SV252 )
| ( c_lessequals @ SV1109 @ ( c_Orderings_Oord__class_Omax @ SY5224 @ SY5225 @ SV252 ) @ SV252 )
| ~ ( c_lessequals @ SV1109 @ SY5224 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3146]) ).
thf(4010,plain,
! [SV1110: $i,SV253: $i] :
( ( ! [SY5226: $i,SY5227: $i] :
( ~ ( class_Orderings_Olinorder @ SV253 )
| ( c_lessequals @ SV1110 @ SY5226 @ SV253 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY5227 @ SV1110 @ SV253 ) @ SY5226 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3147]) ).
thf(4011,plain,
! [SV1111: $i,SV254: $i] :
( ( ! [SY5228: $i,SY5229: $i] :
( ~ ( class_Orderings_Olinorder @ SV254 )
| ( c_lessequals @ SV1111 @ SY5228 @ SV254 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1111 @ SY5229 @ SV254 ) @ SY5228 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3148]) ).
thf(4012,plain,
! [SV1112: $i,SV255: $i] :
( ( ! [SY5230: $i] :
( ( c_lessequals @ SV255 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1112 ) @ SY5230 ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV255 @ SY5230 @ tc_nat ) @ SV1112 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(4013,plain,
! [SV1113: $i,SV256: $i] :
( ( ! [SY5231: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV256 @ SV1113 @ tc_nat ) @ SY5231 @ tc_nat )
| ~ ( c_lessequals @ SV256 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5231 ) @ SV1113 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(4014,plain,
! [SV1114: $i,SV257: $i] :
( ( ! [SY5232: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV257 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ ( c_Power_Opower__class_Opower @ SV1114 @ SY5232 @ SV257 ) @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV1114 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(4015,plain,
! [SV1115: $i,SV258: $i] :
( ( ! [SY5233: $i,SY5234: $i] :
( ~ ( class_Orderings_Olinorder @ SV258 )
| ( c_HOL_Oord__class_Oless @ SV1115 @ SY5233 @ SV258 )
| ( c_HOL_Oord__class_Oless @ SV1115 @ SY5234 @ SV258 )
| ~ ( c_HOL_Oord__class_Oless @ SV1115 @ ( c_Orderings_Oord__class_Omax @ SY5234 @ SY5233 @ SV258 ) @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(4016,plain,
! [SV1116: $i,SV259: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV259 @ ( c_Suc @ SV1116 ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV259 ) @ ( c_HOL_Otimes__class_Otimes @ SV259 @ SV1116 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(4017,plain,
! [SV1117: $i,SV260: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV260 ) @ SV1117 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1117 ) @ ( c_HOL_Otimes__class_Otimes @ SV260 @ SV1117 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3154]) ).
thf(4018,plain,
! [SV1118: $i,SV261: $i] :
( ( ! [SY5235: $i] :
( ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV261 ) ) @ SV1118 ) @ SY5235 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_InductTermi_OIT @ SV1118 )
| ~ ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV261 @ SV1118 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY5235 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(4019,plain,
! [SV1119: $i,SV262: $i] :
( ( ! [SY5236: $i,SY5237: $i] :
( ( c_List_Ofoldl @ SV262 @ SV1119 @ ( c_List_Olist_ONil @ SY5236 ) @ SY5237 @ SY5236 )
= SV1119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(4020,plain,
! [SV1120: $i,SV263: $i] :
( ( ! [SY5238: $i,SY5239: $i] :
( ( c_Nat_Onat_Onat__case @ SV263 @ SV1120 @ ( c_Suc @ SY5238 ) @ SY5239 )
= ( hAPP @ SV1120 @ SY5238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(4021,plain,
! [SV1121: $i,SV264: $i] :
( ( ! [SY5240: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV264 ) @ ( c_HOL_Otimes__class_Otimes @ SV1121 @ SV1121 @ SV264 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY5240 @ SY5240 @ SV264 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(4022,plain,
! [SV1122: $i,SV265: $i] :
( ( ! [SY5241: $i,SY5242: $i,SY5243: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV265 @ SV1122 @ tc_nat ) @ SY5241 @ tc_nat ) ) @ SY5242 ) @ SY5243 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV265 @ SY5241 @ tc_nat ) ) @ SY5242 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SY5241 @ tc_nat ) ) @ SY5243 ) @ tc_nat )
| ~ ( c_lessequals @ SV1122 @ SV265 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(4023,plain,
! [SV1123: $i,SV266: $i] :
( ( ! [SY5244: $i,SY5245: $i,SY5246: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV266 @ SV1123 @ tc_nat ) ) @ SY5244 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5245 @ SV1123 @ tc_nat ) ) @ SY5246 ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV266 @ SY5245 @ tc_nat ) @ SV1123 @ tc_nat ) ) @ SY5244 ) @ SY5246 @ tc_nat )
| ~ ( c_lessequals @ SY5245 @ SV266 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(4024,plain,
! [SV1124: $i,SV267: $i] :
( ( ! [SY5247: $i,SY5248: $i,SY5249: $i] :
( ( c_lessequals @ SV267 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1124 @ SY5247 @ tc_nat ) @ SY5248 @ tc_nat ) ) @ SY5249 ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5247 @ SY5248 @ tc_nat ) ) @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1124 @ SY5248 @ tc_nat ) ) @ SY5249 ) @ tc_nat )
| ~ ( c_lessequals @ SY5247 @ SV1124 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3161]) ).
thf(4025,plain,
! [SV1125: $i,SV268: $i] :
( ( ! [SY5250: $i,SY5251: $i,SY5252: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SV1125 @ tc_nat ) ) @ SY5250 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5251 @ SV1125 @ tc_nat ) ) @ SY5252 ) @ tc_nat )
| ~ ( c_lessequals @ SY5250 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY5251 @ SV268 @ tc_nat ) @ SV1125 @ tc_nat ) ) @ SY5252 ) @ tc_nat )
| ~ ( c_lessequals @ SV268 @ SY5251 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3162]) ).
thf(4026,plain,
! [SV1126: $i,SV269: $i] :
( ( ! [SY5253: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV269 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SV1126 @ SY5253 @ tc_nat ) @ SV269 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1126 @ SV269 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY5253 @ SV269 ) @ SV269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3163]) ).
thf(4027,plain,
! [SV1127: $i,SV270: $i] :
( ( ! [SY5254: $i,SY5255: $i] :
( ~ ( class_Orderings_Olinorder @ SV270 )
| ( c_HOL_Oord__class_Oless @ SV1127 @ SY5254 @ SV270 )
| ( c_HOL_Oord__class_Oless @ SY5255 @ SY5254 @ SV270 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY5255 @ SV1127 @ SV270 ) @ SY5254 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3164]) ).
thf(4028,plain,
! [SV1128: $i,SV271: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV271 ) @ ( c_Suc @ SV1128 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV271 @ SV1128 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3165]) ).
thf(4029,plain,
! [SV1129: $i,SV272: $i] :
( ( ! [SY5256: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV272 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1129 ) @ SY5256 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
| ~ ( c_HOL_Oord__class_Oless @ SY5256 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
| ~ ( c_lessequals @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3166]) ).
thf(4030,plain,
! [SV1130: $i,SV273: $i] :
( ( ! [SY5257: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV273 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV1130 ) @ SY5257 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
| ~ ( c_lessequals @ SY5257 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
| ~ ( c_HOL_Oord__class_Oless @ SV1130 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(4031,plain,
! [SV1131: $i,SV274: $i] :
( ( ( SV274 = SV1131 )
| ( c_HOL_Oord__class_Oless @ SV274 @ SV1131 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV274 @ ( c_Suc @ SV1131 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(4032,plain,
! [SV1132: $i,SV275: $i] :
( ( ( SV275 = SV1132 )
| ~ ( c_HOL_Oord__class_Oless @ SV1132 @ ( c_Suc @ SV275 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1132 @ SV275 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3169]) ).
thf(4033,plain,
! [SV1133: $i,SV276: $i] :
( ( ( SV276 = SV1133 )
| ~ ( c_HOL_Oord__class_Oless @ SV276 @ ( c_Suc @ SV1133 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV276 @ SV1133 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(4034,plain,
! [SV277: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV277 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ SV277 ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ SV277 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ SV277 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3171]) ).
thf(4035,plain,
! [SV1134: $i,SV278: $i] :
( ( ! [SY5258: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV278 ) @ SV1134 ) @ SY5258 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV278 ) @ ( c_HOL_Ominus__class_Ominus @ SV1134 @ SY5258 @ tc_nat ) ) )
| ~ ( c_lessequals @ SY5258 @ SV1134 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3172]) ).
thf(4036,plain,
! [SV1135: $i,SV279: $i] :
( ( ! [SY5259: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV279 ) @ SV1135 ) @ SY5259 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV279 @ SY5259 @ tc_nat ) ) @ SV1135 ) )
| ~ ( c_lessequals @ SY5259 @ SV279 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(4037,plain,
! [SV1136: $i,SV280: $i] :
( ( ! [SY5260: $i,SY5261: $i,SY5262: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV280 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1136 @ SY5260 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SY5261 @ SY5262 @ SV280 ) @ SV280 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1136 @ SY5261 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SY5260 @ SY5262 @ SV280 ) @ SV280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3174]) ).
thf(4038,plain,
! [SV1137: $i,SV281: $i] :
( ( ! [SY5263: $i,SY5264: $i,SY5265: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV281 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1137 @ SY5263 @ SV281 ) @ ( c_HOL_Otimes__class_Otimes @ SY5264 @ SY5265 @ SV281 ) @ SV281 )
= ( c_HOL_Otimes__class_Otimes @ SV1137 @ ( c_HOL_Otimes__class_Otimes @ SY5263 @ ( c_HOL_Otimes__class_Otimes @ SY5264 @ SY5265 @ SV281 ) @ SV281 ) @ SV281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(4039,plain,
! [SV1138: $i,SV282: $i] :
( ( ! [SY5266: $i,SY5267: $i,SY5268: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV282 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1138 @ SY5266 @ SV282 ) @ ( c_HOL_Otimes__class_Otimes @ SY5267 @ SY5268 @ SV282 ) @ SV282 )
= ( c_HOL_Otimes__class_Otimes @ SY5267 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1138 @ SY5266 @ SV282 ) @ SY5268 @ SV282 ) @ SV282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(4040,plain,
! [SV1139: $i,SV283: $i] :
( ( ! [SY5269: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_HOL_Ominus__class_Ominus @ SV1139 @ SY5269 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV283 ) @ SY5269 ) @ SV1139 @ tc_nat ) )
| ~ ( c_lessequals @ SY5269 @ SV1139 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3177]) ).
thf(4041,plain,
! [SV1140: $i,SV284: $i] :
( ( ! [SY5270: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV284 @ SV1140 @ tc_nat ) @ SY5270 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV284 @ SY5270 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(4042,plain,
! [SV1141: $i,SV285: $i] :
( ( ! [SY5271: $i,SY5272: $i] :
( ( c_Type_Otype_Otype__rec @ SV285 @ SV1141 @ ( c_Type_Otype_OAtom @ SY5271 ) @ SY5272 )
= ( hAPP @ SV285 @ SY5271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(4043,plain,
! [SV1142: $i,SV286: $i] :
( ( ! [SY5273: $i] :
( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV286 @ SV1142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY5273 @ SV1142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ SV286 @ SY5273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(4044,plain,
! [SV1143: $i,SV287: $i] :
( ( ( c_List_Olist_ONil @ SV287 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1143 @ SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(4045,plain,
! [SV1144: $i,SV288: $i] :
( ( ! [SY5274: $i] :
( ~ ( class_Orderings_Opreorder @ SV288 )
| ( c_HOL_Oord__class_Oless @ SV1144 @ SY5274 @ SV288 )
| ( c_lessequals @ SY5274 @ SV1144 @ SV288 )
| ~ ( c_lessequals @ SV1144 @ SY5274 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(4046,plain,
! [SV289: $i] :
( ( c_HOL_Oord__class_Oless @ SV289 @ SV289 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(4047,plain,
! [SV290: $i] :
( ( c_HOL_Oord__class_Oless @ SV290 @ SV290 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3184]) ).
thf(4048,plain,
! [SV1145: $i,SV291: $i] :
( ( ~ ( class_Orderings_Oorder @ SV291 )
| ~ ( c_HOL_Oord__class_Oless @ SV1145 @ SV1145 @ SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(4049,plain,
! [SV1146: $i,SV292: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV292 )
| ~ ( c_HOL_Oord__class_Oless @ SV1146 @ SV1146 @ SV292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(4050,plain,
! [SV1147: $i,SV293: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV293 )
| ~ ( c_HOL_Oord__class_Oless @ SV1147 @ SV1147 @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3187]) ).
thf(4051,plain,
! [SV1148: $i,SV294: $i] :
( ( ~ ( c_lessequals @ SV294 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1148 ) @ SV294 ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1148 ) @ SV294 ) @ SV294 @ tc_nat )
= SV1148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(4052,plain,
! [SV1149: $i,SV295: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV295 )
| ( ( c_Orderings_Oord__class_Omin @ SV1149 @ SV1149 @ SV295 )
= SV1149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3189]) ).
thf(4053,plain,
! [SV1150: $i,SV296: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV296 ) ) @ SV1150 ) @ ( c_Lambda_Osubst @ SV296 @ SV1150 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(4054,plain,
! [SV1151: $i,SV297: $i] :
( ( ! [SY5275: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV297 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV297 ) @ SV1151 ) @ SY5275 ) @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SY5275 @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1151 @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(4055,plain,
! [SV1152: $i,SV298: $i] :
( ( c_lessequals @ SV298 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV298 ) @ SV1152 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3192]) ).
thf(4056,plain,
! [SV1153: $i,SV299: $i] :
( ( c_lessequals @ SV299 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1153 ) @ SV299 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3193]) ).
thf(4057,plain,
! [SV1154: $i,SV300: $i] :
( ( c_lessequals @ SV300 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV300 ) @ SV1154 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3194]) ).
thf(4058,plain,
! [SV1155: $i,SV301: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV301 @ SV1155 @ tc_nat ) ) @ SV1155 )
= ( c_Orderings_Oord__class_Omax @ SV301 @ SV1155 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3195]) ).
thf(4059,plain,
! [SV1156: $i,SV302: $i] :
( ( ! [SY5276: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV302 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV1156 @ SY5276 @ SV302 ) @ SV302 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV302 ) @ SV1156 ) @ ( c_List_Olistsum @ SY5276 @ SV302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3196]) ).
thf(4060,plain,
! [SV1157: $i,SV303: $i] :
( ( ! [SY5277: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV1157 @ SY5277 @ SV303 )
| ( c_HOL_Oord__class_Oless @ SY5277 @ SV1157 @ SV303 )
| ( SY5277 = SV1157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3197]) ).
thf(4061,plain,
! [SV1158: $i,SV304: $i] :
( ( ! [SY5278: $i] :
( ~ ( class_Orderings_Olinorder @ SV304 )
| ( SV1158 = SY5278 )
| ( c_HOL_Oord__class_Oless @ SY5278 @ SV1158 @ SV304 )
| ( c_HOL_Oord__class_Oless @ SV1158 @ SY5278 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3198]) ).
thf(4062,plain,
! [SV1159: $i,SV305: $i] :
( ( ( SV305 = SV1159 )
| ~ ( c_lessequals @ SV1159 @ SV305 @ tc_nat )
| ~ ( c_lessequals @ SV305 @ SV1159 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(4063,plain,
! [SV1160: $i,SV306: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV306 @ SV1160 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1160 @ SV306 @ tc_nat )
| ( SV1160 = SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(4064,plain,
! [SV1161: $i,SV307: $i] :
( ( ! [SY5279: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV307 @ SV1161 ) @ SY5279 ) )
| ( c_HOL_Oord__class_Oless @ SV1161 @ SY5279 @ tc_nat )
| ( SY5279 = SV1161 )
| ( c_HOL_Oord__class_Oless @ SY5279 @ SV1161 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3201]) ).
thf(4065,plain,
! [SV1162: $i,SV308: $i] :
( ( ! [SY5280: $i,SY5281: $i,SY5282: $i] :
( ( SV308 = SV1162 )
| ~ ( c_Type_Otyping @ SY5280 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY5281 ) @ SY5282 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1162 )
| ~ ( c_Type_Otyping @ SY5280 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY5281 ) @ SY5282 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3202]) ).
thf(4066,plain,
! [SV1163: $i,SV309: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV309 @ SV1163 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1163 @ SV309 @ tc_nat )
| ( SV1163 = SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3203]) ).
thf(4067,plain,
! [SV1164: $i,SV310: $i] :
( ( ! [SY5283: $i] :
( ~ ( class_Orderings_Oorder @ SV310 )
| ( SV1164 = SY5283 )
| ~ ( c_lessequals @ SY5283 @ SV1164 @ SV310 )
| ~ ( c_lessequals @ SV1164 @ SY5283 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3204]) ).
thf(4068,plain,
! [SV1165: $i,SV311: $i] :
( ( ! [SY5284: $i] :
( ~ ( class_Orderings_Olinorder @ SV311 )
| ( c_HOL_Oord__class_Oless @ SV1165 @ SY5284 @ SV311 )
| ( c_HOL_Oord__class_Oless @ SY5284 @ SV1165 @ SV311 )
| ( SY5284 = SV1165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3205]) ).
thf(4069,plain,
! [SV1166: $i,SV312: $i] :
( ( ! [SY5285: $i] :
( ~ ( class_Orderings_Oorder @ SV312 )
| ( SV1166 = SY5285 )
| ~ ( c_lessequals @ SY5285 @ SV1166 @ SV312 )
| ~ ( c_lessequals @ SV1166 @ SY5285 @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(4070,plain,
! [SV1167: $i,SV313: $i] :
( ( ! [SY5286: $i] :
( ~ ( class_Orderings_Oorder @ SV313 )
| ( SV1167 = SY5286 )
| ~ ( c_lessequals @ SV1167 @ SY5286 @ SV313 )
| ~ ( c_lessequals @ SY5286 @ SV1167 @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(4071,plain,
! [SV1168: $i,SV314: $i] :
( ( ! [SY5287: $i,SY5288: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV314 @ SV1168 @ SY5287 ) @ ( c_List_Oreplicate @ SY5288 @ SV1168 @ SY5287 ) @ SY5287 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY5288 @ SV1168 @ SY5287 ) @ ( c_List_Oreplicate @ SV314 @ SV1168 @ SY5287 ) @ SY5287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(4072,plain,
! [SV1169: $i,SV315: $i] :
( ( ! [SY5289: $i] :
( ~ ( class_Orderings_Olinorder @ SV315 )
| ( c_HOL_Oord__class_Oless @ SV1169 @ SY5289 @ SV315 )
| ( SY5289 = SV1169 )
| ( c_HOL_Oord__class_Oless @ SY5289 @ SV1169 @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(4073,plain,
! [SV1170: $i,SV316: $i] :
( ( ! [SY5290: $i] :
( ~ ( class_Orderings_Olinorder @ SV316 )
| ( SV1170 = SY5290 )
| ( c_HOL_Oord__class_Oless @ SV1170 @ SY5290 @ SV316 )
| ( c_HOL_Oord__class_Oless @ SY5290 @ SV1170 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3210]) ).
thf(4074,plain,
! [SV1171: $i,SV317: $i] :
( ( ! [SY5291: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV317 )
| ( c_lessequals @ SV1171 @ SY5291 @ SV317 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1171 @ SY5291 @ SV317 ) @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(4075,plain,
! [SV1172: $i,SV318: $i] :
( ( ! [SY5292: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV318 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1172 @ SY5292 @ SV318 ) @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV318 )
| ~ ( c_lessequals @ SV1172 @ SY5292 @ SV318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3212]) ).
thf(4076,plain,
! [SV1173: $i,SV319: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV319 )
| ( ( c_Orderings_Oord__class_Omax @ SV1173 @ SV1173 @ SV319 )
= SV1173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(4077,plain,
! [SV1174: $i,SV320: $i] :
( ( ! [SY5293: $i,SY5294: $i,SY5295: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV1174 ) @ SY5293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SY5294 ) @ SY5295 ) @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SY5293 @ SY5295 @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SY5294 @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3214]) ).
thf(4078,plain,
! [SV1175: $i,SV321: $i] :
( ( ! [SY5296: $i,SY5297: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV1175 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5296 ) @ SY5297 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1175 @ SY5297 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV321 @ SY5296 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(4079,plain,
! [SV1176: $i,SV322: $i] :
( ( ( c_lessequals @ SV322 @ SV1176 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV322 @ SV1176 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(4080,plain,
! [SV1177: $i,SV323: $i] :
( ( ( c_lessequals @ SV323 @ SV1177 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV323 @ SV1177 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3217]) ).
thf(4081,plain,
! [SV1178: $i,SV324: $i] :
( ( ! [SY5298: $i] :
( ~ ( class_Orderings_Oorder @ SV324 )
| ( c_lessequals @ SV1178 @ SY5298 @ SV324 )
| ~ ( c_HOL_Oord__class_Oless @ SV1178 @ SY5298 @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3218]) ).
thf(4082,plain,
! [SV1179: $i,SV325: $i] :
( ( ! [SY5299: $i] :
( ~ ( class_Orderings_Opreorder @ SV325 )
| ( c_lessequals @ SV1179 @ SY5299 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV1179 @ SY5299 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3219]) ).
thf(4083,plain,
! [SV1180: $i,SV326: $i] :
( ( ! [SY5300: $i,SY5301: $i] :
( ~ ( class_Orderings_Olinorder @ SV326 )
| ( c_HOL_Oord__class_Oless @ SV1180 @ SY5300 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ SV1180 @ ( c_Orderings_Oord__class_Omin @ SY5300 @ SY5301 @ SV326 ) @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(4084,plain,
! [SV1181: $i,SV327: $i] :
( ( ! [SY5302: $i,SY5303: $i] :
( ~ ( class_Orderings_Olinorder @ SV327 )
| ( c_HOL_Oord__class_Oless @ SV1181 @ SY5302 @ SV327 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_Orderings_Oord__class_Omin @ SY5303 @ SY5302 @ SV327 ) @ SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(4085,plain,
! [SV1182: $i,SV328: $i] :
( ( ! [SY5304: $i,SY5305: $i] :
( ~ ( class_Orderings_Olinorder @ SV328 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1182 @ SY5304 @ SV328 ) @ SY5305 @ SV328 )
| ~ ( c_HOL_Oord__class_Oless @ SV1182 @ SY5305 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3222]) ).
thf(4086,plain,
! [SV1183: $i,SV329: $i] :
( ( ! [SY5306: $i,SY5307: $i] :
( ~ ( class_Orderings_Olinorder @ SV329 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1183 @ SY5306 @ SV329 ) @ SY5307 @ SV329 )
| ~ ( c_HOL_Oord__class_Oless @ SY5306 @ SY5307 @ SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(4087,plain,
! [SV1184: $i,SV330: $i] :
( ( ! [SY5308: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV330 @ SV1184 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY5308 @ SV1184 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV330 @ SY5308 @ tc_nat ) )
| ~ ( c_lessequals @ SV1184 @ SY5308 @ tc_nat )
| ~ ( c_lessequals @ SV1184 @ SV330 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3224]) ).
thf(4088,plain,
! [SV1185: $i,SV331: $i] :
( ( ! [SY5309: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV331 @ SV1185 @ tc_nat ) @ SY5309 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV331 @ SY5309 @ tc_nat ) @ SV1185 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(4089,plain,
! [SV1186: $i,SV332: $i] :
( ( ! [SY5310: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV332 ) @ SV1186 ) @ SY5310 ) @ SV332 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SY5310 @ SV332 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1186 @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(4090,plain,
! [SV1187: $i,SV333: $i] :
( ( ! [SY5311: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV333 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV333 ) @ SV1187 ) @ SY5311 ) @ SV333 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SY5311 @ SV333 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1187 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(4091,plain,
! [SV1188: $i,SV334: $i] :
( ( ! [SY5312: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV334 @ SV1188 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY5312 @ SV1188 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1188 @ SV334 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV334 @ SY5312 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3228]) ).
thf(4092,plain,
! [SV1189: $i,SV335: $i] :
( ( ! [SY5313: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV335 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1189 @ SY5313 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
| ~ ( c_lessequals @ SY5313 @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV1189 @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3229]) ).
thf(4093,plain,
! [SV1190: $i,SV336: $i] :
( ( ! [SY5314: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV336 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1190 @ SY5314 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SY5314 @ SV336 )
| ~ ( c_lessequals @ SV1190 @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3230]) ).
thf(4094,plain,
! [SV1191: $i,SV337: $i] :
( ( ! [SY5315: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV337 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1191 @ SY5315 @ SV337 ) @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
| ~ ( c_lessequals @ SY5315 @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV1191 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(4095,plain,
! [SV1192: $i,SV338: $i] :
( ( ! [SY5316: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV338 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1192 @ SY5316 @ SV338 ) @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SY5316 @ SV338 )
| ~ ( c_lessequals @ SV1192 @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(4096,plain,
! [SV1193: $i,SV339: $i] :
( ( ! [SY5317: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV339 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1193 @ SY5317 @ SV339 ) @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
| ~ ( c_lessequals @ SY5317 @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV1193 @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3233]) ).
thf(4097,plain,
! [SV1194: $i,SV340: $i] :
( ( ! [SY5318: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV340 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SY5318 @ SV340 ) @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SY5318 @ SV340 )
| ~ ( c_lessequals @ SV1194 @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(4098,plain,
! [SV1195: $i,SV341: $i] :
( ( ! [SY5319: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV341 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1195 @ SY5319 @ SV341 ) @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
| ~ ( c_lessequals @ SV1195 @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SY5319 @ SV341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(4099,plain,
! [SV1196: $i,SV342: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV342 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1196 @ SV1196 @ SV342 ) @ ( c_HOL_Ozero__class_Ozero @ SV342 ) @ SV342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(4100,plain,
! [SV1197: $i,SV343: $i] :
( ( ! [SY5320: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV343 ) @ SV1197 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV343 ) @ SY5320 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1197 @ SY5320 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3237]) ).
thf(4101,plain,
! [SV1198: $i,SV344: $i] :
( ( ! [SY5321: $i] :
( ( c_HOL_Oord__class_Oless @ SV344 @ SV1198 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY5321 ) @ SV344 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY5321 ) @ SV1198 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3238]) ).
thf(4102,plain,
! [SV1199: $i,SV345: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV345 ) @ SV1199 @ tc_nat )
| ( ( c_Suc @ SV345 )
= SV1199 )
| ~ ( c_HOL_Oord__class_Oless @ SV345 @ SV1199 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(4103,plain,
! [SV1200: $i,SV346: $i] :
( ( ~ ( c_lessequals @ SV346 @ SV1200 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV1200 ) @ SV346 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3240]) ).
thf(4104,plain,
! [SV1201: $i,SV347: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV347 ) @ SV1201 @ tc_nat )
| ( c_lessequals @ SV1201 @ SV347 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3241]) ).
thf(4105,plain,
! [SV1202: $i,SV348: $i] :
( ( ! [SY5322: $i,SY5323: $i] :
( ( c_List_Olist_OCons @ SV348 @ ( c_List_Oappend @ SV1202 @ SY5322 @ SY5323 ) @ SY5323 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV348 @ SV1202 @ SY5323 ) @ SY5322 @ SY5323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(4106,plain,
! [SV1203: $i,SV349: $i] :
( ( ! [SY5324: $i,SY5325: $i] :
( ( c_List_Olist_OCons @ SV349 @ ( c_List_Oappend @ SV1203 @ SY5324 @ SY5325 ) @ SY5325 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV349 @ SV1203 @ SY5325 ) @ SY5324 @ SY5325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(4107,plain,
! [SV1204: $i,SV350: $i] :
( ( ! [SY5326: $i,SY5327: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV350 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ ( c_Orderings_Oord__class_Omin @ SV1204 @ SY5326 @ SV350 ) ) @ SY5327 )
= ( c_Orderings_Oord__class_Omin @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV1204 ) @ SY5327 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SY5326 ) @ SY5327 ) @ SV350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3244]) ).
thf(4108,plain,
! [SV1205: $i,SV351: $i] :
( ( ! [SY5328: $i] :
( ( c_lessequals @ SV351 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1205 ) @ SV351 ) @ SY5328 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY5328 @ SV1205 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(4109,plain,
! [SV1206: $i,SV352: $i] :
( ( ! [SY5329: $i,SY5330: $i,SY5331: $i,SY5332: $i,SY5333: $i,SY5334: $i,SY5335: $i] :
( ( ( hAPP @ ( hAPP @ SV352 @ ( hAPP @ ( hAPP @ SV1206 @ SY5329 ) @ SY5330 ) ) @ SY5331 )
= ( hAPP @ ( hAPP @ SV1206 @ ( hAPP @ ( hAPP @ SV352 @ SY5329 ) @ SY5331 ) ) @ ( hAPP @ ( hAPP @ SV352 @ SY5330 ) @ SY5331 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5332 @ SV1206 @ SV352 @ SY5333 @ SY5334 @ SY5335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(4110,plain,
! [SV1207: $i,SV353: $i] :
( ( ! [SY5336: $i,SY5337: $i,SY5338: $i,SY5339: $i,SY5340: $i,SY5341: $i,SY5342: $i] :
( ( ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ ( hAPP @ ( hAPP @ SY5336 @ SY5337 ) @ SY5338 ) )
= ( hAPP @ ( hAPP @ SY5336 @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SY5337 ) ) @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SY5338 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5336 @ SV353 @ SY5339 @ SY5340 @ SY5341 @ SY5342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(4111,plain,
! [SV1208: $i,SV354: $i] :
( ( ! [SY5343: $i,SY5344: $i,SY5345: $i,SY5346: $i,SY5347: $i,SY5348: $i] :
( ( ( hAPP @ ( hAPP @ SV354 @ SV1208 ) @ SY5343 )
= ( hAPP @ ( hAPP @ SV354 @ SY5343 ) @ SV1208 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5344 @ SV354 @ SY5345 @ SY5346 @ SY5347 @ SY5348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(4112,plain,
! [SV1209: $i,SV355: $i] :
( ( ! [SY5349: $i,SY5350: $i,SY5351: $i,SY5352: $i,SY5353: $i,SY5354: $i,SY5355: $i] :
( ( ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ ( hAPP @ ( hAPP @ SV355 @ SY5349 ) @ SY5350 ) )
= ( hAPP @ ( hAPP @ SV355 @ ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ SY5349 ) ) @ SY5350 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5351 @ SV355 @ SY5352 @ SY5353 @ SY5354 @ SY5355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3249]) ).
thf(4113,plain,
! [SV1210: $i,SV356: $i] :
( ( ! [SY5356: $i,SY5357: $i,SY5358: $i,SY5359: $i,SY5360: $i] :
( ( ( hAPP @ ( hAPP @ SV356 @ SV1210 ) @ SY5356 )
= SY5356 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5357 @ SV356 @ SY5358 @ SY5359 @ SV1210 @ SY5360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3250]) ).
thf(4114,plain,
! [SV1211: $i,SV357: $i] :
( ( ! [SY5361: $i,SY5362: $i,SY5363: $i,SY5364: $i,SY5365: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV1211 ) @ SY5361 )
= SV1211 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5362 @ SV357 @ SY5363 @ SV1211 @ SY5364 @ SY5365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3251]) ).
thf(4115,plain,
! [SV1212: $i,SV358: $i] :
( ( ! [SY5366: $i,SY5367: $i,SY5368: $i,SY5369: $i,SY5370: $i,SY5371: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV1212 ) @ SY5366 )
= ( hAPP @ ( hAPP @ SV358 @ SY5366 ) @ SV1212 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV358 @ SY5367 @ SY5368 @ SY5369 @ SY5370 @ SY5371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3252]) ).
thf(4116,plain,
! [SV1213: $i,SV359: $i] :
( ( ! [SY5372: $i,SY5373: $i,SY5374: $i,SY5375: $i,SY5376: $i,SY5377: $i,SY5378: $i] :
( ( ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ ( hAPP @ ( hAPP @ SV359 @ SY5372 ) @ SY5373 ) )
= ( hAPP @ ( hAPP @ SV359 @ ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ SY5372 ) ) @ SY5373 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV359 @ SY5374 @ SY5375 @ SY5376 @ SY5377 @ SY5378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3253]) ).
thf(4117,plain,
! [SV1214: $i,SV360: $i] :
( ( ! [SY5379: $i,SY5380: $i,SY5381: $i,SY5382: $i,SY5383: $i] :
( ( ( hAPP @ ( hAPP @ SV360 @ SV1214 ) @ SY5379 )
= SY5379 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV360 @ SY5380 @ SY5381 @ SV1214 @ SY5382 @ SY5383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3254]) ).
thf(4118,plain,
! [SV1215: $i,SV361: $i] :
( ( ! [SY5384: $i,SY5385: $i,SY5386: $i,SY5387: $i,SY5388: $i,SY5389: $i,SY5390: $i] :
( ( ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ ( hAPP @ ( hAPP @ SV361 @ SY5384 ) @ SY5385 ) )
= ( hAPP @ ( hAPP @ SV361 @ ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ SY5384 ) ) @ SY5385 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV361 @ SY5386 @ SY5387 @ SY5388 @ SY5389 @ SY5390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3255]) ).
thf(4119,plain,
! [SV1216: $i,SV362: $i] :
( ( ! [SY5391: $i,SY5392: $i,SY5393: $i,SY5394: $i,SY5395: $i,SY5396: $i] :
( ( ( hAPP @ ( hAPP @ SV362 @ SV1216 ) @ SY5391 )
= ( hAPP @ ( hAPP @ SV362 @ SY5391 ) @ SV1216 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV362 @ SY5392 @ SY5393 @ SY5394 @ SY5395 @ SY5396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3256]) ).
thf(4120,plain,
! [SV1217: $i,SV363: $i] :
( ( ! [SY5397: $i,SY5398: $i,SY5399: $i,SY5400: $i,SY5401: $i,SY5402: $i,SY5403: $i] :
( ( ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SY5397 ) ) @ SY5398 )
= ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SY5398 ) ) @ SY5397 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV363 @ SY5399 @ SY5400 @ SY5401 @ SY5402 @ SY5403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3257]) ).
thf(4121,plain,
! [SV1218: $i,SV364: $i] :
( ( ! [SY5404: $i,SY5405: $i,SY5406: $i,SY5407: $i,SY5408: $i,SY5409: $i,SY5410: $i] :
( ( ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ ( hAPP @ ( hAPP @ SV364 @ SY5404 ) @ SY5405 ) )
= ( hAPP @ ( hAPP @ SV364 @ SY5404 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ SY5405 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV364 @ SY5406 @ SY5407 @ SY5408 @ SY5409 @ SY5410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3258]) ).
thf(4122,plain,
! [SV1219: $i,SV365: $i] :
( ( ! [SY5411: $i,SY5412: $i,SY5413: $i,SY5414: $i,SY5415: $i,SY5416: $i,SY5417: $i] :
( ( ( hAPP @ ( hAPP @ SV365 @ ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ SY5411 ) ) @ SY5412 )
= ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ ( hAPP @ ( hAPP @ SV365 @ SY5411 ) @ SY5412 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV365 @ SY5413 @ SY5414 @ SY5415 @ SY5416 @ SY5417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3259]) ).
thf(4123,plain,
! [SV1220: $i,SV366: $i] :
( ( ! [SY5418: $i,SY5419: $i,SY5420: $i,SY5421: $i,SY5422: $i,SY5423: $i,SY5424: $i,SY5425: $i] :
( ( ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SY5418 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SY5419 ) @ SY5420 ) )
= ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SY5419 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SY5418 ) @ SY5420 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV366 @ SY5421 @ SY5422 @ SY5423 @ SY5424 @ SY5425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3260]) ).
thf(4124,plain,
! [SV1221: $i,SV367: $i] :
( ( ! [SY5426: $i,SY5427: $i,SY5428: $i,SY5429: $i,SY5430: $i,SY5431: $i,SY5432: $i] :
( ( ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ ( hAPP @ ( hAPP @ SV367 @ SY5426 ) @ SY5427 ) )
= ( hAPP @ ( hAPP @ SV367 @ SY5426 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ SY5427 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5428 @ SV367 @ SY5429 @ SY5430 @ SY5431 @ SY5432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3261]) ).
thf(4125,plain,
! [SV1222: $i,SV368: $i] :
( ( ! [SY5433: $i,SY5434: $i,SY5435: $i,SY5436: $i,SY5437: $i,SY5438: $i,SY5439: $i] :
( ( ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ ( hAPP @ ( hAPP @ SV368 @ SY5433 ) @ SY5434 ) )
= ( hAPP @ ( hAPP @ SV368 @ ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ SY5433 ) ) @ SY5434 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5435 @ SV368 @ SY5436 @ SY5437 @ SY5438 @ SY5439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3262]) ).
thf(4126,plain,
! [SV1223: $i,SV369: $i] :
( ( ! [SY5440: $i,SY5441: $i,SY5442: $i,SY5443: $i,SY5444: $i,SY5445: $i,SY5446: $i] :
( ( ( hAPP @ ( hAPP @ SV369 @ ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ SY5440 ) ) @ SY5441 )
= ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ ( hAPP @ ( hAPP @ SV369 @ SY5440 ) @ SY5441 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5442 @ SV369 @ SY5443 @ SY5444 @ SY5445 @ SY5446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3263]) ).
thf(4127,plain,
! [SV1224: $i,SV370: $i] :
( ( ! [SY5447: $i,SY5448: $i,SY5449: $i,SY5450: $i,SY5451: $i,SY5452: $i,SY5453: $i] :
( ( ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SY5447 ) ) @ SY5448 )
= ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SY5448 ) ) @ SY5447 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5449 @ SV370 @ SY5450 @ SY5451 @ SY5452 @ SY5453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(4128,plain,
! [SV1225: $i,SV371: $i] :
( ( ! [SY5454: $i,SY5455: $i,SY5456: $i,SY5457: $i,SY5458: $i,SY5459: $i,SY5460: $i,SY5461: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SY5454 ) ) @ ( hAPP @ ( hAPP @ SV371 @ SY5455 ) @ SY5456 ) )
= ( hAPP @ ( hAPP @ SV371 @ SY5455 ) @ ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SY5454 ) ) @ SY5456 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5457 @ SV371 @ SY5458 @ SY5459 @ SY5460 @ SY5461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3265]) ).
thf(4129,plain,
! [SV1226: $i,SV372: $i] :
( ( ! [SY5462: $i,SY5463: $i,SY5464: $i,SY5465: $i,SY5466: $i,SY5467: $i,SY5468: $i,SY5469: $i] :
( ( ( hAPP @ ( hAPP @ SV372 @ ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ SY5462 ) ) @ ( hAPP @ ( hAPP @ SV372 @ SY5463 ) @ SY5464 ) )
= ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ ( hAPP @ ( hAPP @ SV372 @ SY5462 ) @ ( hAPP @ ( hAPP @ SV372 @ SY5463 ) @ SY5464 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5465 @ SV372 @ SY5466 @ SY5467 @ SY5468 @ SY5469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3266]) ).
thf(4130,plain,
! [SV1227: $i,SV373: $i] :
( ( ! [SY5470: $i,SY5471: $i,SY5472: $i,SY5473: $i,SY5474: $i,SY5475: $i,SY5476: $i,SY5477: $i] :
( ( ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SY5470 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SY5471 ) @ SY5472 ) )
= ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SY5471 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SY5470 ) @ SY5472 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5473 @ SV373 @ SY5474 @ SY5475 @ SY5476 @ SY5477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(4131,plain,
! [SV1228: $i,SV374: $i] :
( ( ! [SY5478: $i,SY5479: $i,SY5480: $i,SY5481: $i,SY5482: $i] :
( ( ( hAPP @ ( hAPP @ SV374 @ SV1228 ) @ SY5478 )
= SV1228 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5479 @ SV374 @ SY5480 @ SY5481 @ SY5478 @ SY5482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3268]) ).
thf(4132,plain,
! [SV1229: $i,SV375: $i] :
( ( ! [SY5483: $i,SY5484: $i,SY5485: $i,SY5486: $i,SY5487: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV1229 ) @ SY5483 )
= SY5483 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5484 @ SV375 @ SY5485 @ SY5486 @ SV1229 @ SY5487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3269]) ).
thf(4133,plain,
! [SV1230: $i,SV376: $i] :
( ( ! [SY5488: $i,SY5489: $i,SY5490: $i,SY5491: $i,SY5492: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ SV1230 ) @ SY5488 )
= SY5488 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5489 @ SV376 @ SY5490 @ SY5488 @ SY5491 @ SY5492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3270]) ).
thf(4134,plain,
! [SV1231: $i,SV377: $i] :
( ( ! [SY5493: $i,SY5494: $i,SY5495: $i,SY5496: $i,SY5497: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SV1231 ) @ SY5493 )
= SV1231 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5494 @ SV377 @ SY5495 @ SV1231 @ SY5496 @ SY5497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3271]) ).
thf(4135,plain,
! [SV1232: $i,SV378: $i] :
( ( ! [SY5498: $i,SY5499: $i,SY5500: $i,SY5501: $i,SY5502: $i,SY5503: $i,SY5504: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ ( hAPP @ ( hAPP @ SV1232 @ SY5498 ) @ SY5499 ) ) @ SY5500 )
= ( hAPP @ ( hAPP @ SV1232 @ ( hAPP @ ( hAPP @ SV378 @ SY5498 ) @ SY5500 ) ) @ ( hAPP @ ( hAPP @ SV378 @ SY5499 ) @ SY5500 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1232 @ SV378 @ SY5501 @ SY5502 @ SY5503 @ SY5504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3272]) ).
thf(4136,plain,
! [SV1233: $i,SV379: $i] :
( ( ! [SY5505: $i,SY5506: $i,SY5507: $i,SY5508: $i,SY5509: $i,SY5510: $i] :
( ( ( hAPP @ ( hAPP @ SV379 @ SV1233 ) @ SY5505 )
= ( hAPP @ ( hAPP @ SV379 @ SY5505 ) @ SV1233 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5506 @ SV379 @ SY5507 @ SY5508 @ SY5509 @ SY5510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(4137,plain,
! [SV1234: $i,SV380: $i] :
( ( ! [SY5511: $i,SY5512: $i,SY5513: $i,SY5514: $i,SY5515: $i] :
( ( ( hAPP @ ( hAPP @ SV380 @ SV1234 ) @ SY5511 )
= SV1234 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV380 @ SY5512 @ SY5513 @ SY5511 @ SY5514 @ SY5515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(4138,plain,
! [SV1235: $i,SV381: $i] :
( ( ! [SY5516: $i,SY5517: $i,SY5518: $i,SY5519: $i,SY5520: $i] :
( ( ( hAPP @ ( hAPP @ SV381 @ SV1235 ) @ SY5516 )
= SY5516 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV381 @ SY5517 @ SY5518 @ SV1235 @ SY5519 @ SY5520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3275]) ).
thf(4139,plain,
! [SV1236: $i,SV382: $i] :
( ( ! [SY5521: $i,SY5522: $i,SY5523: $i,SY5524: $i,SY5525: $i] :
( ( ( hAPP @ ( hAPP @ SV382 @ SV1236 ) @ SV1236 )
= ( hAPP @ ( hAPP @ SY5521 @ ( hAPP @ ( hAPP @ SV382 @ SY5522 ) @ SY5522 ) ) @ SV1236 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV382 @ SY5521 @ SY5523 @ SY5524 @ SY5522 @ SY5525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3276]) ).
thf(4140,plain,
! [SV1237: $i,SV383: $i] :
( ( ! [SY5526: $i,SY5527: $i,SY5528: $i,SY5529: $i,SY5530: $i,SY5531: $i] :
( ( ( hAPP @ ( hAPP @ SV383 @ SV1237 ) @ ( hAPP @ ( hAPP @ SY5526 @ SY5527 ) @ SV1237 ) )
= ( hAPP @ ( hAPP @ SY5526 @ ( hAPP @ ( hAPP @ SV383 @ SY5527 ) @ SY5528 ) ) @ SV1237 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV383 @ SY5526 @ SY5529 @ SY5530 @ SY5528 @ SY5531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(4141,plain,
! [SV1238: $i,SV384: $i] :
( ( ! [SY5532: $i,SY5533: $i,SY5534: $i,SY5535: $i,SY5536: $i,SY5537: $i] :
( ( ( hAPP @ ( hAPP @ SV384 @ ( hAPP @ ( hAPP @ SV1238 @ SY5532 ) @ SY5533 ) ) @ SY5533 )
= ( hAPP @ ( hAPP @ SV1238 @ ( hAPP @ ( hAPP @ SV384 @ SY5532 ) @ SY5534 ) ) @ SY5533 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV384 @ SV1238 @ SY5535 @ SY5536 @ SY5534 @ SY5537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(4142,plain,
! [SV1239: $i,SV385: $i] :
( ( ! [SY5538: $i,SY5539: $i,SY5540: $i,SY5541: $i,SY5542: $i,SY5543: $i,SY5544: $i] :
( ( ( hAPP @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ SV1239 @ SY5538 ) @ SY5539 ) ) @ ( hAPP @ ( hAPP @ SV1239 @ SY5540 ) @ SY5539 ) )
= ( hAPP @ ( hAPP @ SV1239 @ ( hAPP @ ( hAPP @ SV385 @ SY5538 ) @ SY5540 ) ) @ SY5539 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV385 @ SV1239 @ SY5541 @ SY5542 @ SY5543 @ SY5544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(4143,plain,
! [SV1240: $i,SV386: $i] :
( ( ! [SY5545: $i,SY5546: $i] :
( ~ ( hBOOL @ ( hAPP @ SV386 @ ( c_Type_Otype_Otype__case @ SV1240 @ SY5545 @ ( c_Type_Otype_OAtom @ SY5546 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV386 @ ( hAPP @ SV1240 @ SY5546 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3280]) ).
thf(4144,plain,
! [SV1241: $i,SV387: $i] :
( ( ! [SY5547: $i,SY5548: $i] :
( ~ ( hBOOL @ ( hAPP @ SV387 @ ( c_Type_Otype_Otype__case @ SV1241 @ SY5547 @ ( c_Type_Otype_OAtom @ SY5548 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV387 @ ( hAPP @ SV1241 @ SY5548 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3281]) ).
thf(4145,plain,
! [SV1242: $i,SV388: $i] :
( ( ! [SY5549: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV388 ) @ SV1242 @ tc_nat ) @ ( c_Suc @ SY5549 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV388 @ SV1242 @ tc_nat ) @ SY5549 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3282]) ).
thf(4146,plain,
! [SV1243: $i,SV389: $i] :
( ( ! [SY5550: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV389 ) @ SV1243 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV389 ) @ SY5550 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1243 @ SY5550 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3283]) ).
thf(4147,plain,
! [SV1244: $i,SV390: $i] :
( ( ! [SY5551: $i] :
( ( c_lessequals @ SV390 @ SV1244 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY5551 ) @ SV390 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY5551 ) @ SV1244 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3284]) ).
thf(4148,plain,
! [SV1245: $i,SV391: $i] :
( ( ! [SY5552: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV391 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV391 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV391 ) @ ( c_HOL_Otimes__class_Otimes @ SV1245 @ SV1245 @ SV391 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY5552 @ SY5552 @ SV391 ) ) @ SV391 )
| ( SV1245
= ( c_HOL_Ozero__class_Ozero @ SV391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3285]) ).
thf(4149,plain,
! [SV1246: $i,SV392: $i] :
( ( ! [SY5553: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV392 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV392 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV392 ) @ ( c_HOL_Otimes__class_Otimes @ SV1246 @ SV1246 @ SV392 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY5553 @ SY5553 @ SV392 ) ) @ SV392 )
| ( SY5553
= ( c_HOL_Ozero__class_Ozero @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3286]) ).
thf(4150,plain,
! [SV393: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV393 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(4151,plain,
! [SV1247: $i,SV394: $i] :
( ( ! [SY5554: $i,SY5555: $i,SY5556: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV394 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1247 ) @ SY5554 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SY5555 ) @ SY5556 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1247 ) @ SY5555 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SY5554 ) @ SY5556 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(4152,plain,
! [SV1248: $i,SV395: $i] :
( ( ! [SY5557: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV395 ) @ SV1248 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV395 ) @ SY5557 ) )
| ~ ( c_Lambda_Obeta @ SV1248 @ SY5557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(4153,plain,
! [SV1249: $i,SV396: $i] :
( ( ! [SY5558: $i] :
( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV396 ) @ SV1249 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY5558 ) @ SV1249 ) )
| ~ ( c_Lambda_Obeta @ SV396 @ SY5558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3290]) ).
thf(4154,plain,
! [SV1250: $i,SV397: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV397 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1250 @ SV397 ) @ ( c_HOL_Ozero__class_Ozero @ SV397 ) @ SV397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3291]) ).
thf(4155,plain,
! [SV1251: $i,SV398: $i] :
( ( ! [SY5559: $i] :
( ~ ( class_Orderings_Olinorder @ SV398 )
| ( ( c_Orderings_Oord__class_Omax @ SV1251 @ SY5559 @ SV398 )
= ( c_Orderings_Oord__class_Omax @ SY5559 @ SV1251 @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3292]) ).
thf(4156,plain,
! [SV1252: $i,SV400: $i] :
( ( ! [SY5560: $i,SY5561: $i] :
( ( c_List_Odrop @ SV400 @ ( c_List_Oreplicate @ SV1252 @ SY5560 @ SY5561 ) @ SY5561 )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ SV1252 @ SV400 @ tc_nat ) @ SY5560 @ SY5561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3294]) ).
thf(4157,plain,
! [SV1253: $i,SV401: $i] :
( ( ! [SY5562: $i,SY5563: $i] :
( ~ ( class_Orderings_Olinorder @ SV401 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV1253 @ SY5562 @ SV401 ) @ ( c_Orderings_Oord__class_Omin @ SV1253 @ SY5563 @ SV401 ) @ SV401 ) @ ( c_Orderings_Oord__class_Omin @ SV1253 @ ( c_Orderings_Oord__class_Omax @ SY5562 @ SY5563 @ SV401 ) @ SV401 ) @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3295]) ).
thf(4158,plain,
! [SV1254: $i,SV402: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV402 @ SV1254 )
= ( c_List_Olist_ONil @ SV1254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(4159,plain,
! [SV1255: $i,SV404: $i] :
( ( ! [SY5564: $i] :
( ~ ( class_Orderings_Olinorder @ SV404 )
| ( ( c_Orderings_Oord__class_Omax @ SV1255 @ ( c_Orderings_Oord__class_Omin @ SV1255 @ SY5564 @ SV404 ) @ SV404 )
= SV1255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3298]) ).
thf(4160,plain,
! [SV1256: $i,SV406: $i] :
( ( ! [SY5565: $i,SY5566: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV406 )
| ( c_HOL_Oord__class_Oless @ SV1256 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1256 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SY5565 @ SV406 ) @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SY5566 @ SV406 ) @ SV406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3300]) ).
thf(4161,plain,
! [SV1257: $i,SV407: $i] :
( ( ! [SY5567: $i,SY5568: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV407 )
| ( c_HOL_Oord__class_Oless @ SV1257 @ SY5567 @ SV407 )
| ( c_HOL_Oord__class_Oless @ SY5567 @ SV1257 @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY5568 @ SY5567 @ SV407 ) @ ( c_HOL_Otimes__class_Otimes @ SY5568 @ SV1257 @ SV407 ) @ SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(4162,plain,
! [SV1258: $i,SV408: $i] :
( ( ! [SY5569: $i,SY5570: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV408 )
| ( c_HOL_Oord__class_Oless @ SV1258 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV1258 @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY5569 @ SV1258 @ SV408 ) @ ( c_HOL_Otimes__class_Otimes @ SY5570 @ SV1258 @ SV408 ) @ SV408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(4163,plain,
! [SV1259: $i,SV409: $i] :
( ( ! [SY5571: $i,SY5572: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV409 )
| ( c_HOL_Oord__class_Oless @ SV1259 @ SY5571 @ SV409 )
| ( c_HOL_Oord__class_Oless @ SY5571 @ SV1259 @ SV409 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY5571 @ SY5572 @ SV409 ) @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SY5572 @ SV409 ) @ SV409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3303]) ).
thf(4164,plain,
! [SV1260: $i,SV410: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV410 @ ( c_HOL_Ominus__class_Ominus @ SV410 @ SV1260 @ tc_nat ) @ tc_nat )
= SV1260 )
| ~ ( c_lessequals @ SV1260 @ SV410 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3304]) ).
thf(4165,plain,
! [SV1261: $i,SV411: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV411 ) @ SV1261 )
= ( c_Lambda_OdB_OVar @ SV411 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ SV1261 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3305]) ).
thf(4166,plain,
! [SV1262: $i,SV412: $i] :
( ( ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV412 ) @ SV1262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3306]) ).
thf(4167,plain,
! [SV1263: $i,SV413: $i] :
( ( ! [SY5573: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV413 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV1263 @ SY5573 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV413 ) @ SY5573 ) @ ( c_Suc @ SV1263 ) @ tc_nat ) )
| ~ ( c_lessequals @ SY5573 @ SV1263 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(4168,plain,
! [SV1264: $i,SV414: $i] :
( ( ! [SY5574: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV414 )
| ( c_HOL_Oord__class_Oless @ SV1264 @ SY5574 @ SV414 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1264 @ SY5574 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3308]) ).
thf(4169,plain,
! [SV1265: $i,SV415: $i] :
( ( ! [SY5575: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV415 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SY5575 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 )
| ~ ( c_HOL_Oord__class_Oless @ SV1265 @ SY5575 @ SV415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3309]) ).
thf(4170,plain,
! [SV1266: $i,SV416: $i] :
( ( ! [SY5576: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV416 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1266 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY5576 @ SV416 ) @ SV416 )
| ~ ( c_HOL_Oord__class_Oless @ SV1266 @ SY5576 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(4171,plain,
! [SV1267: $i,SV417: $i] :
( ( ! [SY5577: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV417 )
| ( c_HOL_Oord__class_Oless @ SV1267 @ SY5577 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1267 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY5577 @ SV417 ) @ SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(4172,plain,
! [SV1268: $i,SV420: $i] :
( ( ! [SY5578: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV420 ) @ SV1268 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY5578 @ SV1268 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV420 @ SY5578 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3314]) ).
thf(4173,plain,
! [SV1269: $i,SV421: $i] :
( ( ! [SY5579: $i,SY5580: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV1269 ) @ SY5579 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SY5580 ) @ SY5579 ) @ SV421 )
| ~ ( c_lessequals @ SV1269 @ SY5580 @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(4174,plain,
! [SV1270: $i,SV422: $i] :
( ( ! [SY5581: $i,SY5582: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
| ( c_lessequals @ SV1270 @ SY5581 @ SV422 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1270 ) @ SY5582 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SY5581 ) @ SY5582 ) @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3316]) ).
thf(4175,plain,
! [SV1271: $i,SV423: $i] :
( ( ! [SY5583: $i,SY5584: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV423 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SY5583 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SY5584 ) @ SV423 )
| ~ ( c_lessequals @ SY5583 @ SY5584 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(4176,plain,
! [SV1272: $i,SV424: $i] :
( ( ! [SY5585: $i,SY5586: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
| ( c_lessequals @ SV1272 @ SY5585 @ SV424 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SY5586 ) @ SV1272 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SY5586 ) @ SY5585 ) @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(4177,plain,
! [SV1273: $i,SV425: $i] :
( ( ! [SY5587: $i,SY5588: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV425 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV1273 ) @ SY5587 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SY5588 ) @ SY5587 ) @ SV425 )
| ~ ( c_lessequals @ SV1273 @ SY5588 @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(4178,plain,
! [SV1274: $i,SV426: $i] :
( ( ! [SY5589: $i,SY5590: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV426 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SY5589 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SY5590 ) @ SV426 )
| ~ ( c_lessequals @ SY5589 @ SY5590 @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3320]) ).
thf(4179,plain,
! [SV1275: $i,SV427: $i] :
( ( ! [SY5591: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV427 ) @ SV1275 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5591 ) @ SV1275 ) @ tc_nat )
| ~ ( c_lessequals @ SV427 @ SY5591 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(4180,plain,
! [SV1276: $i,SV428: $i] :
( ( ! [SY5592: $i] :
( ( c_lessequals @ SV428 @ SV1276 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5592 ) @ SV428 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5592 ) @ SV1276 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3322]) ).
thf(4181,plain,
! [SV1277: $i,SV429: $i] :
( ( ! [SY5593: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV429 ) @ SV1277 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV429 ) @ SY5593 ) @ tc_nat )
| ~ ( c_lessequals @ SV1277 @ SY5593 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3323]) ).
thf(4182,plain,
! [SV1278: $i,SV430: $i] :
( ( ~ ( c_lessequals @ SV430 @ SV1278 @ tc_nat )
| ( SV1278
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1278 @ SV430 @ tc_nat ) ) @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(4183,plain,
! [SV1279: $i,SV431: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV431 ) @ ( c_HOL_Ominus__class_Ominus @ SV1279 @ SV431 @ tc_nat ) )
= SV1279 )
| ~ ( c_lessequals @ SV431 @ SV1279 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3325]) ).
thf(4184,plain,
! [SV1280: $i,SV432: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV432 @ SV1280 @ tc_nat ) ) @ SV1280 )
= SV432 )
| ~ ( c_lessequals @ SV1280 @ SV432 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3326]) ).
thf(4185,plain,
! [SV1281: $i,SV433: $i] :
( ( ! [SY5594: $i,SY5595: $i,SY5596: $i,SY5597: $i,SY5598: $i,SY5599: $i] :
( ( ( hAPP @ ( hAPP @ SV433 @ SV1281 ) @ ( hAPP @ ( hAPP @ SY5594 @ SV1281 ) @ SY5595 ) )
= ( hAPP @ ( hAPP @ SY5594 @ SV1281 ) @ ( c_Suc @ SY5595 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5596 @ SV433 @ SY5594 @ SY5597 @ SY5598 @ SY5599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3327]) ).
thf(4186,plain,
! [SV1282: $i,SV434: $i] :
( ( ! [SY5600: $i,SY5601: $i,SY5602: $i,SY5603: $i,SY5604: $i,SY5605: $i] :
( ( ( hAPP @ ( hAPP @ SV434 @ ( hAPP @ ( hAPP @ SV1282 @ SY5600 ) @ SY5601 ) ) @ SY5600 )
= ( hAPP @ ( hAPP @ SV1282 @ SY5600 ) @ ( c_Suc @ SY5601 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5602 @ SV434 @ SV1282 @ SY5603 @ SY5604 @ SY5605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3328]) ).
thf(4187,plain,
! [SV1283: $i,SV435: $i] :
( ( ! [SY5606: $i,SY5607: $i,SY5608: $i,SY5609: $i,SY5610: $i,SY5611: $i] :
( ( ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ ( c_Suc @ SY5606 ) )
= ( hAPP @ ( hAPP @ SY5607 @ SV1283 ) @ ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ SY5606 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5608 @ SY5607 @ SV435 @ SY5609 @ SY5610 @ SY5611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3329]) ).
thf(4188,plain,
! [SV1284: $i,SV436: $i] :
( ( ! [SY5612: $i,SY5613: $i,SY5614: $i,SY5615: $i,SY5616: $i,SY5617: $i] :
( ( ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ ( c_Suc @ SY5612 ) )
= ( hAPP @ ( hAPP @ SY5613 @ SV1284 ) @ ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ SY5612 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5614 @ SY5613 @ SV436 @ SY5615 @ SY5616 @ SY5617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3330]) ).
thf(4189,plain,
! [SV1285: $i,SV437: $i] :
( ( ! [SY5618: $i] :
( ( c_HOL_Oord__class_Oless @ SV437 @ SV1285 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY5618 @ SV437 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5618 @ SV1285 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(4190,plain,
! [SV1286: $i,SV438: $i] :
( ( ! [SY5619: $i] :
( ( c_HOL_Oord__class_Oless @ SV438 @ SV1286 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV438 @ SY5619 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1286 @ SY5619 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3332]) ).
thf(4191,plain,
! [SV1287: $i,SV439: $i] :
( ( ! [SY5620: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV439 ) @ ( c_HOL_Ominus__class_Ominus @ SV1287 @ SY5620 @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV439 ) @ SV1287 ) @ SY5620 @ tc_nat ) )
| ~ ( c_lessequals @ SY5620 @ SV1287 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3333]) ).
thf(4192,plain,
! [SV1288: $i,SV440: $i] :
( ( ! [SY5621: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV440 @ SV1288 @ tc_nat ) ) @ SY5621 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV440 ) @ SY5621 ) @ SV1288 @ tc_nat ) )
| ~ ( c_lessequals @ SV1288 @ SV440 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(4193,plain,
! [SV1289: $i,SV441: $i] :
( ( ! [SY5622: $i,SY5623: $i] :
( ( c_List_Odrop @ SV441 @ ( c_List_Odrop @ SV1289 @ SY5622 @ SY5623 ) @ SY5623 )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV441 ) @ SV1289 ) @ SY5622 @ SY5623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3335]) ).
thf(4194,plain,
! [SV1290: $i,SV442: $i] :
( ( ! [SY5624: $i,SY5625: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV442 )
| ( c_lessequals @ SV1290 @ SY5624 @ SV442 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV442 ) @ SY5624 @ SV442 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1290 @ ( c_Suc @ SY5625 ) @ SV442 ) @ ( c_Power_Opower__class_Opower @ SY5624 @ ( c_Suc @ SY5625 ) @ SV442 ) @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(4195,plain,
! [SV1291: $i,SV443: $i] :
( ( ! [SY5626: $i,SY5627: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV443 ) @ SV1291 ) @ SY5626 @ SY5627 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV443 @ SY5626 @ SY5627 ) @ ( c_List_Oreplicate @ SV1291 @ SY5626 @ SY5627 ) @ SY5627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3337]) ).
thf(4196,plain,
! [SV1292: $i,SV444: $i] :
( ( ! [SY5628: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV444 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1292 @ ( c_HOL_Otimes__class_Otimes @ SV1292 @ SY5628 @ SV444 ) @ SV444 )
= ( c_HOL_Otimes__class_Otimes @ SV1292 @ SY5628 @ SV444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3338]) ).
thf(4197,plain,
! [SV1293: $i,SV445: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV445 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV445 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1293 @ SV445 ) @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1293 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3339]) ).
thf(4198,plain,
! [SV1294: $i,SV446: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV446 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1294 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1294 @ SV446 ) @ SV446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3340]) ).
thf(4199,plain,
! [SV1295: $i,SV447: $i] :
( ( ! [SY5629: $i,SY5630: $i,SY5631: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SY5629 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SY5630 @ SY5631 @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SY5629 @ SV447 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
| ~ ( c_lessequals @ SY5629 @ SY5631 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SY5630 @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3341]) ).
thf(4200,plain,
! [SV1296: $i,SV448: $i] :
( ( ! [SY5632: $i,SY5633: $i,SY5634: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SY5632 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SY5633 @ SY5634 @ SV448 ) @ SV448 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SY5632 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ SY5632 @ SY5634 @ SV448 )
| ~ ( c_lessequals @ SV1296 @ SY5633 @ SV448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3342]) ).
thf(4201,plain,
! [SV1297: $i,SV449: $i] :
( ( ! [SY5635: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV449 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1297 @ ( c_Power_Opower__class_Opower @ SV1297 @ SY5635 @ SV449 ) @ SV449 )
= ( c_Power_Opower__class_Opower @ SV1297 @ ( c_Suc @ SY5635 ) @ SV449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(4202,plain,
! [SV1298: $i,SV450: $i] :
( ( ! [SY5636: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV450 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1298 @ SY5636 @ SV450 ) @ SV1298 @ SV450 )
= ( c_Power_Opower__class_Opower @ SV1298 @ ( c_Suc @ SY5636 ) @ SV450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(4203,plain,
! [SV1299: $i,SV451: $i] :
( ( ! [SY5637: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV451 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV1299 @ SV451 )
| ( c_lessequals @ SV1299 @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY5637 @ SV1299 @ SV451 ) @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(4204,plain,
! [SV1300: $i,SV452: $i] :
( ( ! [SY5638: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV452 )
| ( c_lessequals @ SV1300 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
| ( c_lessequals @ SY5638 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1300 @ SY5638 @ SV452 ) @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(4205,plain,
! [SV1301: $i,SV453: $i] :
( ( ! [SY5639: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV453 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV1301 @ SV453 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SY5639 @ SV453 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY5639 @ SV1301 @ SV453 ) @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3347]) ).
thf(4206,plain,
! [SV1302: $i,SV454: $i] :
( ( ! [SY5640: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV454 )
| ( c_lessequals @ SV1302 @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV1302 @ SV454 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1302 @ SY5640 @ SV454 ) @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(4207,plain,
! [SV1303: $i,SV455: $i] :
( ( ! [SY5641: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV455 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1303 @ SY5641 @ SV455 ) @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SV1303 @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SY5641 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(4208,plain,
! [SV1304: $i,SV456: $i] :
( ( ! [SY5642: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV456 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1304 @ SY5642 @ SV456 ) @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SY5642 @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1304 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(4209,plain,
! [SV1305: $i,SV457: $i] :
( ( ! [SY5643: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV457 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1305 @ SY5643 @ SV457 ) @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SY5643 @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SV1305 @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(4210,plain,
! [SV1306: $i,SV458: $i] :
( ( ( c_lessequals @ SV458 @ SV1306 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV458 ) @ SV1306 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(4211,plain,
! [SV1307: $i,SV459: $i] :
( ( ( c_lessequals @ SV459 @ ( c_Suc @ SV1307 ) @ tc_nat )
| ~ ( c_lessequals @ SV459 @ SV1307 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3353]) ).
thf(4212,plain,
! [SV1308: $i,SV460: $i] :
( ( ! [SY5644: $i,SY5645: $i] :
( ( c_Type_Otypings @ SV460 @ SV1308 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY5644 @ SV460 @ SY5645 @ SV1308 ) )
| ~ ( c_Type_Otyping @ SV460 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY5645 @ SV1308 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY5644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3354]) ).
thf(4213,plain,
! [SV1309: $i,SV461: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV461 @ ( c_HOL_Otimes__class_Otimes @ SV1309 @ SV461 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1309 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV461 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3355]) ).
thf(4214,plain,
! [SV1310: $i,SV462: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV462 @ ( c_HOL_Otimes__class_Otimes @ SV462 @ SV1310 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1310 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV462 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(4215,plain,
! [SV463: $i] :
( ( c_lessequals @ ( c_Suc @ SV463 ) @ SV463 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3357]) ).
thf(4216,plain,
! [SV1311: $i,SV464: $i] :
( ( ! [SY5646: $i] :
( ( c_HOL_Oord__class_Oless @ SV464 @ SV1311 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SY5646 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1311 @ SY5646 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY5646 @ SV1311 @ tc_nat )
| ~ ( c_lessequals @ SY5646 @ SV464 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(4217,plain,
! [SV1312: $i,SV465: $i] :
( ( ! [SY5647: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV465 @ SV1312 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY5647 @ SV1312 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV465 @ SY5647 @ tc_nat )
| ~ ( c_lessequals @ SV1312 @ SY5647 @ tc_nat )
| ~ ( c_lessequals @ SV1312 @ SV465 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(4218,plain,
! [SV1313: $i,SV466: $i] :
( ( ! [SY5648: $i,SY5649: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV466 )
| ( c_HOL_Oord__class_Oless @ SV1313 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ SY5648 ) @ SY5649 ) @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ SV1313 @ SY5649 @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SY5648 @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(4219,plain,
! [SV1314: $i,SV467: $i] :
( ( ! [SY5650: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV467 ) @ SV1314 @ SY5650 )
= ( c_Lambda_OdB_OVar @ SV467 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV467 @ SY5650 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3361]) ).
thf(4220,plain,
! [SV1315: $i,SV468: $i] :
( ( ! [SY5651: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV468 @ ( c_Lambda_OdB_OVar @ SV1315 ) @ SY5651 ) )
| ~ ( c_InductTermi_OIT @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3362]) ).
thf(4221,plain,
! [SV1316: $i,SV469: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV469 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV469 ) @ SV1316 ) @ SV1316 ) @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1316 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(4222,plain,
! [SV1317: $i,SV470: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV470 )
| ( c_lessequals @ SV1317 @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV470 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV470 ) @ SV1317 ) @ SV1317 ) @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV470 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3364]) ).
thf(4223,plain,
! [SV1318: $i,SV471: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV471 ) @ SV1318 ) @ SV471 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3365]) ).
thf(4224,plain,
! [SV1319: $i,SV472: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV472 ) @ SV1319 ) @ SV1319 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3366]) ).
thf(4225,plain,
! [SV1320: $i,SV473: $i] :
( ( ! [SY5652: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ SV473 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1320 @ SY5652 @ tc_nat ) @ SV473 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1320 @ SV473 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY5652 @ SV473 ) @ SV473 ) )
| ~ ( c_lessequals @ SY5652 @ SV1320 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3367]) ).
thf(4226,plain,
! [SV1321: $i,SV474: $i] :
( ( ! [SY5653: $i,SY5654: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV474 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1321 @ SY5653 @ SV474 ) @ ( c_HOL_Otimes__class_Otimes @ SY5654 @ SY5653 @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SY5653 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SY5654 @ SV1321 @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(4227,plain,
! [SV1322: $i,SV475: $i] :
( ( ! [SY5655: $i,SY5656: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV475 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SY5655 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SY5656 @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SY5656 @ SY5655 @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3369]) ).
thf(4228,plain,
! [SV1323: $i,SV476: $i] :
( ( ! [SY5657: $i,SY5658: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ SV476 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1323 @ SY5657 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SY5658 @ SY5657 @ SV476 ) @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SY5657 @ SV476 )
| ~ ( c_lessequals @ SV1323 @ SY5658 @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3370]) ).
thf(4229,plain,
! [SV1324: $i,SV477: $i] :
( ( ! [SY5659: $i,SY5660: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ SV477 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SY5659 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SY5660 @ SV477 ) @ SV477 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV477 ) @ SV1324 @ SV477 )
| ~ ( c_lessequals @ SY5659 @ SY5660 @ SV477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(4230,plain,
! [SV1325: $i,SV478: $i] :
( ( ! [SY5661: $i,SY5662: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ SV478 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SY5661 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SY5662 @ SV478 ) @ SV478 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV478 ) @ SV1325 @ SV478 )
| ~ ( c_lessequals @ SY5661 @ SY5662 @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3372]) ).
thf(4231,plain,
! [SV1326: $i,SV479: $i] :
( ( ! [SY5663: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV479 ) @ ( c_List_Olist_OCons @ SV1326 @ SY5663 @ SV479 ) @ SV479 )
= ( c_List_Olist_OCons @ SV1326 @ SY5663 @ SV479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(4232,plain,
! [SV1327: $i,SV480: $i] :
( ( ! [SY5664: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV480 ) @ SV1327 ) @ SY5664 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV480 @ ( c_HOL_Ominus__class_Ominus @ SY5664 @ SV1327 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3374]) ).
thf(4233,plain,
! [SV1328: $i,SV481: $i] :
( ( ! [SY5665: $i] :
( ( c_HOL_Oord__class_Oless @ SV481 @ ( c_HOL_Ominus__class_Ominus @ SV1328 @ SY5665 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SY5665 ) @ SV1328 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(4234,plain,
! [SV1329: $i,SV482: $i] :
( ( ! [SY5666: $i,SY5667: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV482 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SV1329 ) @ SY5666 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SY5667 ) @ SY5666 ) @ SV482 )
| ~ ( c_HOL_Oord__class_Oless @ SV1329 @ SY5667 @ SV482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3376]) ).
thf(4235,plain,
! [SV1330: $i,SV483: $i] :
( ( ! [SY5668: $i,SY5669: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV483 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SV1330 ) @ SY5668 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SY5669 ) @ SY5668 ) @ SV483 )
| ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SY5669 @ SV483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3377]) ).
thf(4236,plain,
! [SV1331: $i,SV484: $i] :
( ( ! [SY5670: $i,SY5671: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV484 )
| ( c_HOL_Oord__class_Oless @ SV1331 @ SY5670 @ SV484 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV1331 ) @ SY5671 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SY5670 ) @ SY5671 ) @ SV484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3378]) ).
thf(4237,plain,
! [SV1332: $i,SV485: $i] :
( ( ! [SY5672: $i,SY5673: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV485 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SY5672 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SY5673 ) @ SV485 )
| ~ ( c_HOL_Oord__class_Oless @ SY5672 @ SY5673 @ SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(4238,plain,
! [SV1333: $i,SV486: $i] :
( ( ! [SY5674: $i,SY5675: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV486 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SY5674 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SY5675 ) @ SV486 )
| ~ ( c_HOL_Oord__class_Oless @ SY5674 @ SY5675 @ SV486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(4239,plain,
! [SV1334: $i,SV487: $i] :
( ( ! [SY5676: $i,SY5677: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV487 )
| ( c_HOL_Oord__class_Oless @ SV1334 @ SY5676 @ SV487 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SY5677 ) @ SV1334 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SY5677 ) @ SY5676 ) @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3381]) ).
thf(4240,plain,
! [SV1335: $i,SV488: $i] :
( ( ! [SY5678: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV488 ) @ SV1335 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5678 ) @ SV1335 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV488 @ SY5678 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3382]) ).
thf(4241,plain,
! [SV1336: $i,SV489: $i] :
( ( ! [SY5679: $i] :
( ( c_HOL_Oord__class_Oless @ SV489 @ SV1336 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5679 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY5679 ) @ SV1336 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(4242,plain,
! [SV1337: $i,SV490: $i] :
( ( ! [SY5680: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV490 ) @ SV1337 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV490 ) @ SY5680 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1337 @ SY5680 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3384]) ).
thf(4243,plain,
! [SV1338: $i,SV491: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV491 @ SV1338 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1338 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV491 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3385]) ).
thf(4244,plain,
! [SV1339: $i,SV492: $i] :
( ( ! [SY5681: $i,SY5682: $i] :
( ~ ( class_Orderings_Oorder @ SV492 )
| ( c_lessequals @ SV1339 @ SY5681 @ SV492 )
| ~ ( c_lessequals @ SV1339 @ SY5682 @ SV492 )
| ~ ( c_lessequals @ SY5682 @ SY5681 @ SV492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3386]) ).
thf(4245,plain,
! [SV1340: $i,SV493: $i] :
( ( ! [SY5683: $i,SY5684: $i] :
( ~ ( class_Orderings_Oorder @ SV493 )
| ( c_HOL_Oord__class_Oless @ SV1340 @ SY5683 @ SV493 )
| ~ ( c_lessequals @ SV1340 @ SY5684 @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SY5684 @ SY5683 @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3387]) ).
thf(4246,plain,
! [SV1341: $i,SV494: $i] :
( ( ! [SY5685: $i,SY5686: $i] :
( ~ ( class_Orderings_Oorder @ SV494 )
| ( c_HOL_Oord__class_Oless @ SV1341 @ SY5685 @ SV494 )
| ~ ( c_HOL_Oord__class_Oless @ SV1341 @ SY5686 @ SV494 )
| ~ ( c_lessequals @ SY5686 @ SY5685 @ SV494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(4247,plain,
! [SV1342: $i,SV495: $i] :
( ( ! [SY5687: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV495 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1342 ) @ SY5687 ) @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
| ~ ( c_lessequals @ SY5687 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
| ~ ( c_lessequals @ SV1342 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(4248,plain,
! [SV1343: $i,SV496: $i] :
( ( ! [SY5688: $i,SY5689: $i] :
( ~ ( class_Orderings_Opreorder @ SV496 )
| ( c_lessequals @ SV1343 @ SY5688 @ SV496 )
| ~ ( c_lessequals @ SY5689 @ SY5688 @ SV496 )
| ~ ( c_lessequals @ SV1343 @ SY5689 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3390]) ).
thf(4249,plain,
! [SV1344: $i,SV498: $i] :
( ( ! [SY5690: $i] :
( ( c_lessequals @ SV498 @ SV1344 @ tc_nat )
| ~ ( c_lessequals @ SY5690 @ SV1344 @ tc_nat )
| ~ ( c_lessequals @ SV498 @ SY5690 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(4250,plain,
! [SV1345: $i,SV500: $i] :
( ( ( c_Orderings_Oord__class_Omin @ ( c_Suc @ SV500 ) @ ( c_Suc @ SV1345 ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omin @ SV500 @ SV1345 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(4251,plain,
! [SV1346: $i,SV501: $i] :
( ( ( SV501
= ( c_Suc @ SV1346 ) )
| ( c_lessequals @ SV501 @ SV1346 @ tc_nat )
| ~ ( c_lessequals @ SV501 @ ( c_Suc @ SV1346 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(4252,plain,
! [SV502: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV502 @ SV502 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV502 @ ( c_Suc @ SV502 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(4253,plain,
! [SV1347: $i,SV503: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV503 @ SV1347 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1347 @ ( c_Suc @ SV503 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(4254,plain,
! [SV1348: $i,SV504: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV504 @ ( c_Suc @ SV1348 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1348 @ SV504 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3398]) ).
thf(4255,plain,
! [SV1349: $i,SV505: $i] :
( ( ! [SY5691: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV1349 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5691 @ SV1349 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV505 @ SY5691 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1349 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(4256,plain,
! [SV1350: $i,SV506: $i] :
( ( ! [SY5692: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV1350 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SY5692 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1350 @ SY5692 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV506 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3400]) ).
thf(4257,plain,
! [SV1351: $i,SV507: $i] :
( ( ! [SY5693: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SV1351 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SY5693 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV507 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1351 @ SY5693 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(4258,plain,
! [SV1352: $i,SV508: $i] :
( ( ! [SY5694: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV508 @ SV1352 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5694 @ SV1352 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1352 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV508 @ SY5694 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(4259,plain,
! [SV1353: $i,SV509: $i] :
( ( ! [SY5695: $i] :
( ( c_HOL_Oord__class_Oless @ SV509 @ SV1353 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY5695 @ SV509 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5695 @ SV1353 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5695 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3403]) ).
thf(4260,plain,
! [SV1354: $i,SV510: $i] :
( ( ! [SY5696: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SV1354 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SY5696 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1354 @ SY5696 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV510 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(4261,plain,
! [SV1355: $i,SV511: $i] :
( ( ! [SY5697: $i,SY5698: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV511 )
| ( c_HOL_Oord__class_Oless @ SV1355 @ SY5697 @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY5698 @ SY5697 @ SV511 ) @ ( c_HOL_Otimes__class_Otimes @ SY5698 @ SV1355 @ SV511 ) @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ SY5698 @ ( c_HOL_Ozero__class_Ozero @ SV511 ) @ SV511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(4262,plain,
! [SV1356: $i,SV512: $i] :
( ( ! [SY5699: $i,SY5700: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV512 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SY5699 @ SV512 ) @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SY5700 @ SV512 ) @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SY5700 @ SY5699 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SV1356 @ ( c_HOL_Ozero__class_Ozero @ SV512 ) @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(4263,plain,
! [SV1357: $i,SV513: $i] :
( ( ! [SY5701: $i,SY5702: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV513 )
| ( c_HOL_Oord__class_Oless @ SV1357 @ SY5701 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY5702 @ SV1357 @ SV513 ) @ ( c_HOL_Otimes__class_Otimes @ SY5702 @ SY5701 @ SV513 ) @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV513 ) @ SY5702 @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(4264,plain,
! [SV1358: $i,SV514: $i] :
( ( ! [SY5703: $i,SY5704: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV514 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SY5703 @ SV514 ) @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SY5704 @ SV514 ) @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ SY5703 @ SY5704 @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SV1358 @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3408]) ).
thf(4265,plain,
! [SV1359: $i,SV515: $i] :
( ( ! [SY5705: $i,SY5706: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV515 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SY5705 @ SV515 ) @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SY5706 @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SV1359 @ ( c_HOL_Ozero__class_Ozero @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SY5706 @ SY5705 @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3409]) ).
thf(4266,plain,
! [SV1360: $i,SV516: $i] :
( ( ! [SY5707: $i,SY5708: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV516 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SY5707 @ SV516 ) @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SY5708 @ SV516 ) @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV516 ) @ SV1360 @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ SY5707 @ SY5708 @ SV516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(4267,plain,
! [SV1361: $i,SV517: $i] :
( ( ! [SY5709: $i,SY5710: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV517 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SY5709 @ SV517 ) @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SY5710 @ SV517 ) @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ SY5709 @ SY5710 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1361 @ SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(4268,plain,
! [SV1362: $i,SV518: $i] :
( ( ! [SY5711: $i,SY5712: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV518 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SY5711 @ SV518 ) @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SY5712 @ SV518 ) @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SY5712 @ SY5711 @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SV1362 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(4269,plain,
! [SV1363: $i,SV519: $i] :
( ( ! [SY5713: $i,SY5714: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV519 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1363 @ SY5713 @ SV519 ) @ ( c_HOL_Otimes__class_Otimes @ SY5714 @ SY5713 @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SY5713 @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SY5714 @ SV1363 @ SV519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(4270,plain,
! [SV1364: $i,SV520: $i] :
( ( ! [SY5715: $i,SY5716: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV520 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1364 @ SY5715 @ SV520 ) @ ( c_HOL_Otimes__class_Otimes @ SY5716 @ SY5715 @ SV520 ) @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SY5715 @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ SV1364 @ SY5716 @ SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3414]) ).
thf(4271,plain,
! [SV1365: $i,SV521: $i] :
( ( ! [SY5717: $i,SY5718: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV521 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1365 @ SY5717 @ SV521 ) @ ( c_HOL_Otimes__class_Otimes @ SY5718 @ SY5717 @ SV521 ) @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ SV1365 @ SY5718 @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV521 ) @ SY5717 @ SV521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3415]) ).
thf(4272,plain,
! [SV1366: $i,SV522: $i] :
( ( ! [SY5719: $i,SY5720: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV522 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1366 @ SY5719 @ SV522 ) @ ( c_HOL_Otimes__class_Otimes @ SY5720 @ SY5719 @ SV522 ) @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SY5720 @ SV1366 @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SY5719 @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3416]) ).
thf(4273,plain,
! [SV1367: $i,SV523: $i] :
( ( ! [SY5721: $i,SY5722: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV523 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SY5721 @ SV523 ) @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SY5722 @ SV523 ) @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV1367 @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ SY5721 @ SY5722 @ SV523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(4274,plain,
! [SV1368: $i,SV524: $i] :
( ( ! [SY5723: $i] :
( ( c_List_Olist_OCons @ SV524 @ SV1368 @ SY5723 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY5723 ) @ ( c_List_Olist_OCons @ SV524 @ SV1368 @ SY5723 ) @ SY5723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(4275,plain,
! [SV1369: $i,SV525: $i] :
( ( ! [SY5724: $i,SY5725: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV525 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ ( c_Orderings_Oord__class_Omax @ SV1369 @ SY5724 @ SV525 ) ) @ SY5725 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ SV1369 ) @ SY5725 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ SY5724 ) @ SY5725 ) @ SV525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(4276,plain,
! [SV1370: $i,SV526: $i] :
( ( ( c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV526 ) @ ( c_Lambda_OdB_OVar @ SV1370 ) ) )
| ~ ( c_InductTermi_OIT @ SV526 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(4277,plain,
! [SV1371: $i,SV527: $i] :
( ( ! [SY5726: $i,SY5727: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV527 @ SV1371 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5726 @ SY5727 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1371 @ SY5727 @ tc_nat )
| ~ ( c_lessequals @ SV527 @ SY5726 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(4278,plain,
! [SV1372: $i,SV529: $i] :
( ( ! [SY5728: $i,SY5729: $i,SY5730: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV529 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SY5728 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SY5729 @ SY5730 @ SV529 ) @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SY5728 @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SY5729 @ SV529 )
| ~ ( c_lessequals @ SY5728 @ SY5730 @ SV529 )
| ~ ( c_lessequals @ SV1372 @ SY5729 @ SV529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(4279,plain,
! [SV1373: $i,SV530: $i] :
( ( ! [SY5731: $i,SY5732: $i,SY5733: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV530 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SY5731 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SY5732 @ SY5733 @ SV530 ) @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SY5731 @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
| ~ ( c_lessequals @ SY5731 @ SY5733 @ SV530 )
| ~ ( c_lessequals @ SV1373 @ SY5732 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(4280,plain,
! [SV1374: $i,SV531: $i] :
( ( ! [SY5734: $i,SY5735: $i] :
( ~ ( class_Orderings_Olinorder @ SV531 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV1374 @ SY5734 @ SV531 ) @ SY5735 @ SV531 )
= ( c_Orderings_Oord__class_Omax @ SV1374 @ ( c_Orderings_Oord__class_Omax @ SY5734 @ SY5735 @ SV531 ) @ SV531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3425]) ).
thf(4281,plain,
! [SV1375: $i,SV532: $i] :
( ( ! [SY5736: $i,SY5737: $i] :
( ~ ( class_Orderings_Olinorder @ SV532 )
| ( ( c_Orderings_Oord__class_Omax @ SV1375 @ ( c_Orderings_Oord__class_Omax @ SY5736 @ SY5737 @ SV532 ) @ SV532 )
= ( c_Orderings_Oord__class_Omax @ SY5736 @ ( c_Orderings_Oord__class_Omax @ SV1375 @ SY5737 @ SV532 ) @ SV532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3426]) ).
thf(4282,plain,
! [SV1376: $i,SV534: $i] :
( ( ! [SY5738: $i,SY5739: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV534 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV534 ) @ ( c_HOL_Otimes__class_Otimes @ SV1376 @ SY5738 @ SV534 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY5739 @ SY5738 @ SV534 ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV534 ) @ SV1376 ) @ SY5739 ) @ SY5738 @ SV534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(4283,plain,
! [SV1377: $i,SV535: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV535 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV535 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1377 @ SV535 ) @ SV535 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(4284,plain,
! [SV1378: $i,SV536: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV536 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1378 @ SV536 ) @ SV536 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(4285,plain,
! [SV537: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV537 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV537 ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV537 ) ) @ SV537 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3431]) ).
thf(4286,plain,
! [SV1379: $i,SV538: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV538 ) @ ( c_Lambda_OdB_OAbs @ SV1379 ) )
| ~ ( c_Lambda_Obeta @ SV538 @ SV1379 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3432]) ).
thf(4287,plain,
! [SV1380: $i,SV539: $i] :
( ( ! [SY5740: $i] :
( ~ ( class_Orderings_Olinorder @ SV539 )
| ( ( c_Orderings_Oord__class_Omax @ SV1380 @ ( c_Orderings_Oord__class_Omax @ SV1380 @ SY5740 @ SV539 ) @ SV539 )
= ( c_Orderings_Oord__class_Omax @ SV1380 @ SY5740 @ SV539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(4288,plain,
! [SV1381: $i,SV540: $i] :
( ( ! [SY5741: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV540 @ SV1381 @ SY5741 ) @ ( c_List_Olist_OCons @ SV1381 @ ( c_List_Olist_ONil @ SY5741 ) @ SY5741 ) @ SY5741 )
= ( c_List_Olist_OCons @ SV1381 @ ( c_List_Oreplicate @ SV540 @ SV1381 @ SY5741 ) @ SY5741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(4289,plain,
! [SV1382: $i,SV541: $i] :
( ( ! [SY5742: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV541 )
| ( c_lessequals @ SV1382 @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV541 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV1382 @ SV541 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SY5742 @ SV541 ) @ SV541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(4290,plain,
! [SV1383: $i,SV542: $i] :
( ( ! [SY5743: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV542 )
| ( c_lessequals @ SV1383 @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV542 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SY5743 @ SV542 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ ( c_HOL_Otimes__class_Otimes @ SY5743 @ SV1383 @ SV542 ) @ SV542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(4291,plain,
! [SV1384: $i,SV543: $i] :
( ( ! [SY5744: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV543 )
| ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV543 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SY5744 @ SV543 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ ( c_HOL_Otimes__class_Otimes @ SV1384 @ SY5744 @ SV543 ) @ SV543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3437]) ).
thf(4292,plain,
! [SV1385: $i,SV544: $i] :
( ( ! [SY5745: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV544 )
| ( c_lessequals @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV544 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV1385 @ SV544 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ ( c_HOL_Otimes__class_Otimes @ SY5745 @ SV1385 @ SV544 ) @ SV544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3438]) ).
thf(4293,plain,
! [SV1386: $i,SV545: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV545 ) @ SV1386 ) @ SV1386 @ tc_nat )
= SV545 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3439]) ).
thf(4294,plain,
! [SV1387: $i,SV546: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV546 ) @ SV1387 ) @ SV546 @ tc_nat )
= SV1387 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3440]) ).
thf(4295,plain,
! [SV1388: $i,SV547: $i] :
( ( ! [SY5746: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV547 )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV547 ) @ SV1388 ) @ SY5746 ) @ SY5746 @ SV547 )
= SV1388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3441]) ).
thf(4296,plain,
! [SV1389: $i,SV548: $i] :
( ( ! [SY5747: $i,SY5748: $i,SY5749: $i,SY5750: $i] :
( ( c_List_Ofoldl @ SV548 @ SV1389 @ ( c_List_Oappend @ SY5747 @ SY5748 @ SY5749 ) @ SY5750 @ SY5749 )
= ( c_List_Ofoldl @ SV548 @ ( c_List_Ofoldl @ SV548 @ SV1389 @ SY5747 @ SY5750 @ SY5749 ) @ SY5748 @ SY5750 @ SY5749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3442]) ).
thf(4297,plain,
! [SV1390: $i,SV549: $i] :
( ( ! [SY5751: $i,SY5752: $i] :
( ( c_Type_Otype_Otype__case @ SV549 @ SV1390 @ ( c_Type_Otype_OAtom @ SY5751 ) @ SY5752 )
= ( hAPP @ SV549 @ SY5751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3443]) ).
thf(4298,plain,
! [SV1391: $i,SV550: $i] :
( ( ! [SY5753: $i,SY5754: $i,SY5755: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV550 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV1391 ) @ SY5753 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SY5754 ) @ SY5755 ) @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SY5753 @ SY5755 @ SV550 )
| ~ ( c_lessequals @ SV1391 @ SY5754 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3444]) ).
thf(4299,plain,
! [SV1392: $i,SV551: $i] :
( ( ! [SY5756: $i,SY5757: $i,SY5758: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV551 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV1392 ) @ SY5756 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SY5757 ) @ SY5758 ) @ SV551 )
| ~ ( c_lessequals @ SY5756 @ SY5758 @ SV551 )
| ~ ( c_HOL_Oord__class_Oless @ SV1392 @ SY5757 @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3445]) ).
thf(4300,plain,
! [SV1393: $i,SV552: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV552 ) @ ( c_Suc @ SV1393 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV552 @ SV1393 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3446]) ).
thf(4301,plain,
! [SV1394: $i,SV553: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV553 @ SV1394 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV553 ) @ ( c_Suc @ SV1394 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3447]) ).
thf(4302,plain,
! [SV1395: $i,SV554: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV554 ) @ ( c_Suc @ SV1395 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV554 @ SV1395 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3448]) ).
thf(4303,plain,
! [SV1396: $i,SV555: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV555 ) @ SV1396 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1396 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3449]) ).
thf(4304,plain,
! [SV1397: $i,SV556: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV556 ) @ SV1397 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV556 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3450]) ).
thf(4305,plain,
! [SV1398: $i,SV557: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV557 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV557 ) @ SV1398 @ SV557 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV557 ) @ SV1398 ) @ SV1398 ) @ SV557 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3451]) ).
thf(4306,plain,
! [SV1399: $i,SV558: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV558 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV558 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV558 ) @ SV1399 ) @ SV1399 ) @ SV558 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV558 ) @ SV1399 @ SV558 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3452]) ).
thf(4307,plain,
! [SV1400: $i,SV559: $i] :
( ( ! [SY5759: $i] :
( ( SV559
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV559 @ SV1400 @ SY5759 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV559 @ SV1400 @ SY5759 ) ) )
| ~ ( c_Type_Otyping @ SV1400 @ ( c_Lambda_OdB_OAbs @ SY5759 ) @ SV559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3453]) ).
thf(4308,plain,
! [SV1401: $i,SV560: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV560 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV560 ) @ SV1401 @ SV560 )
= ( c_HOL_Ozero__class_Ozero @ SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(4309,plain,
! [SV1402: $i,SV561: $i] :
( ( ~ ( class_Ring__and__Field_Omult__zero @ SV561 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV1402 @ SV561 )
= ( c_HOL_Ozero__class_Ozero @ SV561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3455]) ).
thf(4310,plain,
! [SV1403: $i,SV562: $i] :
( ( ~ ( class_Ring__and__Field_Omult__zero @ SV562 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1403 @ ( c_HOL_Ozero__class_Ozero @ SV562 ) @ SV562 )
= ( c_HOL_Ozero__class_Ozero @ SV562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3456]) ).
thf(4311,plain,
! [SV1404: $i,SV563: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV563 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV563 ) @ SV1404 @ SV563 )
= ( c_HOL_Ozero__class_Ozero @ SV563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3457]) ).
thf(4312,plain,
! [SV1405: $i,SV564: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV564 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1405 @ ( c_HOL_Ozero__class_Ozero @ SV564 ) @ SV564 )
= ( c_HOL_Ozero__class_Ozero @ SV564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(4313,plain,
! [SV1406: $i,SV565: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV565 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1406 @ ( c_HOL_Ozero__class_Ozero @ SV565 ) @ SV565 )
= ( c_HOL_Ozero__class_Ozero @ SV565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(4314,plain,
! [SV1407: $i,SV566: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV566 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV566 ) @ SV1407 @ SV566 )
= ( c_HOL_Ozero__class_Ozero @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(4315,plain,
! [SV1408: $i,SV567: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV567 )
| ~ ( class_Int_Onumber__ring @ SV567 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1408 @ SV1408 @ SV567 )
= ( c_HOL_Ozero__class_Ozero @ SV567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3461]) ).
thf(4316,plain,
! [SV1409: $i,SV568: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV568 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1409 @ SV1409 @ SV568 )
= ( c_HOL_Ozero__class_Ozero @ SV568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3462]) ).
thf(4317,plain,
! [SV1410: $i,SV569: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV569 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1410 @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SV569 )
= SV1410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(4318,plain,
! [SV1411: $i,SV570: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV570 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1411 @ SV1411 @ SV570 )
= ( c_HOL_Ozero__class_Ozero @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3464]) ).
thf(4319,plain,
! [SV1412: $i,SV571: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV571 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1412 @ SV1412 @ SV571 )
= ( c_HOL_Ozero__class_Ozero @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(4320,plain,
! [SV572: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV572 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV572 ) @ ( c_HOL_Ozero__class_Ozero @ SV572 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV572 ) )
= ( c_HOL_Ozero__class_Ozero @ SV572 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3466]) ).
thf(4321,plain,
! [SV1413: $i,SV573: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV573 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV573 ) @ ( c_HOL_Ozero__class_Ozero @ SV573 ) ) @ SV1413 )
= SV1413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(4322,plain,
! [SV1414: $i,SV574: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV574 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV574 ) @ ( c_HOL_Ozero__class_Ozero @ SV574 ) ) @ SV1414 )
= SV1414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(4323,plain,
! [SV1415: $i,SV575: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV575 )
| ~ ( class_Int_Onumber__ring @ SV575 )
| ( SV1415
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1415 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(4324,plain,
! [SV1416: $i,SV576: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV576 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SV1416 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) )
= SV1416 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3470]) ).
thf(4325,plain,
! [SV1417: $i,SV577: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV577 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV577 ) @ ( c_HOL_Ozero__class_Ozero @ SV577 ) ) @ SV1417 )
= SV1417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3471]) ).
thf(4326,plain,
! [SV1418: $i,SV578: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV578 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV578 ) @ SV1418 ) @ ( c_HOL_Ozero__class_Ozero @ SV578 ) )
= SV1418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3472]) ).
thf(4327,plain,
! [SV1419: $i,SV579: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV579 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV579 ) @ SV1419 ) @ ( c_HOL_Ozero__class_Ozero @ SV579 ) )
= SV1419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3473]) ).
thf(4328,plain,
! [SV1420: $i,SV580: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV580 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV580 ) @ ( c_HOL_Ozero__class_Ozero @ SV580 ) ) @ SV1420 )
= SV1420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3474]) ).
thf(4329,plain,
! [SV1421: $i,SV581: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV581 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV1421 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3475]) ).
thf(4330,plain,
! [SV1422: $i,SV582: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV582 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1422 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(4331,plain,
! [SV583: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV583 @ tc_nat )
= $true )
| ( ( SV583
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3478]) ).
thf(4332,plain,
! [SV1423: $i,SV584: $i] :
( ( ~ ( class_Orderings_Oorder @ SV584 )
| ( c_lessequals @ SV1423 @ SV1423 @ SV584 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(4333,plain,
! [SV1424: $i,SV585: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV585 )
| ( c_lessequals @ SV1424 @ SV1424 @ SV585 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3480]) ).
thf(4334,plain,
! [SV1425: $i,SV586: $i] :
( ( ! [SY5760: $i,SY5761: $i] :
( ~ ( class_Orderings_Opreorder @ SV586 )
| ( c_HOL_Oord__class_Oless @ SV1425 @ SY5760 @ SV586 )
| ~ ( c_HOL_Oord__class_Oless @ SY5761 @ SY5760 @ SV586 )
| ~ ( c_lessequals @ SV1425 @ SY5761 @ SV586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(4335,plain,
! [SV1426: $i,SV587: $i] :
( ( ! [SY5762: $i,SY5763: $i] :
( ~ ( class_Orderings_Opreorder @ SV587 )
| ( c_HOL_Oord__class_Oless @ SV1426 @ SY5762 @ SV587 )
| ~ ( c_lessequals @ SY5763 @ SY5762 @ SV587 )
| ~ ( c_HOL_Oord__class_Oless @ SV1426 @ SY5763 @ SV587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3482]) ).
thf(4336,plain,
! [SV1427: $i,SV588: $i] :
( ( ! [SY5764: $i,SY5765: $i,SY5766: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV588 )
| ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SY5764 ) @ SY5765 ) @ SV588 )
| ~ ( c_lessequals @ SY5766 @ SY5765 @ SV588 )
| ~ ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SY5764 ) @ SY5766 ) @ SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3483]) ).
thf(4337,plain,
! [SV1428: $i,SV589: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV589 ) @ SV1428 @ SV589 )
= SV1428 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(4338,plain,
! [SV1429: $i,SV590: $i] :
( ( ! [SY5767: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV590 @ SV1429 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY5767 @ SV1429 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV590 @ SY5767 @ tc_nat ) @ SV1429 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3485]) ).
thf(4339,plain,
! [SV1430: $i,SV591: $i] :
( ( ! [SY5768: $i] :
( ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1430 @ SY5768 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ominus__class_Ominus @ SV1430 @ SY5768 @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3486]) ).
thf(4340,plain,
! [SV1431: $i,SV592: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV592 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1431 @ SV1431 @ SV592 )
= SV1431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3487]) ).
thf(4341,plain,
! [SV1432: $i,SV593: $i] :
( ( ! [SY5769: $i] :
( ~ ( hBOOL @ ( hAPP @ SV593 @ SV1432 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1432 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV593 @ SY5769 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV593 @ SY5769 ) )
| ( hBOOL @ ( hAPP @ SV593 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3488]) ).
thf(4342,plain,
! [SV1433: $i,SV594: $i] :
( ( ! [SY5770: $i,SY5771: $i,SY5772: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SY5770 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SY5771 @ SY5772 @ SV594 ) @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SY5770 @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SY5770 @ SY5772 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SY5771 @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(4343,plain,
! [SV1434: $i,SV595: $i] :
( ( ( SV595 = SV1434 )
| ~ ( c_HOL_Oord__class_Oless @ SV595 @ ( c_Suc @ SV1434 ) @ tc_nat )
| ~ ( c_lessequals @ SV1434 @ SV595 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3490]) ).
thf(4344,plain,
! [SV1435: $i,SV596: $i] :
( ( ! [SY5773: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV596 @ SV1435 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5773 @ SV1435 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV596 @ SY5773 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3491]) ).
thf(4345,plain,
! [SV1436: $i,SV597: $i] :
( ( ! [SY5774: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV597 @ SV1436 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV597 @ SY5774 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1436 @ SY5774 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3492]) ).
thf(4346,plain,
! [SV1437: $i,SV598: $i] :
( ( ! [SY5775: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV598 @ SV1437 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV598 @ SY5775 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1437 @ SY5775 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3493]) ).
thf(4347,plain,
! [SV1438: $i,SV599: $i] :
( ( ! [SY5776: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV599 @ SV1438 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5776 @ SV1438 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV599 @ SY5776 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3494]) ).
thf(4348,plain,
! [SV1439: $i,SV600: $i] :
( ( ! [SY5777: $i,SY5778: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV600 @ SV1439 @ SY5777 ) @ ( c_List_Olist_OCons @ SV1439 @ SY5778 @ SY5777 ) @ SY5777 )
= ( c_List_Olist_OCons @ SV1439 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV600 @ SV1439 @ SY5777 ) @ SY5778 @ SY5777 ) @ SY5777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(4349,plain,
! [SV1440: $i,SV601: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV601 @ SV1440 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1440 @ SV601 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3496]) ).
thf(4350,plain,
! [SV1441: $i,SV602: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV602 @ SV1441 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1441 @ SV602 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(4351,plain,
! [SV1442: $i,SV603: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV603 @ SV1442 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV603 ) @ SV1442 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3498]) ).
thf(4352,plain,
! [SV1443: $i,SV604: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV604 @ ( c_Suc @ SV1443 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV604 @ SV1443 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(4353,plain,
! [SV605: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV605 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV605 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV605 ) @ ( c_HOL_Ozero__class_Ozero @ SV605 ) @ SV605 ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV605 ) @ ( c_HOL_Ozero__class_Ozero @ SV605 ) @ SV605 ) )
= ( c_HOL_Ozero__class_Ozero @ SV605 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3500]) ).
thf(4354,plain,
! [SV1444: $i,SV606: $i] :
( ( ! [SY5779: $i,SY5780: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV606 )
| ( c_HOL_Oord__class_Oless @ SV1444 @ ( c_HOL_Ozero__class_Ozero @ SV606 ) @ SV606 )
| ( c_HOL_Oord__class_Oless @ SY5779 @ SY5780 @ SV606 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY5779 @ SV1444 @ SV606 ) @ ( c_HOL_Otimes__class_Otimes @ SY5780 @ SV1444 @ SV606 ) @ SV606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(4355,plain,
! [SV1445: $i,SV607: $i] :
( ( ! [SY5781: $i,SY5782: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV607 )
| ( c_HOL_Oord__class_Oless @ SV1445 @ SY5781 @ SV607 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV607 ) @ SY5782 @ SV607 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY5781 @ SY5782 @ SV607 ) @ ( c_HOL_Otimes__class_Otimes @ SV1445 @ SY5782 @ SV607 ) @ SV607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3502]) ).
thf(4356,plain,
! [SV1446: $i,SV608: $i] :
( ( ! [SY5783: $i,SY5784: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV608 )
| ( c_HOL_Oord__class_Oless @ SV1446 @ ( c_HOL_Ozero__class_Ozero @ SV608 ) @ SV608 )
| ( c_HOL_Oord__class_Oless @ SY5783 @ SY5784 @ SV608 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SY5783 @ SV608 ) @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SY5784 @ SV608 ) @ SV608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3503]) ).
thf(4357,plain,
! [SV1447: $i,SV609: $i] :
( ( ! [SY5785: $i,SY5786: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV609 )
| ( c_HOL_Oord__class_Oless @ SV1447 @ SY5785 @ SV609 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV609 ) @ SY5786 @ SV609 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY5786 @ SY5785 @ SV609 ) @ ( c_HOL_Otimes__class_Otimes @ SY5786 @ SV1447 @ SV609 ) @ SV609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3504]) ).
thf(4358,plain,
! [SV1448: $i,SV610: $i] :
( ( ! [SY5787: $i,SY5788: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV610 ) @ SV1448 ) @ SY5787 @ SY5788 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV610 @ SY5787 @ SY5788 ) ) @ ( c_Lambda_Osubst @ SV1448 @ SY5787 @ SY5788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3505]) ).
thf(4359,plain,
! [SV611: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV611 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV611 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV611 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3506]) ).
thf(4360,plain,
! [SV1449: $i,SV612: $i] :
( ( ! [SY5789: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV612 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1449 ) @ SY5789 ) @ SV612 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV612 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1449 @ SV612 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY5789 @ SV612 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3507]) ).
thf(4361,plain,
! [SV1450: $i,SV613: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV613 @ SV1450 @ tc_nat ) @ SV613 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV613 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1450 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(4362,plain,
! [SV1451: $i,SV614: $i] :
( ( ! [SY5790: $i,SY5791: $i] :
( ~ ( class_Orderings_Olinorder @ SV614 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1451 @ ( c_Orderings_Oord__class_Omin @ SY5790 @ SY5791 @ SV614 ) @ SV614 ) @ ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1451 @ SY5790 @ SV614 ) @ ( c_Orderings_Oord__class_Omax @ SV1451 @ SY5791 @ SV614 ) @ SV614 ) @ SV614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3509]) ).
thf(4363,plain,
! [SV1452: $i,SV615: $i] :
( ( ! [SY5792: $i,SY5793: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV615 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV1452 @ SY5792 @ SV615 ) @ SY5793 @ SV615 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1452 @ SY5793 @ SV615 ) @ ( c_Power_Opower__class_Opower @ SY5792 @ SY5793 @ SV615 ) @ SV615 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3510]) ).
thf(4364,plain,
! [SV1453: $i,SV616: $i] :
( ( ! [SY5794: $i,SY5795: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV616 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV1453 @ SY5794 @ SV616 ) @ SY5795 @ SV616 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1453 @ SY5795 @ SV616 ) @ ( c_Power_Opower__class_Opower @ SY5794 @ SY5795 @ SV616 ) @ SV616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3511]) ).
thf(4365,plain,
! [SV1454: $i,SV617: $i] :
( ( ! [SY5796: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV617 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SV1454 @ SY5796 @ SV617 ) @ SV617 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ ( c_List_Olistsum @ SV1454 @ SV617 ) ) @ ( c_List_Olistsum @ SY5796 @ SV617 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3512]) ).
thf(4366,plain,
! [SV1455: $i,SV618: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV618 ) @ ( c_HOL_Ominus__class_Ominus @ SV1455 @ SV618 @ tc_nat ) )
= SV1455 )
| ( c_HOL_Oord__class_Oless @ SV1455 @ SV618 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3513]) ).
thf(4367,plain,
! [SV1456: $i,SV619: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV619 @ ( c_Suc @ SV1456 ) @ tc_nat ) @ SV619 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV619 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3514]) ).
thf(4368,plain,
! [SV1457: $i,SV620: $i] :
( ( ! [SY5797: $i,SY5798: $i] :
( ~ ( class_Orderings_Olinorder @ SV620 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV1457 @ SY5797 @ SV620 ) @ SY5798 @ SV620 )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1457 @ SY5798 @ SV620 ) @ ( c_Orderings_Oord__class_Omax @ SY5797 @ SY5798 @ SV620 ) @ SV620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3515]) ).
thf(4369,plain,
! [SV1458: $i,SV621: $i] :
( ( ! [SY5799: $i,SY5800: $i] :
( ~ ( class_Orderings_Olinorder @ SV621 )
| ( ( c_Orderings_Oord__class_Omax @ SV1458 @ ( c_Orderings_Oord__class_Omin @ SY5799 @ SY5800 @ SV621 ) @ SV621 )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1458 @ SY5799 @ SV621 ) @ ( c_Orderings_Oord__class_Omax @ SV1458 @ SY5800 @ SV621 ) @ SV621 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3516]) ).
thf(4370,plain,
! [SV1459: $i,SV622: $i] :
( ( ! [SY5801: $i,SY5802: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV622 )
| ( ( c_Power_Opower__class_Opower @ SV1459 @ ( c_HOL_Otimes__class_Otimes @ SY5801 @ SY5802 @ tc_nat ) @ SV622 )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV1459 @ SY5801 @ SV622 ) @ SY5802 @ SV622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3517]) ).
thf(4371,plain,
! [SV1460: $i,SV623: $i] :
( ( ! [SY5803: $i] :
( ~ ( class_Orderings_Oorder @ SV623 )
| ( c_HOL_Oord__class_Oless @ SV1460 @ SY5803 @ SV623 )
| ( SY5803 = SV1460 )
| ~ ( c_lessequals @ SV1460 @ SY5803 @ SV623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3518]) ).
thf(4372,plain,
! [SV1461: $i,SV624: $i] :
( ( ! [SY5804: $i] :
( ~ ( class_Orderings_Oorder @ SV624 )
| ( c_HOL_Oord__class_Oless @ SV1461 @ SY5804 @ SV624 )
| ~ ( c_lessequals @ SV1461 @ SY5804 @ SV624 )
| ( SY5804 = SV1461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(4373,plain,
! [SV1462: $i,SV625: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV625 @ SV1462 @ tc_nat )
| ( SV625 = SV1462 )
| ~ ( c_lessequals @ SV625 @ SV1462 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3520]) ).
thf(4374,plain,
! [SV1463: $i,SV626: $i] :
( ( ( SV626 = SV1463 )
| ( c_HOL_Oord__class_Oless @ SV626 @ SV1463 @ tc_nat )
| ~ ( c_lessequals @ SV626 @ SV1463 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(4375,plain,
! [SV1464: $i,SV627: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV627 @ SV1464 @ tc_nat )
| ( SV627 = SV1464 )
| ~ ( c_lessequals @ SV627 @ SV1464 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3522]) ).
thf(4376,plain,
! [SV1465: $i,SV628: $i] :
( ( ! [SY5805: $i] :
( ~ ( class_Orderings_Oorder @ SV628 )
| ( SV1465 = SY5805 )
| ( c_HOL_Oord__class_Oless @ SV1465 @ SY5805 @ SV628 )
| ~ ( c_lessequals @ SV1465 @ SY5805 @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3523]) ).
thf(4377,plain,
! [SV1466: $i,SV629: $i] :
( ( ! [SY5806: $i] :
( ~ ( class_Orderings_Oorder @ SV629 )
| ( c_HOL_Oord__class_Oless @ SV1466 @ SY5806 @ SV629 )
| ( SV1466 = SY5806 )
| ~ ( c_lessequals @ SV1466 @ SY5806 @ SV629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(4378,plain,
! [SV1467: $i,SV630: $i] :
( ( ! [SY5807: $i] :
( ~ ( class_Orderings_Oorder @ SV630 )
| ( c_HOL_Oord__class_Oless @ SV1467 @ SY5807 @ SV630 )
| ( SV1467 = SY5807 )
| ~ ( c_lessequals @ SV1467 @ SY5807 @ SV630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3525]) ).
thf(4379,plain,
! [SV1468: $i,SV631: $i] :
( ( ! [SY5808: $i] :
( ~ ( class_Orderings_Oorder @ SV631 )
| ( c_HOL_Oord__class_Oless @ SV1468 @ SY5808 @ SV631 )
| ~ ( c_lessequals @ SV1468 @ SY5808 @ SV631 )
| ( SV1468 = SY5808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(4380,plain,
! [SV1469: $i,SV632: $i] :
( ( ! [SY5809: $i] :
( ~ ( class_Orderings_Olinorder @ SV632 )
| ( SV1469 = SY5809 )
| ~ ( c_lessequals @ SV1469 @ SY5809 @ SV632 )
| ( c_HOL_Oord__class_Oless @ SV1469 @ SY5809 @ SV632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(4381,plain,
! [SV1470: $i,SV633: $i] :
( ( ! [SY5810: $i] :
( ~ ( class_Orderings_Olinorder @ SV633 )
| ( SV1470 = SY5810 )
| ( c_HOL_Oord__class_Oless @ SV1470 @ SY5810 @ SV633 )
| ~ ( c_lessequals @ SV1470 @ SY5810 @ SV633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3528]) ).
thf(4382,plain,
! [SV1471: $i,SV634: $i] :
( ( ! [SY5811: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV634 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ ( c_HOL_Otimes__class_Otimes @ SV1471 @ SY5811 @ SV634 ) @ SV634 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SY5811 @ SV634 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV1471 @ SV634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3529]) ).
thf(4383,plain,
! [SV1472: $i,SV635: $i] :
( ( ! [SY5812: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV635 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ ( c_HOL_Otimes__class_Otimes @ SV1472 @ SY5812 @ SV635 ) @ SV635 )
| ~ ( c_lessequals @ SY5812 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 )
| ~ ( c_lessequals @ SV1472 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3530]) ).
thf(4384,plain,
! [SV1473: $i,SV636: $i] :
( ( ! [SY5813: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV636 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ ( c_HOL_Otimes__class_Otimes @ SV1473 @ SY5813 @ SV636 ) @ SV636 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SY5813 @ SV636 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV1473 @ SV636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3531]) ).
thf(4385,plain,
! [SV1474: $i,SV637: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV637 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV637 ) @ ( c_HOL_Otimes__class_Otimes @ SV1474 @ SV1474 @ SV637 ) @ SV637 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3532]) ).
thf(4386,plain,
! [SV1475: $i,SV638: $i] :
( ( ! [SY5814: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV638 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ ( c_HOL_Otimes__class_Otimes @ SV1475 @ SY5814 @ SV638 ) @ SV638 )
| ~ ( c_lessequals @ SY5814 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 )
| ~ ( c_lessequals @ SV1475 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(4387,plain,
! [SV1476: $i,SV639: $i] :
( ( ! [SY5815: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV639 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ ( c_HOL_Otimes__class_Otimes @ SV1476 @ SY5815 @ SV639 ) @ SV639 )
| ~ ( c_lessequals @ SY5815 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 )
| ~ ( c_lessequals @ SV1476 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3534]) ).
thf(4388,plain,
! [SV1477: $i,SV640: $i] :
( ( ! [SY5816: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV640 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ ( c_HOL_Otimes__class_Otimes @ SV1477 @ SY5816 @ SV640 ) @ SV640 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SY5816 @ SV640 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV1477 @ SV640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(4389,plain,
! [SV1478: $i,SV642: $i] :
( ( ( c_lessequals @ SV642 @ SV1478 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV642 ) @ ( c_Suc @ SV1478 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(4390,plain,
! [SV1479: $i,SV643: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV643 ) @ ( c_Suc @ SV1479 ) @ tc_nat )
| ~ ( c_lessequals @ SV643 @ SV1479 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3538]) ).
thf(4391,plain,
! [SV1480: $i,SV644: $i] :
( ( ! [SY5817: $i,SY5818: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV644 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1480 @ SY5817 @ SV644 ) @ SY5818 @ SV644 )
= ( c_HOL_Otimes__class_Otimes @ SV1480 @ ( c_HOL_Otimes__class_Otimes @ SY5817 @ SY5818 @ SV644 ) @ SV644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(4392,plain,
! [SV1481: $i,SV645: $i] :
( ( ! [SY5819: $i,SY5820: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV645 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1481 @ SY5819 @ SV645 ) @ SY5820 @ SV645 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1481 @ SY5820 @ SV645 ) @ SY5819 @ SV645 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3540]) ).
thf(4393,plain,
! [SV1482: $i,SV646: $i] :
( ( ! [SY5821: $i,SY5822: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV646 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1482 @ SY5821 @ SV646 ) @ SY5822 @ SV646 )
= ( c_HOL_Otimes__class_Otimes @ SV1482 @ ( c_HOL_Otimes__class_Otimes @ SY5821 @ SY5822 @ SV646 ) @ SV646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3541]) ).
thf(4394,plain,
! [SV1483: $i,SV647: $i] :
( ( ! [SY5823: $i,SY5824: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV647 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1483 @ ( c_HOL_Otimes__class_Otimes @ SY5823 @ SY5824 @ SV647 ) @ SV647 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1483 @ SY5823 @ SV647 ) @ SY5824 @ SV647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3542]) ).
thf(4395,plain,
! [SV1484: $i,SV648: $i] :
( ( ! [SY5825: $i,SY5826: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV648 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1484 @ ( c_HOL_Otimes__class_Otimes @ SY5825 @ SY5826 @ SV648 ) @ SV648 )
= ( c_HOL_Otimes__class_Otimes @ SY5825 @ ( c_HOL_Otimes__class_Otimes @ SV1484 @ SY5826 @ SV648 ) @ SV648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(4396,plain,
! [SV1485: $i,SV649: $i] :
( ( ! [SY5827: $i,SY5828: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV649 @ SV1485 @ SY5827 ) @ SY5828 @ SY5827 )
= ( c_List_Oappend @ SV649 @ ( c_List_Oappend @ SV1485 @ SY5828 @ SY5827 ) @ SY5827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3544]) ).
thf(4397,plain,
! [SV1486: $i,SV650: $i] :
( ( ! [SY5829: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV650 @ SV1486 @ tc_nat ) @ SY5829 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV650 @ ( c_HOL_Otimes__class_Otimes @ SV1486 @ SY5829 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(4398,plain,
! [SV1487: $i,SV651: $i] :
( ( ! [SY5830: $i,SY5831: $i] :
( ( c_List_Oappend @ SV651 @ ( c_List_Oappend @ SV1487 @ SY5830 @ SY5831 ) @ SY5831 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV651 @ SV1487 @ SY5831 ) @ SY5830 @ SY5831 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3546]) ).
thf(4399,plain,
! [SV1488: $i,SV652: $i] :
( ( ! [SY5832: $i,SY5833: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV652 @ SV1488 @ SY5832 ) @ SY5833 @ SY5832 )
= ( c_List_Oappend @ SV652 @ ( c_List_Oappend @ SV1488 @ SY5833 @ SY5832 ) @ SY5832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(4400,plain,
! [SV1489: $i,SV653: $i] :
( ( ! [SY5834: $i,SY5835: $i] :
( ( c_List_Oappend @ SV653 @ ( c_List_Oappend @ SV1489 @ SY5834 @ SY5835 ) @ SY5835 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV653 @ SV1489 @ SY5835 ) @ SY5834 @ SY5835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3548]) ).
thf(4401,plain,
! [SV1490: $i,SV654: $i] :
( ( ! [SY5836: $i,SY5837: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV654 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1490 @ ( c_HOL_Otimes__class_Otimes @ SY5836 @ SY5837 @ SV654 ) @ SV654 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1490 @ SY5836 @ SV654 ) @ SY5837 @ SV654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(4402,plain,
! [SV1491: $i,SV655: $i] :
( ( ! [SY5838: $i,SY5839: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV655 )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV655 ) @ SV1491 ) @ SY5838 ) @ SY5839 @ SV655 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV655 ) @ ( c_HOL_Otimes__class_Otimes @ SV1491 @ SY5839 @ SV655 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY5838 @ SY5839 @ SV655 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(4403,plain,
! [SV1492: $i,SV656: $i] :
( ( ! [SY5840: $i,SY5841: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV656 )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV656 ) @ SV1492 ) @ SY5840 ) @ SY5841 @ SV656 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV656 ) @ ( c_HOL_Otimes__class_Otimes @ SV1492 @ SY5841 @ SV656 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY5840 @ SY5841 @ SV656 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3551]) ).
thf(4404,plain,
! [SV1493: $i,SV657: $i] :
( ( ! [SY5842: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV657 ) @ SV1493 ) @ SY5842 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV657 @ SY5842 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1493 @ SY5842 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3552]) ).
thf(4405,plain,
! [SV1494: $i,SV658: $i] :
( ( ! [SY5843: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1494 ) @ SY5843 ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV658 @ SV1494 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV658 @ SY5843 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3553]) ).
thf(4406,plain,
! [SV1495: $i,SV659: $i] :
( ( ! [SY5844: $i,SY5845: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV659 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1495 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV659 ) @ SY5844 ) @ SY5845 ) @ SV659 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV659 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SY5844 @ SV659 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SY5845 @ SV659 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3554]) ).
thf(4407,plain,
! [SV1496: $i,SV660: $i] :
( ( ! [SY5846: $i] :
( ~ ( class_Orderings_Oorder @ SV660 )
| ~ ( c_HOL_Oord__class_Oless @ SV1496 @ SY5846 @ SV660 )
| ~ ( c_HOL_Oord__class_Oless @ SY5846 @ SV1496 @ SV660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3555]) ).
thf(4408,plain,
! [SV1497: $i,SV661: $i] :
( ( ! [SY5847: $i] :
( ~ ( class_Orderings_Olinorder @ SV661 )
| ~ ( c_HOL_Oord__class_Oless @ SV1497 @ SY5847 @ SV661 )
| ~ ( c_HOL_Oord__class_Oless @ SY5847 @ SV1497 @ SV661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3556]) ).
thf(4409,plain,
! [SV1498: $i,SV662: $i] :
( ( ( c_lessequals @ SV662 @ SV1498 @ tc_nat )
| ( c_lessequals @ SV1498 @ SV662 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3557]) ).
thf(4410,plain,
! [SV1499: $i,SV663: $i] :
( ( ! [SY5848: $i] :
( ~ ( class_Orderings_Olinorder @ SV663 )
| ( c_lessequals @ SV1499 @ SY5848 @ SV663 )
| ( c_lessequals @ SY5848 @ SV1499 @ SV663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(4411,plain,
! [SV1500: $i,SV664: $i] :
( ( ! [SY5849: $i] :
( ~ ( class_Orderings_Opreorder @ SV664 )
| ~ ( c_HOL_Oord__class_Oless @ SV1500 @ SY5849 @ SV664 )
| ~ ( c_HOL_Oord__class_Oless @ SY5849 @ SV1500 @ SV664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3559]) ).
thf(4412,plain,
! [SV1501: $i,SV665: $i] :
( ( ! [SY5850: $i] :
( ~ ( class_Orderings_Opreorder @ SV665 )
| ~ ( c_HOL_Oord__class_Oless @ SV1501 @ SY5850 @ SV665 )
| ~ ( c_HOL_Oord__class_Oless @ SY5850 @ SV1501 @ SV665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3560]) ).
thf(4413,plain,
! [SV1502: $i,SV666: $i] :
( ( ! [SY5851: $i] :
( ( c_Nat_Onat_Onat__rec @ SV666 @ SV1502 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5851 )
= SV666 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3561]) ).
thf(4414,plain,
! [SV1503: $i,SV667: $i] :
( ( ( hBOOL @ ( hAPP @ SV667 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV667 @ SV1503 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV667 @ SV1503 ) )
| ( hBOOL @ ( hAPP @ SV667 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3562]) ).
thf(4415,plain,
! [SV668: $i] :
( ( ( SV668
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV668 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3563]) ).
thf(4416,plain,
! [SV1504: $i,SV669: $i] :
( ( ( hBOOL @ ( hAPP @ SV669 @ SV1504 ) )
| ( hBOOL @ ( hAPP @ SV669 @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ SV669 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV669 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3564]) ).
thf(4417,plain,
! [SV1505: $i,SV672: $i] :
( ( ! [SY5852: $i] :
( ( c_Nat_Onat_Onat__case @ SV672 @ SV1505 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5852 )
= SV672 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3567]) ).
thf(4418,plain,
! [SV1506: $i,SV673: $i] :
( ( ! [SY5853: $i] :
( ( c_Nat_Onat_Onat__case @ SV673 @ SV1506 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5853 )
= SV673 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3568]) ).
thf(4419,plain,
! [SV1507: $i,SV678: $i] :
( ( ( hBOOL @ ( hAPP @ SV678 @ SV1507 ) )
| ( hBOOL @ ( hAPP @ SV678 @ ( v_sko__List__Xreplicate__Xinduct__1 @ SV678 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV678 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3573]) ).
thf(4420,plain,
! [SV1508: $i,SV679: $i] :
( ( ! [SY5854: $i] :
( ~ ( hBOOL @ ( hAPP @ SV679 @ ( c_Nat_Onat_Onat__case @ SV1508 @ SY5854 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV679 @ SV1508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3574]) ).
thf(4421,plain,
! [SV1509: $i,SV680: $i] :
( ( ( hBOOL @ ( hAPP @ SV680 @ SV1509 ) )
| ( hBOOL @ ( hAPP @ SV680 @ ( v_sko__Nat__Xnat__Xinducts__1 @ SV680 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV680 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3575]) ).
thf(4422,plain,
! [SV1510: $i,SV683: $i] :
( ( ( hBOOL @ ( hAPP @ SV683 @ SV1510 ) )
| ( hBOOL @ ( hAPP @ SV683 @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV683 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV683 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(4423,plain,
! [SV684: $i] :
( ( c_HOL_Oord__class_Oless @ SV684 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3579]) ).
thf(4424,plain,
! [SV685: $i] :
( ( c_HOL_Oord__class_Oless @ SV685 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3580]) ).
thf(4425,plain,
! [SV1511: $i,SV686: $i] :
( ( ( hBOOL @ ( hAPP @ SV686 @ SV1511 ) )
| ( hBOOL @ ( hAPP @ SV686 @ ( v_sko__List__Xupt__Xinduct__1 @ SV686 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV686 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3581]) ).
thf(4426,plain,
! [SV1512: $i,SV687: $i] :
( ( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV687 @ SV1512 )
= SV687 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3582]) ).
thf(4427,plain,
! [SV1513: $i,SV689: $i] :
( ( ( hBOOL @ ( hAPP @ SV689 @ SV1513 ) )
| ~ ( hBOOL @ ( hAPP @ SV689 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV689 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV689 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3584]) ).
thf(4428,plain,
! [SV1514: $i,SV692: $i] :
( ( ! [SY5855: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV692 @ SV1514 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5855 @ SV1514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3587]) ).
thf(4429,plain,
! [SV1515: $i,SV698: $i] :
( ( ! [SY5856: $i,SY5857: $i,SY5858: $i,SY5859: $i,SY5860: $i] :
( ( ( hAPP @ ( hAPP @ SV698 @ SV1515 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SY5856 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY5857 @ SY5858 @ SV698 @ SY5859 @ SY5856 @ SY5860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3593]) ).
thf(4430,plain,
! [SV1516: $i,SV699: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV699 )
| ( ( c_List_Olistsum @ SV1516 @ SV699 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV699 ) @ SV1516 @ ( c_HOL_Ozero__class_Ozero @ SV699 ) @ SV699 @ SV699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3594]) ).
thf(4431,plain,
! [SV1517: $i,SV700: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV700 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV700 ) @ ( c_HOL_Ozero__class_Ozero @ SV700 ) @ SV1517 @ SV700 @ SV700 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV700 ) @ SV1517 @ ( c_HOL_Ozero__class_Ozero @ SV700 ) @ SV700 @ SV700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3595]) ).
thf(4432,plain,
! [SV1518: $i,SV701: $i] :
( ( ! [SY5861: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV701 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SV1518 @ SY5861 @ SV701 @ SV701 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SV1518 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SY5861 @ ( c_HOL_Ozero__class_Ozero @ SV701 ) @ SV701 @ SV701 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3596]) ).
thf(4433,plain,
! [SV1519: $i,SV702: $i] :
( ( ! [SY5862: $i,SY5863: $i] :
( ( c_Type_Otyping @ SV702 @ SV1519 @ SY5862 )
| ~ ( c_Lambda_Obeta @ SY5863 @ SV1519 )
| ~ ( c_Type_Otyping @ SV702 @ SY5863 @ SY5862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3597]) ).
thf(4434,plain,
! [SV1520: $i,SV703: $i] :
( ( ! [SY5864: $i] :
( ( ( hAPP @ SV703 @ SV1520 )
= SY5864 )
| ~ ( c_Type_Otyping @ SV703 @ ( c_Lambda_OdB_OVar @ SV1520 ) @ SY5864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3598]) ).
thf(4435,plain,
! [SV1521: $i,SV704: $i] :
( ( c_Type_Otyping @ SV704 @ ( c_Lambda_OdB_OVar @ SV1521 ) @ ( hAPP @ SV704 @ SV1521 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3599]) ).
thf(4436,plain,
! [SV1522: $i,SV705: $i] :
( ( ! [SY5865: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV705 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV705 @ SV1522 ) @ tc_Type_Otype ) @ SV1522 @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV705 @ SV1522 ) )
| ~ ( c_Type_Otyping @ SV705 @ ( c_Lambda_OdB_OAbs @ SV1522 ) @ SY5865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3600]) ).
thf(4437,plain,
! [SV1523: $i,SV706: $i] :
( ( ! [SY5866: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV706 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV1523 @ SV706 @ SY5866 ) @ tc_Type_Otype ) @ SY5866 @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV1523 @ SV706 @ SY5866 ) )
| ~ ( c_Type_Otyping @ SV706 @ ( c_Lambda_OdB_OAbs @ SY5866 ) @ SV1523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3601]) ).
thf(4438,plain,
! [SV1524: $i,SV707: $i] :
( ( ! [SY5867: $i,SY5868: $i] :
( ( c_Type_Otyping @ SV707 @ SV1524 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SY5867 @ SV707 @ SV1524 @ SY5868 ) ) @ SY5867 ) )
| ~ ( c_Type_Otyping @ SV707 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1524 ) @ SY5868 ) @ SY5867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3602]) ).
thf(4439,plain,
! [SV1525: $i,SV708: $i] :
( ( ! [SY5869: $i,SY5870: $i,SY5871: $i] :
( ( c_Type_Otype_Otype__rec @ SV708 @ SV1525 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5869 ) @ SY5870 ) @ SY5871 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV1525 @ SY5869 ) @ SY5870 ) @ ( c_Type_Otype_Otype__rec @ SV708 @ SV1525 @ SY5869 @ SY5871 ) ) @ ( c_Type_Otype_Otype__rec @ SV708 @ SV1525 @ SY5870 @ SY5871 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3603]) ).
thf(4440,plain,
! [SV1526: $i,SV709: $i] :
( ( ! [SY5872: $i,SY5873: $i,SY5874: $i] :
( ( c_Type_Otype_Otype__case @ SV709 @ SV1526 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5872 ) @ SY5873 ) @ SY5874 )
= ( hAPP @ ( hAPP @ SV1526 @ SY5872 ) @ SY5873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3604]) ).
thf(4441,plain,
! [SV1527: $i,SV710: $i] :
( ( ! [SY5875: $i,SY5876: $i,SY5877: $i] :
( ~ ( hBOOL @ ( hAPP @ SV710 @ ( c_Type_Otype_Otype__case @ SV1527 @ SY5875 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5876 ) @ SY5877 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV710 @ ( hAPP @ ( hAPP @ SY5875 @ SY5876 ) @ SY5877 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3605]) ).
thf(4442,plain,
! [SV1528: $i,SV711: $i] :
( ( ! [SY5878: $i,SY5879: $i,SY5880: $i] :
( ~ ( hBOOL @ ( hAPP @ SV711 @ ( c_Type_Otype_Otype__case @ SV1528 @ SY5878 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5879 ) @ SY5880 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV711 @ ( hAPP @ ( hAPP @ SY5878 @ SY5879 ) @ SY5880 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3606]) ).
thf(4443,plain,
! [SV1529: $i,SV712: $i] :
( ( ! [SY5881: $i,SY5882: $i,SY5883: $i,SY5884: $i] :
( ( c_List_Ofoldr @ SV712 @ ( c_List_Olist_OCons @ SV1529 @ SY5881 @ SY5882 ) @ SY5883 @ SY5882 @ SY5884 )
= ( hAPP @ ( hAPP @ SV712 @ SV1529 ) @ ( c_List_Ofoldr @ SV712 @ SY5881 @ SY5883 @ SY5882 @ SY5884 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3607]) ).
thf(4444,plain,
! [SV1530: $i,SV713: $i] :
( ( ! [SY5885: $i,SY5886: $i,SY5887: $i,SY5888: $i] :
( ( c_List_Ofoldr @ SV713 @ ( c_List_Oappend @ SV1530 @ SY5885 @ SY5886 ) @ SY5887 @ SY5886 @ SY5888 )
= ( c_List_Ofoldr @ SV713 @ SV1530 @ ( c_List_Ofoldr @ SV713 @ SY5885 @ SY5887 @ SY5886 @ SY5888 ) @ SY5886 @ SY5888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3608]) ).
thf(4445,plain,
! [SV1531: $i,SV714: $i] :
( ( ! [SY5889: $i,SY5890: $i] :
( ( c_List_Ofoldr @ SV714 @ ( c_List_Olist_ONil @ SV1531 ) @ SY5889 @ SV1531 @ SY5890 )
= SY5889 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(4446,plain,
! [SV1532: $i,SV715: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ SV715 @ SV1532 ) )
| ~ ( c_InductTermi_OIT @ SV715 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(4447,plain,
! [SV1533: $i,SV716: $i] :
( ( ! [SY5891: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV716 ) @ SV1533 ) @ SY5891 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV716 @ SY5891 ) ) @ ( c_Lambda_Olift @ SV1533 @ SY5891 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3611]) ).
thf(4448,plain,
! [SV1534: $i,SV717: $i] :
( ( ! [SY5892: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV717 @ SV1534 ) @ SY5892 @ SV1534 )
= SV717 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3612]) ).
thf(4449,plain,
! [SV1535: $i,SV718: $i] :
( ( ! [SY5893: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV718 @ SV1535 ) @ ( c_Lambda_Olift @ SY5893 @ SV1535 ) )
| ~ ( c_Lambda_Obeta @ SV718 @ SY5893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3613]) ).
thf(4450,plain,
! [SV1536: $i,SV719: $i] :
( ( ! [SY5894: $i,SY5895: $i,SY5896: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV719 @ SV1536 @ SY5894 @ SY5895 ) @ SY5896 )
= ( hAPP @ SV719 @ SY5896 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5896 @ SV1536 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3614]) ).
thf(4451,plain,
! [SV1537: $i,SV720: $i] :
( ( ! [SY5897: $i,SY5898: $i] :
( ( c_Type_Otyping @ SV720 @ SV1537 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SY5897 @ SV720 @ SV1537 @ SY5898 ) @ SY5897 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV720 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1537 @ SY5898 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY5897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3615]) ).
thf(4452,plain,
! [SV1538: $i,SV721: $i] :
( ( ! [SY5899: $i,SY5900: $i,SY5901: $i] :
( ( c_Type_Otyping @ SV721 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1538 @ SY5899 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY5900 )
| ~ ( c_Type_Otypings @ SV721 @ SY5899 @ SY5901 )
| ~ ( c_Type_Otyping @ SV721 @ SV1538 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY5901 @ SY5900 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(4453,plain,
! [SV1539: $i,SV722: $i] :
( ( ! [SY5902: $i,SY5903: $i] :
( ( c_Type_Otyping @ SV722 @ SV1539 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SY5902 @ SV722 @ SV1539 @ SY5903 ) @ SY5902 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV722 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1539 @ SY5903 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY5902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(4454,plain,
! [SV1540: $i,SV723: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV723 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV723 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV723 )
| ~ ( class_Power_Opower @ SV723 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV723 ) @ SV1540 @ SV723 )
= ( c_HOL_Ozero__class_Ozero @ SV723 ) )
| ( SV1540
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3618]) ).
thf(4455,plain,
! [SV1541: $i,SV724: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV724 )
| ~ ( class_Power_Opower @ SV724 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV724 ) @ SV1541 @ SV724 )
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1541
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3619]) ).
thf(4456,plain,
! [SV725: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV725 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV725 )
= ( c_HOL_Ozero__class_Ozero @ SV725 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3620]) ).
thf(4457,plain,
! [SV1542: $i,SV726: $i] :
( ( ! [SY5904: $i,SY5905: $i,SY5906: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ SV726 @ SV1542 @ SY5904 @ SY5905 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5906 @ SY5905 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV726 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5906 @ SY5905 ) @ ( c_Suc @ SV1542 ) @ SY5904 @ SY5905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3621]) ).
thf(4458,plain,
! [SV1543: $i,SV727: $i] :
( ( ! [SY5907: $i,SY5908: $i,SY5909: $i] :
( ( c_Type_Otyping @ SV727 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1543 ) @ SY5907 ) @ SY5908 )
| ~ ( c_Type_Otyping @ SV727 @ SY5907 @ SY5909 )
| ~ ( c_Type_Otyping @ SV727 @ SV1543 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5909 ) @ SY5908 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3622]) ).
thf(4459,plain,
! [SV1544: $i,SV728: $i] :
( ( ! [SY5910: $i,SY5911: $i,SY5912: $i,SY5913: $i] :
( ~ ( c_Type_Otyping @ SV728 @ SV1544 @ SY5910 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV728 @ SY5911 @ SY5910 @ tc_Type_Otype ) @ SY5912 @ SY5913 )
| ( c_Type_Otyping @ SV728 @ ( c_Lambda_Osubst @ SY5912 @ SV1544 @ SY5911 ) @ SY5913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3623]) ).
thf(4460,plain,
! [SV1545: $i,SV729: $i] :
( ( ! [SY5914: $i,SY5915: $i] :
( ( c_Type_Otyping @ SV729 @ ( c_Lambda_OdB_OAbs @ SV1545 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5914 ) @ SY5915 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV729 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5914 @ tc_Type_Otype ) @ SV1545 @ SY5915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3624]) ).
thf(4461,plain,
! [SV1546: $i,SV730: $i] :
( ( ! [SY5916: $i,SY5917: $i,SY5918: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV730 @ SV1546 @ SY5916 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY5917 @ SV1546 ) @ SY5918 )
| ~ ( c_Type_Otyping @ SV730 @ SY5917 @ SY5918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3625]) ).
thf(4462,plain,
! [SV1547: $i,SV731: $i] :
( ( ! [SY5919: $i,SY5920: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV731 @ SV1547 @ SY5919 @ SY5920 ) @ SV1547 )
= SY5919 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3626]) ).
thf(4463,plain,
! [SV1548: $i,SV732: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV732 @ SV1548 ) )
| ~ ( class_Orderings_Opreorder @ SV1548 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3627]) ).
thf(4464,plain,
! [SV1549: $i,SV733: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV733 @ SV1549 ) )
| ~ ( class_Orderings_Oorder @ SV1549 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3628]) ).
thf(4465,plain,
! [SV1550: $i,SV734: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV734 @ SV1550 ) )
| ~ ( class_Orderings_Obot @ SV1550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3629]) ).
thf(4466,plain,
! [SV1551: $i,SV735: $i] :
( ( c_fequal @ SV735 @ SV735 @ SV1551 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3630]) ).
thf(4467,plain,
! [SV1552: $i,SV736: $i] :
( ( ! [SY5921: $i] :
( ( SV736 = SV1552 )
| ~ ( c_fequal @ SV736 @ SV1552 @ SY5921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3631]) ).
thf(4468,plain,
! [SV1553: $i,SV737: $i] :
( ( ! [SY5922: $i,SY5923: $i,SY5924: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV737 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1553 @ SY5922 @ SV737 )
!= ( c_HOL_Ominus__class_Ominus @ SY5923 @ SY5924 @ SV737 ) )
| ( c_lessequals @ SY5922 @ SV1553 @ SV737 )
| ~ ( c_lessequals @ SY5924 @ SY5923 @ SV737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3633]) ).
thf(4469,plain,
! [SV1554: $i,SV738: $i] :
( ( ! [SY5925: $i,SY5926: $i,SY5927: $i] :
( ( ( c_List_Olist_OCons @ SV738 @ SV1554 @ SY5925 )
!= ( c_List_Olist_OCons @ SY5926 @ SY5927 @ SY5925 ) )
| ( SV738 = SY5926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3634]) ).
thf(4470,plain,
! [SV1555: $i,SV739: $i] :
( ( ! [SY5928: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV739 @ SV1555 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV739 @ SY5928 @ tc_nat ) )
| ( SV1555 = SY5928 )
| ( SV739
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3635]) ).
thf(4471,plain,
! [SV1556: $i,SV740: $i] :
( ( ! [SY5929: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV740 ) @ SV1556 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV740 ) @ SY5929 ) )
| ( SV1556 = SY5929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3636]) ).
thf(4472,plain,
! [SV1557: $i,SV741: $i] :
( ( ! [SY5930: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV741 ) @ SV1557 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV741 ) @ SY5930 ) )
| ( SV1557 = SY5930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3637]) ).
thf(4473,plain,
! [SV1558: $i,SV742: $i] :
( ( ! [SY5931: $i,SY5932: $i,SY5933: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV1558 @ tc_nat ) ) @ SY5931 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY5932 @ SV1558 @ tc_nat ) ) @ SY5933 ) )
| ~ ( c_lessequals @ SY5932 @ SV742 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV742 @ SY5932 @ tc_nat ) @ SV1558 @ tc_nat ) ) @ SY5931 )
= SY5933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3638]) ).
thf(4474,plain,
! [SV1559: $i,SV743: $i] :
( ( ! [SY5934: $i] :
( ( ( c_List_Oappend @ SV743 @ SV1559 @ SY5934 )
!= SV743 )
| ( SV1559
= ( c_List_Olist_ONil @ SY5934 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3639]) ).
thf(4475,plain,
! [SV1560: $i,SV744: $i] :
( ( ! [SY5935: $i,SY5936: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV744 ) @ SV1560 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY5935 ) @ SY5936 ) )
| ( SV744 = SY5935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3640]) ).
thf(4476,plain,
! [SV1561: $i,SV745: $i] :
( ( ! [SY5937: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1561 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SY5937 @ SV1561 @ tc_nat ) )
| ( SV1561
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV745 = SY5937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3641]) ).
thf(4477,plain,
! [SV1562: $i,SV746: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV746 )
!= ( c_Lambda_OdB_OAbs @ SV1562 ) )
| ( SV746 = SV1562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3642]) ).
thf(4478,plain,
! [SV1563: $i,SV747: $i] :
( ( ! [SY5938: $i,SY5939: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV747 ) @ SV1563 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY5938 ) @ SY5939 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1563 = SY5939 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3643]) ).
thf(4479,plain,
! [SV1564: $i,SV748: $i] :
( ( ! [SY5940: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV748 ) @ SV1564 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV748 ) @ SY5940 @ tc_nat ) )
| ( SV1564 = SY5940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3644]) ).
thf(4480,plain,
! [SV1565: $i,SV749: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV749 ) @ SV1565 ) )
| ( SV1565
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1565
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3645]) ).
thf(4481,plain,
! [SV1566: $i,SV750: $i] :
( ( ! [SY5941: $i,SY5942: $i,SY5943: $i,SY5944: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV750 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV1566 @ SY5941 @ SV750 ) ) @ SY5942 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SY5943 @ SY5941 @ SV750 ) ) @ SY5944 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ SY5943 @ SV750 ) @ SY5941 @ SV750 ) ) @ SY5942 )
= SY5944 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3646]) ).
thf(4482,plain,
! [SV1567: $i,SV751: $i] :
( ( ! [SY5945: $i,SY5946: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV751 ) ) @ SV1567 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY5945 ) @ SY5946 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3647]) ).
thf(4483,plain,
! [SV1568: $i,SV752: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV752 ) @ SV1568 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1568
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3648]) ).
thf(4484,plain,
! [SV1569: $i,SV753: $i] :
( ( ( SV753
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV753 ) @ SV1569 ) )
| ( SV1569
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3649]) ).
thf(4485,plain,
! [SV1570: $i,SV754: $i] :
( ( ! [SY5947: $i,SY5948: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV754 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SV1570 ) @ SY5947 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SY5948 ) @ SY5947 ) )
| ( SV1570 = SY5948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3650]) ).
thf(4486,plain,
! [SV1571: $i,SV755: $i] :
( ( ! [SY5949: $i] :
( ( ( c_List_Olist_ONil @ SV755 )
!= ( c_List_Oappend @ SV1571 @ SY5949 @ SV755 ) )
| ( SY5949
= ( c_List_Olist_ONil @ SV755 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3651]) ).
thf(4487,plain,
! [SV1572: $i,SV756: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV756 ) @ SV1572 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1572
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1572
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3652]) ).
thf(4488,plain,
! [SV1573: $i,SV757: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV757 ) @ SV1573 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV757
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1573
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(4489,plain,
! [SV1574: $i,SV758: $i] :
( ( ! [SY5950: $i,SY5951: $i] :
( ( ( c_List_Oappend @ SV758 @ SV1574 @ SY5950 )
!= ( c_List_Oappend @ SY5951 @ SV1574 @ SY5950 ) )
| ( SV758 = SY5951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3654]) ).
thf(4490,plain,
! [SV1575: $i,SV759: $i] :
( ( ! [SY5952: $i,SY5953: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1575 ) @ SY5952 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SY5953 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SY5952 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3655]) ).
thf(4491,plain,
! [SV1576: $i,SV760: $i] :
( ( ! [SY5954: $i,SY5955: $i,SY5956: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV760 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1576 @ SY5954 @ SV760 )
!= ( c_HOL_Ominus__class_Ominus @ SY5955 @ SY5956 @ SV760 ) )
| ( c_HOL_Oord__class_Oless @ SY5955 @ SY5956 @ SV760 )
| ~ ( c_HOL_Oord__class_Oless @ SV1576 @ SY5954 @ SV760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3656]) ).
thf(4492,plain,
! [SV1577: $i,SV761: $i] :
( ( ! [SY5957: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV761 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1577 @ SY5957 @ SV761 )
!= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
| ( SV1577
= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
| ( SY5957
= ( c_HOL_Ozero__class_Ozero @ SV761 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3657]) ).
thf(4493,plain,
! [SV1578: $i,SV762: $i] :
( ( ! [SY5958: $i] :
( SV762
!= ( c_List_Olist_OCons @ SV1578 @ SV762 @ SY5958 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(4494,plain,
! [SV1579: $i,SV763: $i] :
( ( ! [SY5959: $i,SY5960: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV763 )
| ( ( c_Power_Opower__class_Opower @ SV1579 @ SY5959 @ SV763 )
!= ( c_Power_Opower__class_Opower @ SY5960 @ SY5959 @ SV763 ) )
| ( SV1579 = SY5960 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY5959 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SY5960 @ SV763 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3659]) ).
thf(4495,plain,
! [SV1580: $i,SV764: $i] :
( ( ! [SY5961: $i,SY5962: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV764 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SY5961 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SY5962 ) )
| ( SY5961 = SY5962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3660]) ).
thf(4496,plain,
! [SV1581: $i,SV765: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV765 ) @ SV1581 ) )
| ( SV765
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV765
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3661]) ).
thf(4497,plain,
! [SV1582: $i,SV766: $i] :
( ( ! [SY5963: $i,SY5964: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV766 ) @ SV1582 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY5963 ) @ SY5964 ) )
| ( SV1582 = SY5964 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(4498,plain,
! [SV767: $i] :
( ( ( c_Suc @ SV767 )
= SV767 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3663]) ).
thf(4499,plain,
! [SV1583: $i,SV768: $i] :
( ( ( c_Lambda_OdB_OVar @ SV768 )
!= ( c_Lambda_OdB_OAbs @ SV1583 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3664]) ).
thf(4500,plain,
! [SV1584: $i,SV769: $i] :
( ( ! [SY5965: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV769 ) @ SV1584 )
!= ( c_Lambda_OdB_OAbs @ SY5965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3665]) ).
thf(4501,plain,
! [SV1585: $i,SV770: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV770 @ SV1585 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV770
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3666]) ).
thf(4502,plain,
! [SV1586: $i,SV771: $i] :
( ( ! [SY5966: $i] :
( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV771 ) @ SV1586 )
!= ( c_Type_Otype_OAtom @ SY5966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3667]) ).
thf(4503,plain,
! [SV1587: $i,SV772: $i] :
( ( ! [SY5967: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV772 @ SV1587 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY5967 @ SV1587 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV772 = SY5967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3668]) ).
thf(4504,plain,
! [SV1588: $i,SV773: $i] :
( ( ! [SY5968: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV773 )
| ~ ( class_Int_Onumber__ring @ SV773 )
| ( SV1588
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV773 ) @ SV1588 ) @ SY5968 ) )
| ( SY5968
= ( c_HOL_Ozero__class_Ozero @ SV773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3669]) ).
thf(4505,plain,
! [SV1589: $i,SV774: $i] :
( ( ! [SY5969: $i,SY5970: $i,SY5971: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV774 )
| ~ ( class_Int_Onumber__ring @ SV774 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SY5969 @ SY5970 @ SV774 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SY5969 @ SY5971 @ SV774 ) ) )
| ( SY5970 = SY5971 )
| ( SY5969
= ( c_HOL_Ozero__class_Ozero @ SV774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3670]) ).
thf(4506,plain,
! [SV1590: $i,SV775: $i] :
( ( ! [SY5972: $i,SY5973: $i,SY5974: $i] :
( ( ( c_List_Oreplicate @ SV775 @ SV1590 @ SY5972 )
!= ( c_List_Oreplicate @ SY5973 @ SY5974 @ SY5972 ) )
| ( SV775 = SY5973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3671]) ).
thf(4507,plain,
! [SV1591: $i,SV776: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV776 ) @ SV1591 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1591
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV776
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(4508,plain,
! [SV777: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV777 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3673]) ).
thf(4509,plain,
! [SV1592: $i,SV778: $i] :
( ( ! [SY5975: $i,SY5976: $i,SY5977: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV778 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1592 @ SY5975 @ SV778 )
!= ( c_HOL_Ominus__class_Ominus @ SY5976 @ SY5977 @ SV778 ) )
| ( c_HOL_Oord__class_Oless @ SV1592 @ SY5975 @ SV778 )
| ~ ( c_HOL_Oord__class_Oless @ SY5976 @ SY5977 @ SV778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3674]) ).
thf(4510,plain,
! [SV1593: $i,SV779: $i] :
( ( ! [SY5978: $i] :
( ~ ( class_Orderings_Olinorder @ SV779 )
| ( ( c_Orderings_Oord__class_Omax @ SV1593 @ SY5978 @ SV779 )
!= SY5978 )
| ( c_lessequals @ SV1593 @ SY5978 @ SV779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3675]) ).
thf(4511,plain,
! [SV1594: $i,SV780: $i] :
( ( ! [SY5979: $i,SY5980: $i,SY5981: $i] :
( ( ( c_List_Oappend @ SV780 @ ( c_List_Olist_OCons @ SV1594 @ ( c_List_Olist_ONil @ SY5979 ) @ SY5979 ) @ SY5979 )
!= ( c_List_Oappend @ SY5980 @ ( c_List_Olist_OCons @ SY5981 @ ( c_List_Olist_ONil @ SY5979 ) @ SY5979 ) @ SY5979 ) )
| ( SV1594 = SY5981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3676]) ).
thf(4512,plain,
! [SV1595: $i,SV781: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV781 ) @ SV1595 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV781
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3677]) ).
thf(4513,plain,
! [SV1596: $i,SV782: $i] :
( ( ! [SY5982: $i,SY5983: $i] :
( ( ( c_List_Oappend @ SV782 @ SV1596 @ SY5982 )
!= ( c_List_Oappend @ SV782 @ SY5983 @ SY5982 ) )
| ( SV1596 = SY5983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3678]) ).
thf(4514,plain,
! [SV1597: $i,SV783: $i] :
( ( ! [SY5984: $i] :
( ( c_Type_Otype_OAtom @ SV783 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1597 ) @ SY5984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3679]) ).
thf(4515,plain,
! [SV1598: $i,SV784: $i] :
( ( ! [SY5985: $i,SY5986: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SV1598 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SY5985 @ SY5986 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SY5986 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SY5985 @ SV1598 @ tc_nat ) ) )
| ( SV1598 = SY5986 )
| ( SV784 = SY5985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3680]) ).
thf(4516,plain,
! [SV785: $i] :
( ( ( c_Suc @ SV785 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3681]) ).
thf(4517,plain,
! [SV1599: $i,SV786: $i] :
( ( ! [SY5987: $i] :
( ( ( c_List_Olist_ONil @ SV786 )
!= ( c_List_Oreplicate @ SV1599 @ SY5987 @ SV786 ) )
| ( SV1599
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3682]) ).
thf(4518,plain,
! [SV1600: $i,SV787: $i] :
( ( ! [SY5988: $i,SY5989: $i,SY5990: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV787 )
| ~ ( class_Int_Onumber__ring @ SV787 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SY5988 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY5989 @ SY5990 @ SV787 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SY5990 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY5989 @ SY5988 @ SV787 ) ) )
| ( SY5988 = SY5990 )
| ( SV1600 = SY5989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3683]) ).
thf(4519,plain,
! [SV1601: $i,SV788: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV788 @ SV1601 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1601
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3684]) ).
thf(4520,plain,
! [SV1602: $i,SV789: $i] :
( ( ! [SY5991: $i,SY5992: $i,SY5993: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV789 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1602 @ SY5991 @ SV789 )
!= ( c_HOL_Ominus__class_Ominus @ SY5992 @ SY5993 @ SV789 ) )
| ( c_lessequals @ SY5993 @ SY5992 @ SV789 )
| ~ ( c_lessequals @ SY5991 @ SV1602 @ SV789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3685]) ).
thf(4521,plain,
! [SV1603: $i,SV790: $i] :
( ( ! [SY5994: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV790 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1603 @ SY5994 @ SV790 )
!= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
| ( SY5994
= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
| ( SV1603
= ( c_HOL_Ozero__class_Ozero @ SV790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3686]) ).
thf(4522,plain,
! [SV1604: $i,SV791: $i] :
( ( ( ( c_Suc @ SV791 )
!= ( c_Suc @ SV1604 ) )
| ( SV791 = SV1604 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3687]) ).
thf(4523,plain,
! [SV1605: $i,SV792: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV792 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV792 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV792 )
| ~ ( class_Power_Opower @ SV792 )
| ( ( c_Power_Opower__class_Opower @ SV1605 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV792 )
!= ( c_HOL_Ozero__class_Ozero @ SV792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3688]) ).
thf(4524,plain,
! [SV1606: $i,SV793: $i] :
( ( ! [SY5995: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV793 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV793 ) @ SV1606 ) @ SY5995 )
!= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SY5995 @ SV793 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV1606 @ SV793 )
| ( SV1606
= ( c_HOL_Ozero__class_Ozero @ SV793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3689]) ).
thf(4525,plain,
! [SV1607: $i,SV794: $i] :
( ( ! [SY5996: $i,SY5997: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV794 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1607 ) @ SY5996 ) )
| ( hBOOL @ ( hAPP @ SV794 @ SY5997 ) )
| ( hBOOL @ ( hAPP @ SV794 @ SV1607 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3690]) ).
thf(4526,plain,
! [SV1608: $i,SV795: $i] :
( ( ! [SY5998: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV795 @ SV1608 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SY5998 @ SV1608 @ tc_nat ) )
| ~ ( c_lessequals @ SV1608 @ SY5998 @ tc_nat )
| ~ ( c_lessequals @ SV1608 @ SV795 @ tc_nat )
| ( SV795 = SY5998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3691]) ).
thf(4527,plain,
! [SV1609: $i,SV796: $i] :
( ( ! [SY5999: $i,SY6000: $i,SY6001: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV796 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SY5999 ) @ SY6000 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SY5999 ) @ SY6001 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ SY6000 )
= SY6001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3692]) ).
thf(4528,plain,
! [SV1610: $i,SV797: $i] :
( ( ! [SY6002: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV797 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV797 ) @ ( c_HOL_Otimes__class_Otimes @ SV1610 @ SV1610 @ SV797 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY6002 @ SY6002 @ SV797 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV797 ) )
| ( SY6002
= ( c_HOL_Ozero__class_Ozero @ SV797 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3693]) ).
thf(4529,plain,
! [SV1611: $i,SV798: $i] :
( ( ! [SY6003: $i,SY6004: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV798 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1611 @ SV1611 @ SV798 )
!= ( c_HOL_Ominus__class_Ominus @ SY6003 @ SY6004 @ SV798 ) )
| ( SY6003 = SY6004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3694]) ).
thf(4530,plain,
! [SV1612: $i,SV799: $i] :
( ( ! [SY6005: $i,SY6006: $i,SY6007: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV799 @ SV1612 @ tc_nat ) ) @ SY6005 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY6006 @ SV1612 @ tc_nat ) ) @ SY6007 ) )
| ~ ( c_lessequals @ SV799 @ SY6006 @ tc_nat )
| ( SY6005
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6006 @ SV799 @ tc_nat ) @ SV1612 @ tc_nat ) ) @ SY6007 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3695]) ).
thf(4531,plain,
! [SV1613: $i,SV800: $i] :
( ( ! [SY6008: $i,SY6009: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV800 ) @ SV1613 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY6008 ) @ SY6009 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY6008 @ SV1613 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV800 @ SY6009 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3696]) ).
thf(4532,plain,
! [SV1614: $i,SV801: $i] :
( ( ! [SY6010: $i,SY6011: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV801 ) @ SV1614 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY6010 ) @ SY6011 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV801 = SY6010 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3697]) ).
thf(4533,plain,
! [SV1615: $i,SV802: $i] :
( ( ! [SY6012: $i] :
( ( ( c_List_Oappend @ SV802 @ SV1615 @ SY6012 )
!= ( c_List_Olist_ONil @ SY6012 ) )
| ( SV1615
= ( c_List_Olist_ONil @ SY6012 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3698]) ).
thf(4534,plain,
! [SV1616: $i,SV803: $i] :
( ( ! [SY6013: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1616 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV803 @ SY6013 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV803 @ tc_nat )
| ( SV1616 = SY6013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3699]) ).
thf(4535,plain,
! [SV1617: $i,SV804: $i] :
( ( ! [SY6014: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV804 ) @ SV1617 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY6014 ) @ SV1617 ) )
| ( SV804 = SY6014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3700]) ).
thf(4536,plain,
! [SV1618: $i,SV805: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV805 )
!= ( c_Lambda_OdB_OVar @ SV1618 ) )
| ( SV805 = SV1618 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3701]) ).
thf(4537,plain,
! [SV1619: $i,SV806: $i] :
( ( ! [SY6015: $i,SY6016: $i,SY6017: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV806 )
| ~ ( class_Int_Onumber__ring @ SV806 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SY6015 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY6016 @ SY6017 @ SV806 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SY6017 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY6016 @ SY6015 @ SV806 ) ) )
| ( SY6015 = SY6017 )
| ( SV1619 = SY6016 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3702]) ).
thf(4538,plain,
! [SV1620: $i,SV807: $i] :
( ( ! [SY6018: $i,SY6019: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV807 ) @ SV1620 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY6018 ) @ SY6019 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1620 = SY6019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3703]) ).
thf(4539,plain,
! [SV1621: $i,SV808: $i] :
( ( ! [SY6020: $i,SY6021: $i,SY6022: $i,SY6023: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV808 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV1621 @ SY6020 @ SV808 ) ) @ SY6021 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SY6022 @ SY6020 @ SV808 ) ) @ SY6023 ) )
| ( SY6021
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6022 @ SV1621 @ SV808 ) @ SY6020 @ SV808 ) ) @ SY6023 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(4540,plain,
! [SV1622: $i,SV809: $i] :
( ( ! [SY6024: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV809 @ SV1622 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV809 @ SY6024 @ tc_nat ) )
| ( SV809
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1622 = SY6024 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3705]) ).
thf(4541,plain,
! [SV1623: $i,SV810: $i] :
( ( ! [SY6025: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV810 )
| ~ ( class_Int_Onumber__ring @ SV810 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1623 @ SY6025 @ SV810 )
!= ( c_HOL_Ozero__class_Ozero @ SV810 ) )
| ( SV1623 = SY6025 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3706]) ).
thf(4542,plain,
! [SV1624: $i,SV811: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV811 @ SV1624 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SV811 @ SV1624 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3707]) ).
thf(4543,plain,
! [SV1625: $i,SV812: $i] :
( ( ! [SY6026: $i,SY6027: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1625 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SY6026 @ SY6027 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SY6027 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SY6026 @ SV1625 @ tc_nat ) ) )
| ( SV1625 = SY6027 )
| ( SV812 = SY6026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3708]) ).
thf(4544,plain,
! [SV1626: $i,SV813: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV813 )
!= ( c_Lambda_OdB_OVar @ SV1626 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3709]) ).
thf(4545,plain,
! [SV1627: $i,SV814: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV814 @ SV1627 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV1627 @ SV814 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1627 = SV814 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3710]) ).
thf(4546,plain,
! [SV1628: $i,SV815: $i] :
( ( ! [SY6028: $i] :
( ( ( c_Lambda_OdB_OVar @ SV815 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1628 @ SY6028 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV815 )
= SV1628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3711]) ).
thf(4547,plain,
! [SV1629: $i,SV816: $i] :
( ( ! [SY6029: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV816 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1629 @ SY6029 @ SV816 )
!= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
| ( SY6029
= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
| ( SV1629
= ( c_HOL_Ozero__class_Ozero @ SV816 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3712]) ).
thf(4548,plain,
! [SV1630: $i,SV817: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV817 ) @ SV1630 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV817
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV817
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3713]) ).
thf(4549,plain,
! [SV1631: $i,SV818: $i] :
( ( ! [SY6030: $i,SY6031: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV818 ) @ SV1631 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY6030 ) @ SY6031 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3714]) ).
thf(4550,plain,
! [SV1632: $i,SV819: $i] :
( ( ! [SY6032: $i,SY6033: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV819 ) @ SV1632 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY6032 ) @ SY6033 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV819 = SY6032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3715]) ).
thf(4551,plain,
! [SV1633: $i,SV820: $i] :
( ( ! [SY6034: $i,SY6035: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV820 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SY6034 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SY6035 ) )
| ( SY6034 = SY6035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3716]) ).
thf(4552,plain,
! [SV1634: $i,SV821: $i] :
( ( ! [SY6036: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV821 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1634 @ SV821 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY6036 @ SV821 ) )
| ( SV1634 = SY6036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3717]) ).
thf(4553,plain,
! [SV1635: $i,SV822: $i] :
( ( ! [SY6037: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV822 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV822 ) @ ( c_HOL_Otimes__class_Otimes @ SV1635 @ SV1635 @ SV822 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY6037 @ SY6037 @ SV822 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV822 ) )
| ( SV1635
= ( c_HOL_Ozero__class_Ozero @ SV822 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3718]) ).
thf(4554,plain,
! [SV1636: $i,SV823: $i] :
( ( ! [SY6038: $i,SY6039: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV823 )
| ( ( c_Power_Opower__class_Opower @ SV1636 @ ( c_Suc @ SY6038 ) @ SV823 )
!= ( c_Power_Opower__class_Opower @ SY6039 @ ( c_Suc @ SY6038 ) @ SV823 ) )
| ( SV1636 = SY6039 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SY6039 @ SV823 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV1636 @ SV823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3719]) ).
thf(4555,plain,
! [SV1637: $i,SV824: $i] :
( ( ! [SY6040: $i] :
( ( ( c_List_Oappend @ SV824 @ SV1637 @ SY6040 )
!= SV1637 )
| ( SV824
= ( c_List_Olist_ONil @ SY6040 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3720]) ).
thf(4556,plain,
! [SV1638: $i,SV825: $i] :
( ( ! [SY6041: $i] :
( ( c_Lambda_OdB_OAbs @ SV825 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1638 ) @ SY6041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3721]) ).
thf(4557,plain,
! [SV1639: $i,SV826: $i] :
( ( ! [SY6042: $i] :
( ( SV826
!= ( c_List_Oappend @ SV1639 @ SV826 @ SY6042 ) )
| ( SV1639
= ( c_List_Olist_ONil @ SY6042 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3722]) ).
thf(4558,plain,
! [SV1640: $i,SV827: $i] :
( ( ( ( c_Suc @ SV827 )
!= ( c_Suc @ SV1640 ) )
| ( SV827 = SV1640 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3723]) ).
thf(4559,plain,
! [SV1641: $i,SV828: $i] :
( ( ! [SY6043: $i] :
( ( c_List_Olist_OCons @ SV828 @ SV1641 @ SY6043 )
!= ( c_List_Olist_ONil @ SY6043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3724]) ).
thf(4560,plain,
! [SV1642: $i,SV829: $i] :
( ( ! [SY6044: $i] :
( ( c_List_Olist_OCons @ SV829 @ SV1642 @ SY6044 )
!= ( c_List_Olist_ONil @ SY6044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3725]) ).
thf(4561,plain,
! [SV1643: $i,SV830: $i] :
( ( ! [SY6045: $i,SY6046: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV830 ) @ SV1643 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY6045 ) @ SY6046 ) )
| ( SV1643 = SY6046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3726]) ).
thf(4562,plain,
! [SV831: $i] :
( ( SV831
= ( c_Suc @ SV831 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3727]) ).
thf(4563,plain,
! [SV1644: $i,SV832: $i] :
( ( ! [SY6047: $i,SY6048: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV832 )
| ~ ( class_Int_Onumber__ring @ SV832 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SY6047 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SY6048 ) )
| ( SY6047 = SY6048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3728]) ).
thf(4564,plain,
! [SV1645: $i,SV833: $i] :
( ( ! [SY6049: $i] :
( ( ( c_List_Oreplicate @ SV833 @ SV1645 @ SY6049 )
!= ( c_List_Olist_ONil @ SY6049 ) )
| ( SV833
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3729]) ).
thf(4565,plain,
! [SV1646: $i,SV834: $i] :
( ( ! [SY6050: $i] :
( ~ ( class_Orderings_Olinorder @ SV834 )
| ( ( c_Orderings_Oord__class_Omin @ SV1646 @ SY6050 @ SV834 )
!= SV1646 )
| ( c_lessequals @ SV1646 @ SY6050 @ SV834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3730]) ).
thf(4566,plain,
! [SV1647: $i,SV835: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV835 @ SV1647 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1647
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV835
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3731]) ).
thf(4567,plain,
! [SV1648: $i,SV836: $i] :
( ( ! [SY6051: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV836 @ SV1648 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY6051 ) )
| ( SV836
= ( c_Lambda_OdB_OAbs @ SY6051 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3732]) ).
thf(4568,plain,
! [SV1649: $i,SV837: $i] :
( ( ! [SY6052: $i,SY6053: $i,SY6054: $i] :
( ( ( c_List_Oreplicate @ SV837 @ SV1649 @ SY6052 )
!= ( c_List_Oreplicate @ SY6053 @ SY6054 @ SY6052 ) )
| ( SV1649 = SY6054 )
| ( SV837
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3733]) ).
thf(4569,plain,
! [SV1650: $i,SV838: $i] :
( ( ! [SY6055: $i,SY6056: $i,SY6057: $i,SY6058: $i,SY6059: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY6055 @ SY6056 @ SY6057 ) )
| ~ ( c_Type_Otyping @ SY6058 @ SY6056 @ SV1650 )
| ~ ( c_InductTermi_OIT @ SY6056 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY6058 @ SY6057 @ SV1650 @ tc_Type_Otype ) @ SY6055 @ SY6059 )
| ~ ( c_InductTermi_OIT @ SY6055 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3734]) ).
thf(4570,plain,
! [SV1651: $i,SV839: $i] :
( ( ! [SY6060: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV839 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV839 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV839 )
| ~ ( class_Power_Opower @ SV839 )
| ( ( c_Power_Opower__class_Opower @ SV1651 @ SY6060 @ SV839 )
!= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
| ( SV1651
= ( c_HOL_Ozero__class_Ozero @ SV839 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3735]) ).
thf(4571,plain,
! [SV1652: $i,SV840: $i] :
( ( ! [SY6061: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV840 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1652 @ SY6061 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV840 )
= SV1652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3736]) ).
thf(4572,plain,
! [SV1653: $i,SV841: $i] :
( ( ! [SY6062: $i,SY6063: $i,SY6064: $i] :
( ( ( c_List_Oappend @ SV841 @ ( c_List_Olist_OCons @ SV1653 @ ( c_List_Olist_ONil @ SY6062 ) @ SY6062 ) @ SY6062 )
!= ( c_List_Oappend @ SY6063 @ ( c_List_Olist_OCons @ SY6064 @ ( c_List_Olist_ONil @ SY6062 ) @ SY6062 ) @ SY6062 ) )
| ( SV841 = SY6063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3737]) ).
thf(4573,plain,
! [SV1654: $i,SV842: $i] :
( ( ! [SY6065: $i] :
( ( SV842
!= ( c_List_Oappend @ SV842 @ SV1654 @ SY6065 ) )
| ( SV1654
= ( c_List_Olist_ONil @ SY6065 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3738]) ).
thf(4574,plain,
! [SV1655: $i,SV843: $i] :
( ( ! [SY6066: $i] :
( ( c_Lambda_OdB_OVar @ SV843 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1655 ) @ SY6066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3739]) ).
thf(4575,plain,
! [SV844: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV844 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3740]) ).
thf(4576,plain,
! [SV1656: $i,SV845: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV845 ) @ SV1656 ) )
| ( SV1656
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV845
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3741]) ).
thf(4577,plain,
! [SV1657: $i,SV846: $i] :
( ( ! [SY6067: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV846 )
| ( ( c_Power_Opower__class_Opower @ SV1657 @ SY6067 @ SV846 )
!= ( c_HOL_Ozero__class_Ozero @ SV846 ) )
| ( SV1657
= ( c_HOL_Ozero__class_Ozero @ SV846 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3742]) ).
thf(4578,plain,
! [SV1658: $i,SV847: $i] :
( ( ! [SY6068: $i] :
( ( c_List_Olist_ONil @ SV847 )
!= ( c_List_Olist_OCons @ SV1658 @ SY6068 @ SV847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3743]) ).
thf(4579,plain,
! [SV1659: $i,SV848: $i] :
( ( ! [SY6069: $i,SY6070: $i,SY6071: $i] :
( ( ( c_List_Olist_OCons @ SV848 @ SV1659 @ SY6069 )
!= ( c_List_Olist_OCons @ SY6070 @ SY6071 @ SY6069 ) )
| ( SV1659 = SY6071 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3744]) ).
thf(4580,plain,
! [SV1660: $i,SV849: $i] :
( ( ! [SY6072: $i] :
( ( ( c_List_Olist_ONil @ SV849 )
!= ( c_List_Oappend @ SV1660 @ SY6072 @ SV849 ) )
| ( SV1660
= ( c_List_Olist_ONil @ SV849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3745]) ).
thf(4581,plain,
! [SV1661: $i,SV850: $i] :
( ( ( ( c_Type_Otype_OAtom @ SV850 )
!= ( c_Type_Otype_OAtom @ SV1661 ) )
| ( SV850 = SV1661 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3746]) ).
thf(4582,plain,
! [SV1662: $i,SV851: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV851 ) @ SV1662 ) )
| ( SV851
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1662
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3747]) ).
thf(4583,plain,
! [SV1663: $i,SV852: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV852 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV852 ) @ SV1663 ) @ SV1663 )
!= ( c_HOL_Ozero__class_Ozero @ SV852 ) )
| ( SV1663
= ( c_HOL_Ozero__class_Ozero @ SV852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3748]) ).
thf(4584,plain,
! [SV1664: $i,SV853: $i] :
( ( ! [SY6073: $i,SY6074: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV853 ) @ SV1664 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY6073 ) @ SY6074 ) )
| ( SV853 = SY6073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3749]) ).
thf(4585,plain,
! [SV1665: $i,SV854: $i] :
( ( ! [SY6075: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV854 ) @ SV1665 )
!= ( c_Lambda_OdB_OVar @ SY6075 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3750]) ).
thf(4586,plain,
! [SV1666: $i,SV855: $i] :
( ( ! [SY6076: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV855 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV855 ) @ SV1666 ) @ SY6076 )
!= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SY6076 @ SV855 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV1666 @ SV855 )
| ( SY6076
= ( c_HOL_Ozero__class_Ozero @ SV855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3751]) ).
thf(4587,plain,
! [SV1667: $i,SV856: $i] :
( ( ! [SY6077: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV856 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1667 @ SY6077 @ SV856 )
!= ( c_HOL_Ozero__class_Ozero @ SV856 ) )
| ( SV1667 = SY6077 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3752]) ).
thf(4588,plain,
! [SV1668: $i,SV857: $i] :
( ( ! [SY6078: $i] :
( ( ( c_List_Oappend @ SV857 @ SV1668 @ SY6078 )
!= ( c_List_Olist_ONil @ SY6078 ) )
| ( SV857
= ( c_List_Olist_ONil @ SY6078 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3753]) ).
thf(4589,plain,
! [SV1669: $i,SV858: $i] :
( ( ! [SY6079: $i,SY6080: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV858 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1669 @ SY6079 @ SV858 )
!= ( c_HOL_Ominus__class_Ominus @ SY6080 @ SY6080 @ SV858 ) )
| ( SV1669 = SY6079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3754]) ).
thf(4590,plain,
! [SV1670: $i,SV859: $i] :
( ( ! [SY6081: $i] :
( ( c_List_Olist_OCons @ SV859 @ SV1670 @ SY6081 )
!= SV1670 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3755]) ).
thf(4591,plain,
! [SV1671: $i,SV860: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV860 ) @ SV1671 )
!= SV860 )
| ( SV1671
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3756]) ).
thf(4592,plain,
! [SV1672: $i,SV861: $i] :
( ( ! [SY6082: $i,SY6083: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SY6082 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SY6083 @ tc_nat ) ) )
| ( SY6082 = SY6083 )
| ( SV1672
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3757]) ).
thf(4593,plain,
! [SV862: $i] :
( ( ( c_Suc @ SV862 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3758]) ).
thf(4594,plain,
! [SV1673: $i,SV863: $i] :
( ( ! [SY6084: $i,SY6085: $i,SY6086: $i,SY6087: $i,SY6088: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SY6084 @ SY6085 @ SY6086 ) )
| ~ ( c_Type_Otyping @ SY6087 @ SY6085 @ SV863 )
| ~ ( c_InductTermi_OIT @ SY6085 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY6087 @ SY6086 @ SV863 @ tc_Type_Otype ) @ SY6084 @ SY6088 )
| ~ ( c_InductTermi_OIT @ SY6084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3759]) ).
thf(4595,plain,
! [SV1674: $i,SV864: $i] :
( ( ! [SY6089: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV864 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1674 @ SY6089 @ SV864 )
!= ( c_HOL_Ozero__class_Ozero @ SV864 ) )
| ( SV1674 = SY6089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3760]) ).
thf(4596,plain,
! [SV1675: $i,SV865: $i,SV1: $i] :
( ( ! [SY6090: $i,SY6091: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1 @ SV865 @ tc_nat ) ) @ SV1675 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY6090 @ SV865 @ tc_nat ) ) @ SY6091 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1675 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6090 @ SV1 @ tc_nat ) @ SV865 @ tc_nat ) ) @ SY6091 ) @ tc_nat )
| ~ ( c_lessequals @ SV1 @ SY6090 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3761]) ).
thf(4597,plain,
! [SV1676: $i,SV866: $i,SV2: $i] :
( ( ! [SY6092: $i,SY6093: $i] :
( ( c_HOL_Oord__class_Oless @ SV2 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV866 @ SV1676 @ tc_nat ) @ SY6092 @ tc_nat ) ) @ SY6093 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SY6092 @ tc_nat ) ) @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV866 @ SY6092 @ tc_nat ) ) @ SY6093 ) @ tc_nat )
| ~ ( c_lessequals @ SV1676 @ SV866 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(4598,plain,
! [SV1677: $i,SV867: $i,SV3: $i] :
( ( ! [SY6094: $i,SY6095: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV3 @ SV867 @ tc_nat ) ) @ SV1677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY6094 @ SV867 @ tc_nat ) ) @ SY6095 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV3 @ SY6094 @ tc_nat ) @ SV867 @ tc_nat ) ) @ SV1677 ) @ SY6095 @ tc_nat )
| ~ ( c_lessequals @ SY6094 @ SV3 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3763]) ).
thf(4599,plain,
! [SV1678: $i,SV868: $i,SV4: $i] :
( ( ! [SY6096: $i,SY6097: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV868 @ tc_nat ) @ SV1678 @ tc_nat ) ) @ SY6096 ) @ SY6097 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV4 @ SV1678 @ tc_nat ) ) @ SY6096 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV868 @ SV1678 @ tc_nat ) ) @ SY6097 ) @ tc_nat )
| ~ ( c_lessequals @ SV868 @ SV4 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3764]) ).
thf(4600,plain,
! [SV1679: $i,SV869: $i,SV5: $i] :
( ( ! [SY6098: $i,SY6099: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV5 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV869 @ SV1679 @ SV5 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6098 @ SV869 @ SV5 ) @ SV1679 @ SV5 ) ) @ SY6099 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SY6098 @ SV1679 @ SV5 ) ) @ SY6099 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3765]) ).
thf(4601,plain,
! [SV872: $i,SV8: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV8 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV8 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ ( c_Suc @ SV872 ) @ SV8 )
= ( c_HOL_Ozero__class_Ozero @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3768]) ).
thf(4602,plain,
! [SV1680: $i,SV873: $i,SV9: $i] :
( ( ! [SY6100: $i,SY6101: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SY6100 @ SY6101 @ SV9 ) @ SV9 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SY6100 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1680 @ SY6101 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV873 @ SY6100 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3769]) ).
thf(4603,plain,
! [SV874: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ SV10 @ SV874 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV10 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3770]) ).
thf(4604,plain,
! [SV1681: $i,SV875: $i,SV11: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV11 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV875 @ SV1681 @ SV11 ) @ SV875 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3771]) ).
thf(4605,plain,
! [SV1682: $i,SV876: $i,SV12: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV12 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV876 @ SV1682 @ SV12 ) @ SV1682 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3772]) ).
thf(4606,plain,
! [SV1683: $i,SV877: $i,SV13: $i] :
( ( ! [SY6102: $i] :
( ~ ( class_Orderings_Olinorder @ SV13 )
| ( c_lessequals @ SV877 @ ( c_Orderings_Oord__class_Omin @ SV1683 @ SY6102 @ SV13 ) @ SV13 )
| ~ ( c_lessequals @ SV877 @ SY6102 @ SV13 )
| ~ ( c_lessequals @ SV877 @ SV1683 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3773]) ).
thf(4607,plain,
! [SV1684: $i,SV878: $i,SV14: $i] :
( ( ! [SY6103: $i] :
( ~ ( class_Orderings_Olinorder @ SV14 )
| ( c_lessequals @ SV878 @ ( c_Orderings_Oord__class_Omin @ SV1684 @ SY6103 @ SV14 ) @ SV14 )
| ~ ( c_lessequals @ SV878 @ SY6103 @ SV14 )
| ~ ( c_lessequals @ SV878 @ SV1684 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3774]) ).
thf(4608,plain,
! [SV1685: $i,SV879: $i,SV15: $i] :
( ( ! [SY6104: $i] :
( ~ ( class_Orderings_Olinorder @ SV15 )
| ( c_lessequals @ SV879 @ ( c_Orderings_Oord__class_Omin @ SV1685 @ SY6104 @ SV15 ) @ SV15 )
| ~ ( c_lessequals @ SV879 @ SY6104 @ SV15 )
| ~ ( c_lessequals @ SV879 @ SV1685 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3775]) ).
thf(4609,plain,
! [SV1686: $i,SV880: $i,SV16: $i] :
( ( ! [SY6105: $i,SY6106: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV16 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SV880 @ SV1686 @ SV16 ) ) @ SY6105 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SY6106 @ SV1686 @ SV16 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV880 @ SY6106 @ SV16 ) @ SV1686 @ SV16 ) ) @ SY6105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3776]) ).
thf(4610,plain,
! [SV1687: $i,SV881: $i,SV17: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV17 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SV881 @ SV1687 @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV881 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3777]) ).
thf(4611,plain,
! [SV882: $i,SV18: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV18 @ SV882 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV18 @ SV882 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3778]) ).
thf(4612,plain,
! [SV1688: $i,SV883: $i,SV19: $i] :
( ( ! [SY6107: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV19 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV883 @ SV1688 @ SV19 ) @ SY6107 @ SV19 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV883 @ SY6107 @ SV19 ) @ ( c_HOL_Ominus__class_Ominus @ SV1688 @ SY6107 @ SV19 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3779]) ).
thf(4613,plain,
! [SV1689: $i,SV884: $i,SV20: $i] :
( ( ! [SY6108: $i] :
( ~ ( class_Orderings_Olinorder @ SV20 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV884 @ SV1689 @ SV20 ) @ SY6108 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SV1689 @ SY6108 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SV884 @ SY6108 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3780]) ).
thf(4614,plain,
! [SV1690: $i,SV885: $i,SV21: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV21 @ SV885 @ tc_nat ) ) @ SV1690 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV21 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV885 ) @ SV1690 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV885 @ SV21 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3781]) ).
thf(4615,plain,
! [SV1691: $i,SV886: $i,SV22: $i] :
( ( ! [SY6109: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV22 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV22 )
| ( c_HOL_Oord__class_Oless @ SV886 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1691 ) @ SY6109 ) @ SV22 )
| ~ ( c_lessequals @ SV886 @ SY6109 @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV1691 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3782]) ).
thf(4616,plain,
! [SV1692: $i,SV887: $i,SV23: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV23 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV887 ) @ SV1692 ) @ tc_nat )
| ~ ( c_lessequals @ SV23 @ SV887 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1692 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3783]) ).
thf(4617,plain,
! [SV1693: $i,SV888: $i,SV24: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV24 )
| ( c_lessequals @ SV888 @ SV1693 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV888 @ SV24 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1693 @ SV24 ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3784]) ).
thf(4618,plain,
! [SV1694: $i,SV889: $i,SV25: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV25 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV889 @ SV25 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1694 @ SV25 ) @ SV25 )
| ~ ( c_lessequals @ SV889 @ SV1694 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3785]) ).
thf(4619,plain,
! [SV1695: $i,SV890: $i,SV26: $i] :
( ( ! [SY6110: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV26 @ SV890 @ SV1695 ) @ ( c_Lambda_Osubst @ SY6110 @ SV890 @ SV1695 ) )
| ~ ( c_Lambda_Obeta @ SV26 @ SY6110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3786]) ).
thf(4620,plain,
! [SV1696: $i,SV891: $i,SV27: $i] :
( ( ! [SY6111: $i] :
( ~ ( class_Orderings_Olinorder @ SV27 )
| ( c_HOL_Oord__class_Oless @ SV891 @ ( c_Orderings_Oord__class_Omin @ SV1696 @ SY6111 @ SV27 ) @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SY6111 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV1696 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3787]) ).
thf(4621,plain,
! [SV1697: $i,SV892: $i,SV28: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV28 @ SV892 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV28 @ SV1697 @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV28 @ SV1697 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV28 @ SV892 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3788]) ).
thf(4622,plain,
! [SV1698: $i,SV893: $i,SV29: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV29 @ SV893 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV29 @ SV1698 @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV29 @ SV1698 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV29 @ SV893 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3789]) ).
thf(4623,plain,
! [SV1699: $i,SV894: $i,SV30: $i] :
( ( ! [SY6112: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV30 )
| ~ ( class_Int_Onumber__ring @ SV30 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV1699 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SY6112 @ SV30 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SY6112 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV1699 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3790]) ).
thf(4624,plain,
! [SV1700: $i,SV895: $i,SV31: $i] :
( ( ! [SY6113: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV31 )
| ~ ( class_Int_Onumber__ring @ SV31 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1700 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SY6113 @ SV31 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SY6113 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1700 @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3791]) ).
thf(4625,plain,
! [SV33: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV33 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( SV33
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3793]) ).
thf(4626,plain,
! [SV897: $i,SV34: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV34 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV897 @ SV34 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV897 ) @ SV897 ) @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3794]) ).
thf(4627,plain,
! [SV898: $i,SV35: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV35 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV35 ) @ SV898 ) @ SV898 ) @ SV35 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV898 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3795]) ).
thf(4628,plain,
! [SV1701: $i,SV899: $i,SV36: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV36 )
| ( ( c_Orderings_Oord__class_Omin @ SV899 @ ( c_Orderings_Oord__class_Omin @ SV899 @ SV1701 @ SV36 ) @ SV36 )
= ( c_Orderings_Oord__class_Omin @ SV899 @ SV1701 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3796]) ).
thf(4629,plain,
! [SV1702: $i,SV900: $i,SV37: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV37 ) @ SV900 @ SV1702 )
= ( c_Lambda_OdB_OVar @ SV37 ) )
| ( SV37 = SV1702 )
| ( c_HOL_Oord__class_Oless @ SV1702 @ SV37 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3797]) ).
thf(4630,plain,
! [SV1703: $i,SV901: $i,SV38: $i] :
( ( ! [SY6114: $i,SY6115: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV38 @ SV901 @ tc_nat ) ) @ SV1703 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY6114 @ SV901 @ tc_nat ) ) @ SY6115 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1703 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6114 @ SV38 @ tc_nat ) @ SV901 @ tc_nat ) ) @ SY6115 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV38 @ SY6114 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3798]) ).
thf(4631,plain,
! [SV1704: $i,SV902: $i,SV39: $i] :
( ( ! [SY6116: $i,SY6117: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV39 @ SV902 @ tc_nat ) ) @ SV1704 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY6116 @ SV902 @ tc_nat ) ) @ SY6117 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SY6116 @ tc_nat ) @ SV902 @ tc_nat ) ) @ SV1704 ) @ SY6117 @ tc_nat ) )
| ~ ( c_lessequals @ SY6116 @ SV39 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3799]) ).
thf(4632,plain,
! [SV1705: $i,SV903: $i,SV40: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV40 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ ( c_HOL_Ominus__class_Ominus @ SV903 @ SV1705 @ SV40 ) ) @ SV1705 )
= SV903 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3800]) ).
thf(4633,plain,
! [SV1706: $i,SV904: $i,SV41: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV41 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV904 ) @ SV1706 ) @ SV904 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV41 @ SV1706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3801]) ).
thf(4634,plain,
! [SV1707: $i,SV905: $i,SV42: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV42 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV905 ) @ SV1707 ) @ SV905 @ tc_nat ) ) )
| ( hBOOL @ ( hAPP @ SV42 @ SV1707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3802]) ).
thf(4635,plain,
! [SV1708: $i,SV906: $i,SV43: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV43 @ SV906 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1708 @ SV906 @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV906 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3803]) ).
thf(4636,plain,
! [SV1709: $i,SV907: $i,SV44: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV44 @ SV907 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV44 @ SV1709 @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV44 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3804]) ).
thf(4637,plain,
! [SV1710: $i,SV908: $i,SV45: $i] :
( ( ! [SY6118: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV45 )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV908 @ SV1710 @ SV45 ) @ SY6118 @ SV45 )
= ( c_Power_Opower__class_Opower @ SV908 @ ( c_HOL_Otimes__class_Otimes @ SV1710 @ SY6118 @ tc_nat ) @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3805]) ).
thf(4638,plain,
! [SV909: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ SV46 @ SV909 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV46 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ SV46 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV46 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3806]) ).
thf(4639,plain,
! [SV1711: $i,SV910: $i,SV47: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV47 )
| ( ( c_Power_Opower__class_Opower @ SV910 @ ( c_Suc @ SV1711 ) @ SV47 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV910 @ SV1711 @ SV47 ) @ SV910 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3807]) ).
thf(4640,plain,
! [SV1712: $i,SV911: $i,SV48: $i] :
( ( ~ ( class_Power_Opower @ SV48 )
| ( ( c_Power_Opower__class_Opower @ SV911 @ ( c_Suc @ SV1712 ) @ SV48 )
= ( c_HOL_Otimes__class_Otimes @ SV911 @ ( c_Power_Opower__class_Opower @ SV911 @ SV1712 @ SV48 ) @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3808]) ).
thf(4641,plain,
! [SV1713: $i,SV912: $i,SV49: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
| ( ( c_Power_Opower__class_Opower @ SV912 @ ( c_Suc @ SV1713 ) @ SV49 )
= ( c_HOL_Otimes__class_Otimes @ SV912 @ ( c_Power_Opower__class_Opower @ SV912 @ SV1713 @ SV49 ) @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3809]) ).
thf(4642,plain,
! [SV1714: $i,SV913: $i,SV50: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
| ( ( c_Power_Opower__class_Opower @ SV913 @ ( c_Suc @ SV1714 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ SV913 @ ( c_Power_Opower__class_Opower @ SV913 @ SV1714 @ SV50 ) @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3810]) ).
thf(4643,plain,
! [SV1715: $i,SV914: $i,SV51: $i] :
( ( ! [SY6119: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV914 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1715 ) @ SY6119 ) @ tc_nat )
| ~ ( c_lessequals @ SV914 @ SY6119 @ tc_nat )
| ~ ( c_lessequals @ SV51 @ SV1715 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3811]) ).
thf(4644,plain,
! [SV1716: $i,SV915: $i,SV52: $i] :
( ( ! [SY6120: $i,SY6121: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV52 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV915 ) @ SV1716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SY6120 ) @ SY6121 ) @ SV52 )
| ~ ( c_lessequals @ SV1716 @ SY6121 @ SV52 )
| ~ ( c_lessequals @ SV915 @ SY6120 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3812]) ).
thf(4645,plain,
! [SV916: $i,SV53: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV53 @ ( c_Suc @ SV916 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV53 @ SV916 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3813]) ).
thf(4646,plain,
! [SV917: $i,SV54: $i] :
( ( ( c_lessequals @ SV54 @ SV917 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV54 @ ( c_Suc @ SV917 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3814]) ).
thf(4647,plain,
! [SV55: $i] :
( ( ( c_lessequals @ SV55 @ SV55 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV55 @ ( c_Suc @ SV55 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3815]) ).
thf(4648,plain,
! [SV918: $i,SV56: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV56 ) )
= $true )
| ( ( ( c_List_Olistsum @ SV918 @ SV56 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ ( c_HOL_Ozero__class_Ozero @ SV56 ) @ SV918 @ SV56 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3816]) ).
thf(4649,plain,
! [SV1717: $i,SV919: $i,SV57: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV57 )
| ( ( c_HOL_Otimes__class_Otimes @ SV919 @ SV1717 @ SV57 )
= ( c_HOL_Otimes__class_Otimes @ SV1717 @ SV919 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3817]) ).
thf(4650,plain,
! [SV59: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV59 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) )
= ( c_HOL_Ozero__class_Ozero @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3819]) ).
thf(4651,plain,
! [SV1718: $i,SV921: $i,SV60: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV60 )
| ( ( c_HOL_Otimes__class_Otimes @ SV921 @ SV1718 @ SV60 )
= ( c_HOL_Otimes__class_Otimes @ SV1718 @ SV921 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3820]) ).
thf(4652,plain,
! [SV1719: $i,SV923: $i,SV62: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV62 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV923 ) @ SV1719 ) @ SV62 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1719 @ SV62 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV923 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3822]) ).
thf(4653,plain,
! [SV1720: $i,SV924: $i,SV63: $i] :
( ( ! [SY6122: $i] :
( ~ ( class_Orderings_Opreorder @ SV63 )
| ( c_HOL_Oord__class_Oless @ SV924 @ SV1720 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SY6122 @ SV1720 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ SY6122 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3823]) ).
thf(4654,plain,
! [SV1721: $i,SV925: $i,SV64: $i] :
( ( ! [SY6123: $i] :
( ~ ( class_Orderings_Oorder @ SV64 )
| ( c_HOL_Oord__class_Oless @ SV925 @ SV1721 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV925 @ SY6123 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SY6123 @ SV1721 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3824]) ).
thf(4655,plain,
! [SV1722: $i,SV926: $i,SV65: $i] :
( ( ! [SY6124: $i] :
( ( c_Type_Otyping @ SV65 @ SV926 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV1722 @ SV65 @ SY6124 @ SV926 ) )
| ~ ( c_Type_Otyping @ SV65 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY6124 ) @ SV926 ) @ SV1722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3825]) ).
thf(4656,plain,
! [SV1723: $i,SV927: $i,SV66: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV66 )
| ( ( c_Orderings_Oord__class_Omax @ SV927 @ SV1723 @ SV66 )
= SV1723 )
| ~ ( c_lessequals @ SV927 @ SV1723 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3826]) ).
thf(4657,plain,
! [SV1724: $i,SV928: $i,SV67: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV67 )
| ( ( c_Orderings_Oord__class_Omax @ SV928 @ SV1724 @ SV67 )
= SV928 )
| ~ ( c_lessequals @ SV1724 @ SV928 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3827]) ).
thf(4658,plain,
! [SV1725: $i,SV929: $i,SV68: $i] :
( ( ! [SY6125: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV929 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV1725 ) @ SY6125 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV929 ) @ SV1725 ) ) @ SY6125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3828]) ).
thf(4659,plain,
! [SV1726: $i,SV930: $i,SV69: $i] :
( ( ! [SY6126: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV69 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV930 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV1726 ) @ SY6126 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV1726 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV930 ) @ SY6126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3829]) ).
thf(4660,plain,
! [SV1727: $i,SV931: $i,SV70: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV70 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV931 ) @ SV1727 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV931 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV70 ) @ SV1727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3830]) ).
thf(4661,plain,
! [SV1728: $i,SV932: $i,SV71: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV71 ) @ SV932 ) ) @ SV1728 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV71 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV932 ) @ SV1728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3831]) ).
thf(4662,plain,
! [SV1729: $i,SV933: $i,SV72: $i] :
( ( ( hBOOL @ ( hAPP @ SV72 @ SV933 ) )
| ( hBOOL @ ( hAPP @ SV72 @ SV1729 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1729 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV72 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV72 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3832]) ).
thf(4663,plain,
! [SV1730: $i,SV937: $i,SV76: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV76 ) @ SV937 ) @ SV1730 @ tc_nat )
| ~ ( c_lessequals @ SV76 @ ( c_HOL_Ominus__class_Ominus @ SV1730 @ SV937 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV937 @ SV1730 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3836]) ).
thf(4664,plain,
! [SV1731: $i,SV938: $i,SV77: $i] :
( ( ( c_lessequals @ SV77 @ ( c_HOL_Ominus__class_Ominus @ SV938 @ SV1731 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV77 ) @ SV1731 ) @ SV938 @ tc_nat )
| ~ ( c_lessequals @ SV1731 @ SV938 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3837]) ).
thf(4665,plain,
! [SV1732: $i,SV939: $i,SV78: $i] :
( ( ! [SY6127: $i] :
( ~ ( class_Orderings_Olinorder @ SV78 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV939 @ SV1732 @ SV78 ) @ SY6127 @ SV78 )
| ~ ( c_lessequals @ SV1732 @ SY6127 @ SV78 )
| ~ ( c_lessequals @ SV939 @ SY6127 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3838]) ).
thf(4666,plain,
! [SV1733: $i,SV940: $i,SV79: $i] :
( ( ! [SY6128: $i] :
( ~ ( class_Orderings_Olinorder @ SV79 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV940 @ SV1733 @ SV79 ) @ SY6128 @ SV79 )
| ~ ( c_lessequals @ SV1733 @ SY6128 @ SV79 )
| ~ ( c_lessequals @ SV940 @ SY6128 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3839]) ).
thf(4667,plain,
! [SV1734: $i,SV941: $i,SV80: $i] :
( ( ! [SY6129: $i] :
( ~ ( class_Orderings_Olinorder @ SV80 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV941 @ SV1734 @ SV80 ) @ SY6129 @ SV80 )
| ~ ( c_lessequals @ SV1734 @ SY6129 @ SV80 )
| ~ ( c_lessequals @ SV941 @ SY6129 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3840]) ).
thf(4668,plain,
! [SV1735: $i,SV942: $i,SV81: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV81 )
| ( c_lessequals @ SV942 @ ( c_Orderings_Oord__class_Omax @ SV942 @ SV1735 @ SV81 ) @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3841]) ).
thf(4669,plain,
! [SV1736: $i,SV943: $i,SV82: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV82 )
| ( c_lessequals @ SV943 @ ( c_Orderings_Oord__class_Omax @ SV1736 @ SV943 @ SV82 ) @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3842]) ).
thf(4670,plain,
! [SV949: $i,SV88: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV88 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV88 ) @ SV949 @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3848]) ).
thf(4671,plain,
! [SV1737: $i,SV950: $i,SV89: $i] :
( ( ! [SY6130: $i] :
( ( c_Nat_Onat_Onat__rec @ SV89 @ SV950 @ ( c_Suc @ SV1737 ) @ SY6130 )
= ( hAPP @ ( hAPP @ SV950 @ SV1737 ) @ ( c_Nat_Onat_Onat__rec @ SV89 @ SV950 @ SV1737 @ SY6130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3849]) ).
thf(4672,plain,
! [SV1738: $i,SV951: $i,SV90: $i] :
( ( ! [SY6131: $i,SY6132: $i,SY6133: $i,SY6134: $i,SY6135: $i,SY6136: $i] :
( ( ( hAPP @ ( hAPP @ SV90 @ ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ SV1738 ) ) @ SY6131 )
= ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ ( c_HOL_Otimes__class_Otimes @ SV1738 @ SY6131 @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6132 @ SY6133 @ SV90 @ SY6134 @ SY6135 @ SY6136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3850]) ).
thf(4673,plain,
! [SV1739: $i,SV952: $i,SV91: $i] :
( ( ! [SY6137: $i] :
( ~ ( class_Orderings_Olinorder @ SV91 )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV952 @ SV1739 @ SV91 ) @ SY6137 @ SV91 )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV952 @ SY6137 @ SV91 ) @ ( c_Orderings_Oord__class_Omin @ SV1739 @ SY6137 @ SV91 ) @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3851]) ).
thf(4674,plain,
! [SV1740: $i,SV953: $i,SV92: $i] :
( ( ! [SY6138: $i] :
( ~ ( class_Orderings_Olinorder @ SV92 )
| ( ( c_Orderings_Oord__class_Omin @ SV953 @ ( c_Orderings_Oord__class_Omax @ SV1740 @ SY6138 @ SV92 ) @ SV92 )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV953 @ SV1740 @ SV92 ) @ ( c_Orderings_Oord__class_Omin @ SV953 @ SY6138 @ SV92 ) @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3852]) ).
thf(4675,plain,
! [SV1741: $i,SV954: $i,SV93: $i] :
( ( ! [SY6139: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV93 )
| ( c_lessequals @ SV954 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV1741 ) @ SY6139 ) @ SV93 )
| ~ ( c_lessequals @ SV954 @ SY6139 @ SV93 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV1741 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3853]) ).
thf(4676,plain,
! [SV1742: $i,SV955: $i,SV94: $i] :
( ( ! [SY6140: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV94 )
| ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV1742 ) @ SY6140 ) @ SV94 )
| ~ ( c_lessequals @ SV955 @ SV1742 @ SV94 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SY6140 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3854]) ).
thf(4677,plain,
! [SV956: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ SV95 @ SV956 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV95 @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ SV95 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV95 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3855]) ).
thf(4678,plain,
! [SV957: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ SV96 @ SV957 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ SV96 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3856]) ).
thf(4679,plain,
! [SV958: $i,SV97: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV97 ) @ SV958 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV97 @ SV958 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3857]) ).
thf(4680,plain,
! [SV959: $i,SV98: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV98 @ SV959 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV98 ) @ SV959 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3858]) ).
thf(4681,plain,
! [SV960: $i,SV99: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV99 ) @ SV960 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV99 @ SV960 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3859]) ).
thf(4682,plain,
! [SV961: $i,SV100: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV100 @ SV961 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV100 ) @ SV961 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3860]) ).
thf(4683,plain,
! [SV1743: $i,SV962: $i,SV101: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV101 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV962 ) @ SV1743 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV101 @ SV962 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3861]) ).
thf(4684,plain,
! [SV1744: $i,SV963: $i,SV102: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV102 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV963 ) @ SV1744 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV102 @ SV1744 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3862]) ).
thf(4685,plain,
! [SV1745: $i,SV964: $i,SV103: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV103 @ SV964 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV103 ) @ SV1745 ) @ SV964 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3863]) ).
thf(4686,plain,
! [SV1746: $i,SV965: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV104 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV965 ) @ SV1746 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV104 @ SV965 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3864]) ).
thf(4687,plain,
! [SV1747: $i,SV966: $i,SV105: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV105 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV966 ) @ SV1747 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV105 @ SV1747 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3865]) ).
thf(4688,plain,
! [SV1748: $i,SV967: $i,SV106: $i] :
( ( ! [SY6141: $i,SY6142: $i,SY6143: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV106 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV967 @ SV1748 @ SV106 ) ) @ SY6141 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SY6142 @ SV1748 @ SV106 ) ) @ SY6143 ) @ SV106 )
| ~ ( c_lessequals @ SY6141 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6142 @ SV967 @ SV106 ) @ SV1748 @ SV106 ) ) @ SY6143 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3866]) ).
thf(4689,plain,
! [SV1749: $i,SV968: $i,SV107: $i] :
( ( ! [SY6144: $i,SY6145: $i,SY6146: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV107 )
| ( c_lessequals @ SV968 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SY6144 @ SV107 ) @ SY6145 @ SV107 ) ) @ SY6146 ) @ SV107 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SY6144 @ SY6145 @ SV107 ) ) @ SV968 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV1749 @ SY6145 @ SV107 ) ) @ SY6146 ) @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3867]) ).
thf(4690,plain,
! [SV1750: $i,SV969: $i,SV108: $i] :
( ( ! [SY6147: $i,SY6148: $i,SY6149: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV108 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV969 @ SV1750 @ SV108 ) ) @ SY6147 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SY6148 @ SV1750 @ SV108 ) ) @ SY6149 ) @ SV108 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV969 @ SY6148 @ SV108 ) @ SV1750 @ SV108 ) ) @ SY6147 ) @ SY6149 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3868]) ).
thf(4691,plain,
! [SV1751: $i,SV970: $i,SV109: $i] :
( ( ! [SY6150: $i,SY6151: $i,SY6152: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV109 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV970 @ SV1751 @ SV109 ) @ SY6150 @ SV109 ) ) @ SY6151 ) @ SY6152 @ SV109 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV970 @ SY6150 @ SV109 ) ) @ SY6151 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV1751 @ SY6150 @ SV109 ) ) @ SY6152 ) @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3869]) ).
thf(4692,plain,
! [SV971: $i,SV110: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV110 ) @ SV971 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV110 @ SV971 @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV971 @ SV110 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3870]) ).
thf(4693,plain,
! [SV1752: $i,SV972: $i,SV111: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV111 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ ( c_HOL_Otimes__class_Otimes @ SV972 @ SV972 @ SV111 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1752 @ SV1752 @ SV111 ) ) @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3871]) ).
thf(4694,plain,
! [SV1753: $i,SV973: $i,SV112: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV112 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV973 ) @ SV1753 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV1753 ) @ SV973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3872]) ).
thf(4695,plain,
! [SV1754: $i,SV974: $i,SV113: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV974 ) @ SV1754 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1754 ) @ SV974 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3873]) ).
thf(4696,plain,
! [SV1755: $i,SV976: $i,SV115: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV976 ) @ SV1755 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV1755 ) @ SV976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3875]) ).
thf(4697,plain,
! [SV1756: $i,SV977: $i,SV116: $i] :
( ( ! [SY6153: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV116 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV977 ) @ SV1756 ) @ SY6153 @ SV116 @ SV116 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV977 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV1756 @ SY6153 @ SV116 @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3876]) ).
thf(4698,plain,
! [SV1757: $i,SV978: $i,SV117: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV978 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV1757 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1757 @ SV117 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1757 @ SV978 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3877]) ).
thf(4699,plain,
! [SV979: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ SV118 @ SV979 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV118 @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ SV118 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV118 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3878]) ).
thf(4700,plain,
! [SV1758: $i,SV980: $i,SV119: $i] :
( ( ! [SY6154: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV980 @ SV1758 @ SV119 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SY6154 @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV980 @ SY6154 @ SV119 ) @ ( c_HOL_Otimes__class_Otimes @ SV1758 @ SY6154 @ SV119 ) @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3879]) ).
thf(4701,plain,
! [SV1759: $i,SV981: $i,SV120: $i] :
( ( ! [SY6155: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV981 @ SV1759 @ SV120 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SY6155 @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY6155 @ SV981 @ SV120 ) @ ( c_HOL_Otimes__class_Otimes @ SY6155 @ SV1759 @ SV120 ) @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3880]) ).
thf(4702,plain,
! [SV1760: $i,SV982: $i,SV121: $i] :
( ( ! [SY6156: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ SV121 )
| ( c_HOL_Oord__class_Oless @ SV982 @ SV1760 @ SV121 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SY6156 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV982 @ SY6156 @ SV121 ) @ ( c_HOL_Otimes__class_Otimes @ SV1760 @ SY6156 @ SV121 ) @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3881]) ).
thf(4703,plain,
! [SV1761: $i,SV983: $i,SV122: $i] :
( ( ! [SY6157: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ SV122 )
| ( c_HOL_Oord__class_Oless @ SV983 @ SV1761 @ SV122 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SY6157 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY6157 @ SV983 @ SV122 ) @ ( c_HOL_Otimes__class_Otimes @ SY6157 @ SV1761 @ SV122 ) @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3882]) ).
thf(4704,plain,
! [SV1762: $i,SV984: $i,SV123: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV123 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV984 @ SV1762 @ SV123 ) @ SV984 @ SV123 )
= ( c_HOL_Otimes__class_Otimes @ SV984 @ ( c_Power_Opower__class_Opower @ SV984 @ SV1762 @ SV123 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3883]) ).
thf(4705,plain,
! [SV1763: $i,SV985: $i,SV124: $i] :
( ( ! [SY6158: $i] :
( ~ ( class_Orderings_Olinorder @ SV124 )
| ( c_lessequals @ SV985 @ SV1763 @ SV124 )
| ( c_lessequals @ SV985 @ SY6158 @ SV124 )
| ~ ( c_lessequals @ SV985 @ ( c_Orderings_Oord__class_Omax @ SY6158 @ SV1763 @ SV124 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3884]) ).
thf(4706,plain,
! [SV1764: $i,SV986: $i,SV125: $i] :
( ( ! [SY6159: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV986 @ SV1764 @ SV125 ) @ ( c_Power_Opower__class_Opower @ SV986 @ SY6159 @ SV125 ) @ SV125 )
= ( c_Power_Opower__class_Opower @ SV986 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1764 ) @ SY6159 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3885]) ).
thf(4707,plain,
! [SV988: $i,SV127: $i] :
( ( ( c_lessequals @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV127 @ SV988 ) @ SV988 @ tc_nat )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV127 @ SV988 ) )
| ( hBOOL @ ( hAPP @ SV127 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3887]) ).
thf(4708,plain,
! [SV1765: $i,SV989: $i,SV128: $i] :
( ( ! [SY6160: $i,SY6161: $i,SY6162: $i,SY6163: $i,SY6164: $i,SY6165: $i] :
( ( ( hAPP @ ( hAPP @ SV128 @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SY6160 ) ) @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SY6161 ) )
= ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY6160 ) @ SY6161 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6162 @ SV128 @ SV989 @ SY6163 @ SY6164 @ SY6165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3888]) ).
thf(4709,plain,
! [SV1766: $i,SV990: $i,SV129: $i] :
( ( ! [SY6166: $i] :
( ~ ( c_lessequals @ SV129 @ SV990 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SV1766 @ tc_nat ) ) @ SY6166 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV129 @ SV1766 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV990 @ SV129 @ tc_nat ) @ SV1766 @ tc_nat ) ) @ SY6166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3889]) ).
thf(4710,plain,
! [SV1767: $i,SV991: $i,SV131: $i] :
( ( ! [SY6167: $i] :
( ~ ( class_Orderings_Olinorder @ SV131 )
| ( c_lessequals @ SV991 @ SV1767 @ SV131 )
| ~ ( c_lessequals @ SV991 @ ( c_Orderings_Oord__class_Omin @ SY6167 @ SV1767 @ SV131 ) @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3890]) ).
thf(4711,plain,
! [SV1768: $i,SV992: $i,SV132: $i] :
( ( ! [SY6168: $i] :
( ~ ( class_Orderings_Olinorder @ SV132 )
| ( c_lessequals @ SV992 @ SV1768 @ SV132 )
| ~ ( c_lessequals @ SV992 @ ( c_Orderings_Oord__class_Omin @ SV1768 @ SY6168 @ SV132 ) @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3891]) ).
thf(4712,plain,
! [SV1769: $i,SV993: $i,SV133: $i] :
( ( ! [SY6169: $i] :
( ~ ( class_Orderings_Olinorder @ SV133 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV993 @ SV1769 @ SV133 ) @ SY6169 @ SV133 )
| ~ ( c_lessequals @ SV1769 @ SY6169 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3892]) ).
thf(4713,plain,
! [SV1770: $i,SV994: $i,SV134: $i] :
( ( ! [SY6170: $i] :
( ~ ( class_Orderings_Olinorder @ SV134 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV994 @ SV1770 @ SV134 ) @ SY6170 @ SV134 )
| ~ ( c_lessequals @ SV994 @ SY6170 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3893]) ).
thf(4714,plain,
! [SV1771: $i,SV995: $i,SV135: $i] :
( ( ! [SY6171: $i] :
( ~ ( class_Orderings_Olinorder @ SV135 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV995 @ SV1771 @ SV135 ) @ SY6171 @ SV135 )
| ~ ( c_lessequals @ SV1771 @ SY6171 @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3894]) ).
thf(4715,plain,
! [SV1772: $i,SV996: $i,SV136: $i] :
( ( ! [SY6172: $i] :
( ~ ( class_Orderings_Olinorder @ SV136 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV996 @ SV1772 @ SV136 ) @ SY6172 @ SV136 )
| ~ ( c_lessequals @ SV996 @ SY6172 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3895]) ).
thf(4716,plain,
! [SV1773: $i,SV997: $i,SV137: $i] :
( ( ! [SY6173: $i] :
( ~ ( class_Orderings_Olinorder @ SV137 )
| ( c_lessequals @ SV997 @ SV1773 @ SV137 )
| ~ ( c_lessequals @ SV997 @ ( c_Orderings_Oord__class_Omin @ SY6173 @ SV1773 @ SV137 ) @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3896]) ).
thf(4717,plain,
! [SV1774: $i,SV998: $i,SV138: $i] :
( ( ! [SY6174: $i] :
( ~ ( class_Orderings_Olinorder @ SV138 )
| ( c_lessequals @ SV998 @ SV1774 @ SV138 )
| ~ ( c_lessequals @ SV998 @ ( c_Orderings_Oord__class_Omin @ SV1774 @ SY6174 @ SV138 ) @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3897]) ).
thf(4718,plain,
! [SV1775: $i,SV999: $i,SV139: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV139 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV999 @ SV1775 @ SV139 @ SV139 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1775 @ SV999 @ SV139 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3898]) ).
thf(4719,plain,
! [SV1776: $i,SV1000: $i,SV140: $i] :
( ( ! [SY6175: $i,SY6176: $i,SY6177: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV140 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1776 @ SV140 ) ) @ SY6175 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SY6176 @ SV1776 @ SV140 ) ) @ SY6177 ) @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SY6175 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6176 @ SV1000 @ SV140 ) @ SV1776 @ SV140 ) ) @ SY6177 ) @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3899]) ).
thf(4720,plain,
! [SV1777: $i,SV1001: $i,SV141: $i] :
( ( ! [SY6178: $i,SY6179: $i,SY6180: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV141 )
| ( c_HOL_Oord__class_Oless @ SV1001 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1777 @ SY6178 @ SV141 ) @ SY6179 @ SV141 ) ) @ SY6180 ) @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SY6178 @ SY6179 @ SV141 ) ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV1777 @ SY6179 @ SV141 ) ) @ SY6180 ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3900]) ).
thf(4721,plain,
! [SV1778: $i,SV1002: $i,SV142: $i] :
( ( ! [SY6181: $i,SY6182: $i,SY6183: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV142 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1778 @ SV142 ) ) @ SY6181 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SY6182 @ SV1778 @ SV142 ) ) @ SY6183 ) @ SV142 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1002 @ SY6182 @ SV142 ) @ SV1778 @ SV142 ) ) @ SY6181 ) @ SY6183 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3901]) ).
thf(4722,plain,
! [SV1779: $i,SV1003: $i,SV143: $i] :
( ( ! [SY6184: $i,SY6185: $i,SY6186: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV143 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1003 @ SV1779 @ SV143 ) @ SY6184 @ SV143 ) ) @ SY6185 ) @ SY6186 @ SV143 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1003 @ SY6184 @ SV143 ) ) @ SY6185 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1779 @ SY6184 @ SV143 ) ) @ SY6186 ) @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3902]) ).
thf(4723,plain,
! [SV1780: $i,SV1004: $i,SV144: $i] :
( ( ! [SY6187: $i] :
( ~ ( class_Orderings_Olinorder @ SV144 )
| ( c_lessequals @ SV1004 @ SV1780 @ SV144 )
| ( c_lessequals @ SY6187 @ SV1780 @ SV144 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY6187 @ SV1004 @ SV144 ) @ SV1780 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3903]) ).
thf(4724,plain,
! [SV1781: $i,SV1005: $i,SV145: $i] :
( ( ! [SY6188: $i] :
( ~ ( c_lessequals @ SV145 @ SV1005 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV145 @ SV1781 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1005 @ SV145 @ tc_nat ) @ SV1781 @ tc_nat ) ) @ SY6188 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1005 @ SV1781 @ tc_nat ) ) @ SY6188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3904]) ).
thf(4725,plain,
! [SV1006: $i,SV146: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV146 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV1006 ) @ SV1006 ) @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3905]) ).
thf(4726,plain,
! [SV1007: $i,SV147: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV147 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1007 @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1007 ) @ SV1007 ) @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3906]) ).
thf(4727,plain,
! [SV1008: $i,SV148: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV148 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1008 @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV1008 ) @ SV1008 ) @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3907]) ).
thf(4728,plain,
! [SV1009: $i,SV149: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV149 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV1009 ) @ SV1009 ) @ ( c_HOL_Ozero__class_Ozero @ SV149 ) @ SV149 )
| ~ ( c_HOL_Oord__class_Oless @ SV1009 @ ( c_HOL_Ozero__class_Ozero @ SV149 ) @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3908]) ).
thf(4729,plain,
! [SV1782: $i,SV1010: $i,SV150: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV150 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1010 @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1782 @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ ( c_HOL_Otimes__class_Otimes @ SV1010 @ SV1782 @ SV150 ) @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3909]) ).
thf(4730,plain,
! [SV1783: $i,SV1011: $i,SV151: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV151 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1011 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1783 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ ( c_HOL_Otimes__class_Otimes @ SV1783 @ SV1011 @ SV151 ) @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3910]) ).
thf(4731,plain,
! [SV1784: $i,SV1012: $i,SV152: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV152 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SV1784 @ SV152 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1784 @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1012 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3911]) ).
thf(4732,plain,
! [SV1785: $i,SV1013: $i,SV153: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV153 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV1013 @ SV1785 @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1785 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1013 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3912]) ).
thf(4733,plain,
! [SV1014: $i,SV154: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV154 @ SV1014 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1014 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV154 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3913]) ).
thf(4734,plain,
! [SV1786: $i,SV1015: $i,SV155: $i] :
( ( ! [SY6189: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV155 )
| ( c_HOL_Oord__class_Oless @ SV1015 @ SV1786 @ SV155 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV1786 @ SV155 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1015 @ SY6189 @ SV155 ) @ ( c_Power_Opower__class_Opower @ SV1786 @ SY6189 @ SV155 ) @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3914]) ).
thf(4735,plain,
! [SV1787: $i,SV1016: $i,SV156: $i] :
( ( ! [SY6190: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV156 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1016 ) @ SV1787 ) ) @ SY6190 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1787 ) @ SY6190 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3915]) ).
thf(4736,plain,
! [SV1788: $i,SV1017: $i,SV157: $i] :
( ( ! [SY6191: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1017 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1788 ) @ SY6191 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1788 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1017 ) @ SY6191 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(4737,plain,
! [SV1789: $i,SV1018: $i,SV158: $i] :
( ( ! [SY6192: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV158 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1018 ) @ SV1789 ) ) @ SY6192 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1018 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1789 ) @ SY6192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3917]) ).
thf(4738,plain,
! [SV1790: $i,SV1019: $i,SV159: $i] :
( ( ! [SY6193: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV159 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1019 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1790 ) @ SY6193 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1019 ) @ SV1790 ) ) @ SY6193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3918]) ).
thf(4739,plain,
! [SV1791: $i,SV1020: $i,SV160: $i] :
( ( ! [SY6194: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV160 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV1020 ) @ SV1791 ) ) @ SY6194 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV1020 ) @ SY6194 ) ) @ SV1791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3919]) ).
thf(4740,plain,
! [SV1792: $i,SV1021: $i,SV161: $i] :
( ( ! [SY6195: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV161 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1021 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1792 ) @ SY6195 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1021 ) @ SY6195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3920]) ).
thf(4741,plain,
! [SV1793: $i,SV1022: $i,SV162: $i] :
( ( ! [SY6196: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1022 ) @ SV1793 ) ) @ SY6196 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1022 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1793 ) @ SY6196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3921]) ).
thf(4742,plain,
! [SV1023: $i,SV163: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV163 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1023 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1023 ) @ SV163 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3922]) ).
thf(4743,plain,
! [SV1794: $i,SV1024: $i,SV164: $i] :
( ( ! [SY6197: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV164 )
| ( ( c_Power_Opower__class_Opower @ SV1024 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1794 ) @ SY6197 ) @ SV164 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1024 @ SV1794 @ SV164 ) @ ( c_Power_Opower__class_Opower @ SV1024 @ SY6197 @ SV164 ) @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3923]) ).
thf(4744,plain,
! [SV1025: $i,SV165: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV165 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1025 @ SV165 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3924]) ).
thf(4745,plain,
! [SV1026: $i,SV166: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV166 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV166 @ SV1026 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3925]) ).
thf(4746,plain,
! [SV1795: $i,SV1027: $i,SV167: $i] :
( ( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV167 @ SV1027 @ SV1795 ) @ SV1795 )
= ( c_List_Olist_OCons @ SV167 @ SV1027 @ SV1795 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3926]) ).
thf(4747,plain,
! [SV1796: $i,SV1028: $i,SV168: $i] :
( ( ( c_List_Oreplicate @ ( c_Suc @ SV168 ) @ SV1028 @ SV1796 )
= ( c_List_Olist_OCons @ SV1028 @ ( c_List_Oreplicate @ SV168 @ SV1028 @ SV1796 ) @ SV1796 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3927]) ).
thf(4748,plain,
! [SV1797: $i,SV1029: $i,SV169: $i] :
( ( ( c_lessequals @ SV169 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1029 ) @ SV1797 ) @ tc_nat )
| ~ ( c_lessequals @ SV169 @ SV1797 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3928]) ).
thf(4749,plain,
! [SV1798: $i,SV1030: $i,SV170: $i] :
( ( ( c_lessequals @ SV170 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1030 ) @ SV1798 ) @ tc_nat )
| ~ ( c_lessequals @ SV170 @ SV1030 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3929]) ).
thf(4750,plain,
! [SV1799: $i,SV1031: $i,SV171: $i] :
( ( ( c_lessequals @ SV171 @ SV1031 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1799 ) @ SV171 ) @ SV1031 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3930]) ).
thf(4751,plain,
! [SV1800: $i,SV1032: $i,SV172: $i] :
( ( ( c_lessequals @ SV172 @ SV1032 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV172 ) @ SV1800 ) @ SV1032 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3931]) ).
thf(4752,plain,
! [SV1801: $i,SV1033: $i,SV173: $i] :
( ( ( c_lessequals @ SV173 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1033 ) @ SV1801 ) @ tc_nat )
| ~ ( c_lessequals @ SV173 @ SV1801 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3932]) ).
thf(4753,plain,
! [SV1802: $i,SV1034: $i,SV174: $i] :
( ( ( c_lessequals @ SV174 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1034 ) @ SV1802 ) @ tc_nat )
| ~ ( c_lessequals @ SV174 @ SV1034 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3933]) ).
thf(4754,plain,
! [SV1803: $i,SV1035: $i,SV175: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV175 )
| ( ( c_Orderings_Oord__class_Omin @ SV1035 @ SV1803 @ SV175 )
= SV1035 )
| ~ ( c_lessequals @ SV1035 @ SV1803 @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3934]) ).
thf(4755,plain,
! [SV1804: $i,SV1036: $i,SV176: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV176 )
| ( ( c_Orderings_Oord__class_Omin @ SV1036 @ SV1804 @ SV176 )
= SV1804 )
| ~ ( c_lessequals @ SV1804 @ SV1036 @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(4756,plain,
! [SV1805: $i,SV1037: $i,SV177: $i] :
( ( ! [SY6198: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV177 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ SV1037 @ SV1805 @ SV177 ) @ SY6198 @ SV177 )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ SV1037 @ SY6198 @ SV177 ) @ ( c_HOL_Ominus__class_Ominus @ SV1805 @ SY6198 @ SV177 ) @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3936]) ).
thf(4757,plain,
! [SV1806: $i,SV1038: $i,SV178: $i] :
( ( ! [SY6199: $i] :
( ( c_Type_Otypings @ SV178 @ SV1038 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV1806 @ SV178 @ SY6199 @ SV1038 ) )
| ~ ( c_Type_Otyping @ SV178 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY6199 @ SV1038 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3937]) ).
thf(4758,plain,
! [SV1807: $i,SV1039: $i,SV179: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV179 )
| ( c_HOL_Oord__class_Oless @ SV1039 @ SV1807 @ SV179 )
| ( c_lessequals @ SV1807 @ SV1039 @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3938]) ).
thf(4759,plain,
! [SV1040: $i,SV180: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV180 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1040 @ SV1040 @ SV180 )
| ~ ( c_HOL_Oord__class_Oless @ SV1040 @ SV1040 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3939]) ).
thf(4760,plain,
! [SV1041: $i,SV181: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV181 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1041 @ SV1041 @ SV181 )
| ( c_lessequals @ SV1041 @ SV1041 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3940]) ).
thf(4761,plain,
! [SV1808: $i,SV1042: $i,SV182: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SV1808 @ SV182 )
| ~ ( c_lessequals @ SV1808 @ SV1042 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3941]) ).
thf(4762,plain,
! [SV1809: $i,SV1043: $i,SV183: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV183 )
| ( c_lessequals @ SV1043 @ SV1809 @ SV183 )
| ( c_HOL_Oord__class_Oless @ SV1809 @ SV1043 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3942]) ).
thf(4763,plain,
! [SV1810: $i,SV1044: $i,SV184: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV184 )
| ~ ( c_lessequals @ SV1044 @ SV1810 @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ SV1810 @ SV1044 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3943]) ).
thf(4764,plain,
! [SV1811: $i,SV1045: $i,SV185: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV185 )
| ( c_HOL_Oord__class_Oless @ SV1045 @ SV1811 @ SV185 )
| ( c_lessequals @ SV1811 @ SV1045 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3944]) ).
thf(4765,plain,
! [SV1812: $i,SV1046: $i,SV186: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV186 )
| ~ ( c_lessequals @ SV1046 @ SV1812 @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SV1812 @ SV1046 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3945]) ).
thf(4766,plain,
! [SV1047: $i,SV187: $i] :
( ( ( hBOOL @ ( hAPP @ SV187 @ SV1047 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV187 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV187 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3946]) ).
thf(4767,plain,
! [SV1048: $i,SV188: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV188 @ SV188 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV188 ) @ SV1048 @ SV188 )
= SV1048 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3947]) ).
thf(4768,plain,
! [SV1049: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ SV189 @ SV1049 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV189 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV189 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3948]) ).
thf(4769,plain,
! [SV1813: $i,SV1050: $i,SV190: $i] :
( ( ! [SY6200: $i] :
( ~ ( class_Orderings_Olinorder @ SV190 )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ SV1050 @ SV1813 @ SV190 ) @ SY6200 @ SV190 )
= ( c_Orderings_Oord__class_Omin @ SV1050 @ ( c_Orderings_Oord__class_Omin @ SV1813 @ SY6200 @ SV190 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3949]) ).
thf(4770,plain,
! [SV1814: $i,SV1051: $i,SV191: $i] :
( ( ! [SY6201: $i] :
( ~ ( class_Orderings_Olinorder @ SV191 )
| ( ( c_Orderings_Oord__class_Omin @ SV1051 @ ( c_Orderings_Oord__class_Omin @ SV1814 @ SY6201 @ SV191 ) @ SV191 )
= ( c_Orderings_Oord__class_Omin @ SV1814 @ ( c_Orderings_Oord__class_Omin @ SV1051 @ SY6201 @ SV191 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3950]) ).
thf(4771,plain,
! [SV1815: $i,SV1052: $i,SV192: $i] :
( ( ! [SY6202: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV192 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV192 )
| ( c_HOL_Oord__class_Oless @ SV1052 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV1815 ) @ SY6202 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SY6202 @ SV192 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV1815 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3951]) ).
thf(4772,plain,
! [SV1816: $i,SV1053: $i,SV193: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV193 @ SV1053 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV193 @ SV1816 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1816 @ SV1053 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3952]) ).
thf(4773,plain,
! [SV1817: $i,SV1054: $i,SV194: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV194 @ SV1054 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1817 @ SV1054 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV194 @ SV1817 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3953]) ).
thf(4774,plain,
! [SV1818: $i,SV1055: $i,SV195: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV195 @ SV1055 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1818 @ SV1055 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV195 @ SV1818 @ tc_nat )
| ~ ( c_lessequals @ SV1055 @ SV1818 @ tc_nat )
| ~ ( c_lessequals @ SV1055 @ SV195 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3954]) ).
thf(4775,plain,
! [SV1819: $i,SV1056: $i,SV196: $i] :
( ( ( c_lessequals @ SV196 @ SV1056 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV196 @ SV1819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1056 @ SV1819 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1819 @ SV1056 @ tc_nat )
| ~ ( c_lessequals @ SV1819 @ SV196 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3955]) ).
thf(4776,plain,
! [SV1820: $i,SV1058: $i,SV198: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV198 @ SV1058 @ tc_nat ) @ SV1820 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV198 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1058 ) @ SV1820 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3957]) ).
thf(4777,plain,
! [SV1821: $i,SV1059: $i,SV199: $i] :
( ( ! [SY6203: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV199 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1821 @ SV199 ) @ ( c_Power_Opower__class_Opower @ SY6203 @ SV1821 @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV1059 @ SV199 )
| ~ ( c_lessequals @ SV1059 @ SY6203 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3958]) ).
thf(4778,plain,
! [SV1822: $i,SV1060: $i,SV200: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV200 )
| ( ( c_Orderings_Oord__class_Omin @ SV1060 @ ( c_Orderings_Oord__class_Omax @ SV1060 @ SV1822 @ SV200 ) @ SV200 )
= SV1060 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3959]) ).
thf(4779,plain,
! [SV1823: $i,SV1061: $i,SV201: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV201 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1061 @ SV201 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1823 @ SV201 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3960]) ).
thf(4780,plain,
! [SV1824: $i,SV1062: $i,SV202: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV202 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV1062 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV1824 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3961]) ).
thf(4781,plain,
! [SV1825: $i,SV1063: $i,SV203: $i] :
( ( ! [SY6204: $i,SY6205: $i,SY6206: $i] :
( ( c_List_Ofoldl @ SV203 @ SV1063 @ ( c_List_Olist_OCons @ SV1825 @ SY6204 @ SY6205 ) @ SY6206 @ SY6205 )
= ( c_List_Ofoldl @ SV203 @ ( hAPP @ ( hAPP @ SV203 @ SV1063 ) @ SV1825 ) @ SY6204 @ SY6206 @ SY6205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3962]) ).
thf(4782,plain,
! [SV1826: $i,SV1065: $i,SV205: $i] :
( ( ! [SY6207: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV205 ) @ ( c_List_Olist_OCons @ SV1065 @ SV1826 @ SY6207 ) @ SY6207 )
= ( c_List_Odrop @ SV205 @ SV1826 @ SY6207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3964]) ).
thf(4783,plain,
! [SV1827: $i,SV1066: $i,SV206: $i] :
( ( ( c_lessequals @ SV206 @ SV1066 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1827 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV206 @ SV1827 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1066 @ SV1827 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3965]) ).
thf(4784,plain,
! [SV1828: $i,SV1067: $i,SV207: $i] :
( ( ( c_lessequals @ SV207 @ SV1067 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1828 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1828 @ SV207 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1828 @ SV1067 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3966]) ).
thf(4785,plain,
! [SV1829: $i,SV1068: $i,SV208: $i] :
( ( ( c_lessequals @ SV208 @ SV1068 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1829 @ SV208 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1829 @ SV1068 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1829 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3967]) ).
thf(4786,plain,
! [SV1830: $i,SV1069: $i,SV209: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SV1069 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SV1830 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1069 @ SV1830 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV209 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3968]) ).
thf(4787,plain,
! [SV1831: $i,SV1070: $i,SV210: $i] :
( ( ! [SY6208: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV210 )
| ( c_lessequals @ SV1070 @ SV1831 @ SV210 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY6208 @ SV1831 @ SV210 ) @ ( c_HOL_Otimes__class_Otimes @ SY6208 @ SV1070 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SY6208 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3969]) ).
thf(4788,plain,
! [SV1832: $i,SV1071: $i,SV211: $i] :
( ( ! [SY6209: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV211 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV1832 @ SV211 ) @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SY6209 @ SV211 ) @ SV211 )
| ~ ( c_lessequals @ SY6209 @ SV1832 @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3970]) ).
thf(4789,plain,
! [SV1833: $i,SV1072: $i,SV212: $i] :
( ( ! [SY6210: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV212 )
| ( c_lessequals @ SV1072 @ SV1833 @ SV212 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY6210 @ SV1072 @ SV212 ) @ ( c_HOL_Otimes__class_Otimes @ SY6210 @ SV1833 @ SV212 ) @ SV212 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SY6210 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3971]) ).
thf(4790,plain,
! [SV1834: $i,SV1073: $i,SV213: $i] :
( ( ! [SY6211: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV213 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV1834 @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SY6211 @ SV213 ) @ SV213 )
| ~ ( c_lessequals @ SV1834 @ SY6211 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV1073 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3972]) ).
thf(4791,plain,
! [SV1835: $i,SV1074: $i,SV214: $i] :
( ( ! [SY6212: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV214 )
| ( c_lessequals @ SV1074 @ SV1835 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SY6212 @ SV214 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY6212 @ SV1074 @ SV214 ) @ ( c_HOL_Otimes__class_Otimes @ SY6212 @ SV1835 @ SV214 ) @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3973]) ).
thf(4792,plain,
! [SV1836: $i,SV1075: $i,SV215: $i] :
( ( ! [SY6213: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV215 )
| ( c_lessequals @ SV1075 @ SV1836 @ SV215 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SY6213 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1075 @ SY6213 @ SV215 ) @ ( c_HOL_Otimes__class_Otimes @ SV1836 @ SY6213 @ SV215 ) @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3974]) ).
thf(4793,plain,
! [SV1076: $i,SV216: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV216 @ SV1076 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV216 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1076 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3975]) ).
thf(4794,plain,
! [SV1837: $i,SV1077: $i,SV217: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV217 ) @ SV1077 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1837 ) @ SV1077 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV217 @ SV1837 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3976]) ).
thf(4795,plain,
! [SV1838: $i,SV1078: $i,SV218: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV218 ) @ SV1078 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV218 ) @ SV1838 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1078 @ SV1838 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3977]) ).
thf(4796,plain,
! [SV1839: $i,SV1079: $i,SV221: $i] :
( ( ! [SY6214: $i] :
( ~ ( class_Orderings_Olinorder @ SV221 )
| ( c_HOL_Oord__class_Oless @ SV1079 @ ( c_Orderings_Oord__class_Omax @ SV1839 @ SY6214 @ SV221 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SV1079 @ SV1839 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3978]) ).
thf(4797,plain,
! [SV1840: $i,SV1080: $i,SV222: $i] :
( ( ! [SY6215: $i] :
( ~ ( class_Orderings_Olinorder @ SV222 )
| ( c_HOL_Oord__class_Oless @ SV1080 @ ( c_Orderings_Oord__class_Omax @ SV1840 @ SY6215 @ SV222 ) @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ SV1080 @ SY6215 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3979]) ).
thf(4798,plain,
! [SV1841: $i,SV1081: $i,SV223: $i] :
( ( ! [SY6216: $i] :
( ~ ( class_Orderings_Olinorder @ SV223 )
| ( c_HOL_Oord__class_Oless @ SV1081 @ ( c_Orderings_Oord__class_Omax @ SV1841 @ SY6216 @ SV223 ) @ SV223 )
| ~ ( c_HOL_Oord__class_Oless @ SV1081 @ SV1841 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3980]) ).
thf(4799,plain,
! [SV1842: $i,SV1082: $i,SV224: $i] :
( ( ! [SY6217: $i] :
( ~ ( class_Orderings_Olinorder @ SV224 )
| ( c_HOL_Oord__class_Oless @ SV1082 @ ( c_Orderings_Oord__class_Omax @ SV1842 @ SY6217 @ SV224 ) @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ SV1082 @ SY6217 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3981]) ).
thf(4800,plain,
! [SV1843: $i,SV1083: $i,SV225: $i] :
( ( ! [SY6218: $i] :
( ~ ( class_Orderings_Olinorder @ SV225 )
| ( c_HOL_Oord__class_Oless @ SV1083 @ SV1843 @ SV225 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SY6218 @ SV225 ) @ SV1843 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3982]) ).
thf(4801,plain,
! [SV1844: $i,SV1084: $i,SV226: $i] :
( ( ! [SY6219: $i] :
( ~ ( class_Orderings_Olinorder @ SV226 )
| ( c_HOL_Oord__class_Oless @ SV1084 @ SV1844 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY6219 @ SV1084 @ SV226 ) @ SV1844 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3983]) ).
thf(4802,plain,
! [SV227: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV227 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV227 ) @ SV227 )
= ( c_HOL_Ozero__class_Ozero @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3984]) ).
thf(4803,plain,
! [SV1845: $i,SV1085: $i,SV228: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV228 )
| ( ( c_Orderings_Oord__class_Omin @ SV1085 @ SV1845 @ SV228 )
= ( c_Orderings_Oord__class_Omin @ SV1845 @ SV1085 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3985]) ).
thf(4804,plain,
! [SV1846: $i,SV1086: $i,SV229: $i] :
( ( ! [SY6220: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV229 @ SV1086 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1846 @ SV1086 @ tc_nat ) ) @ SY6220 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV229 ) @ SV1846 ) @ SV1086 @ tc_nat ) ) @ SY6220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3986]) ).
thf(4805,plain,
! [SV1847: $i,SV1087: $i,SV230: $i] :
( ( ! [SY6221: $i,SY6222: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV230 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SV1087 @ SV1847 @ SV230 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SY6221 @ SV1847 @ SV230 ) ) @ SY6222 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ SV1087 ) @ SY6221 ) @ SV1847 @ SV230 ) ) @ SY6222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3987]) ).
thf(4806,plain,
! [SV1089: $i,SV232: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV232 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV232 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3989]) ).
thf(4807,plain,
! [SV1090: $i,SV233: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV233 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV233 @ SV1090 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3990]) ).
thf(4808,plain,
! [SV1848: $i,SV1091: $i,SV234: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV1091 ) @ SV1848 ) @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV1848 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV1091 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3991]) ).
thf(4809,plain,
! [SV1849: $i,SV1092: $i,SV235: $i] :
( ( ! [SY6223: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV235 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1092 @ SV1849 @ SV235 ) @ ( c_Power_Opower__class_Opower @ SY6223 @ SV1849 @ SV235 ) @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1849 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV235 ) @ SV1092 @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SY6223 @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3992]) ).
thf(4810,plain,
! [SV1850: $i,SV1093: $i,SV236: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV236 )
| ( SV1093
= ( c_HOL_Ozero__class_Ozero @ SV236 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ ( c_HOL_Otimes__class_Otimes @ SV1093 @ SV1093 @ SV236 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1850 @ SV1850 @ SV236 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV236 ) @ SV236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3993]) ).
thf(4811,plain,
! [SV1851: $i,SV1094: $i,SV237: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV237 )
| ( SV1094
= ( c_HOL_Ozero__class_Ozero @ SV237 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( c_HOL_Otimes__class_Otimes @ SV1851 @ SV1851 @ SV237 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1094 @ SV1094 @ SV237 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV237 ) @ SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3994]) ).
thf(4812,plain,
! [SV1852: $i,SV1095: $i,SV238: $i] :
( ( ! [SY6224: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV238 @ SV1095 @ SV1852 ) @ SY6224 @ SV1852 )
= ( c_List_Olist_OCons @ SV238 @ ( c_List_Oappend @ SV1095 @ SY6224 @ SV1852 ) @ SV1852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3995]) ).
thf(4813,plain,
! [SV1853: $i,SV1096: $i,SV239: $i] :
( ( ! [SY6225: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV239 @ SV1096 @ SV1853 ) @ SY6225 @ SV1853 )
= ( c_List_Olist_OCons @ SV239 @ ( c_List_Oappend @ SV1096 @ SY6225 @ SV1853 ) @ SV1853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3996]) ).
thf(4814,plain,
! [SV1854: $i,SV1097: $i,SV240: $i] :
( ( ! [SY6226: $i] :
( ~ ( hBOOL @ ( hAPP @ SV240 @ ( c_Nat_Onat_Onat__case @ SV1097 @ SV1854 @ ( c_Suc @ SY6226 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV240 @ ( hAPP @ SV1854 @ SY6226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3997]) ).
thf(4815,plain,
! [SV1855: $i,SV1098: $i,SV241: $i] :
( ( ! [SY6227: $i] :
( ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_Nat_Onat_Onat__case @ SV1098 @ SV1855 @ ( c_Suc @ SY6227 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV241 @ ( hAPP @ SV1855 @ SY6227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3998]) ).
thf(4816,plain,
! [SV1856: $i,SV1099: $i,SV242: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV242 @ ( c_HOL_Ominus__class_Ominus @ SV1099 @ SV1856 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV242 @ SV1099 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV242 @ SV1856 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3999]) ).
thf(4817,plain,
! [SV1857: $i,SV1100: $i,SV243: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV243 @ SV1100 @ tc_nat ) @ SV1857 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV243 @ SV1857 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1100 @ SV1857 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4000]) ).
thf(4818,plain,
! [SV1858: $i,SV1101: $i,SV244: $i] :
( ( ! [SY6228: $i] :
( ~ ( class_Orderings_Olinorder @ SV244 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1101 @ SV1858 @ SV244 ) @ SY6228 @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ SV1101 @ SY6228 @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4001]) ).
thf(4819,plain,
! [SV1859: $i,SV1102: $i,SV245: $i] :
( ( ! [SY6229: $i] :
( ~ ( class_Orderings_Olinorder @ SV245 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1102 @ SV1859 @ SV245 ) @ SY6229 @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ SV1859 @ SY6229 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4002]) ).
thf(4820,plain,
! [SV1860: $i,SV1103: $i,SV246: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV246 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ SV1103 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ ( c_HOL_Ozero__class_Ozero @ SV246 ) @ SV1860 @ SV246 @ SV246 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ SV1103 @ SV1860 @ SV246 @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4003]) ).
thf(4821,plain,
! [SV1861: $i,SV1104: $i,SV247: $i] :
( ( ! [SY6230: $i] :
( ~ ( class_Orderings_Olinorder @ SV247 )
| ( c_lessequals @ SV1104 @ SV1861 @ SV247 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY6230 @ SV1104 @ SV247 ) @ SV1861 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4004]) ).
thf(4822,plain,
! [SV1862: $i,SV1105: $i,SV248: $i] :
( ( ! [SY6231: $i] :
( ~ ( class_Orderings_Olinorder @ SV248 )
| ( c_lessequals @ SV1105 @ SV1862 @ SV248 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1105 @ SY6231 @ SV248 ) @ SV1862 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4005]) ).
thf(4823,plain,
! [SV1863: $i,SV1106: $i,SV249: $i] :
( ( ! [SY6232: $i] :
( ~ ( class_Orderings_Olinorder @ SV249 )
| ( c_lessequals @ SV1106 @ ( c_Orderings_Oord__class_Omax @ SV1863 @ SY6232 @ SV249 ) @ SV249 )
| ~ ( c_lessequals @ SV1106 @ SY6232 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4006]) ).
thf(4824,plain,
! [SV1864: $i,SV1107: $i,SV250: $i] :
( ( ! [SY6233: $i] :
( ~ ( class_Orderings_Olinorder @ SV250 )
| ( c_lessequals @ SV1107 @ ( c_Orderings_Oord__class_Omax @ SV1864 @ SY6233 @ SV250 ) @ SV250 )
| ~ ( c_lessequals @ SV1107 @ SV1864 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4007]) ).
thf(4825,plain,
! [SV1865: $i,SV1108: $i,SV251: $i] :
( ( ! [SY6234: $i] :
( ~ ( class_Orderings_Olinorder @ SV251 )
| ( c_lessequals @ SV1108 @ ( c_Orderings_Oord__class_Omax @ SV1865 @ SY6234 @ SV251 ) @ SV251 )
| ~ ( c_lessequals @ SV1108 @ SY6234 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4008]) ).
thf(4826,plain,
! [SV1866: $i,SV1109: $i,SV252: $i] :
( ( ! [SY6235: $i] :
( ~ ( class_Orderings_Olinorder @ SV252 )
| ( c_lessequals @ SV1109 @ ( c_Orderings_Oord__class_Omax @ SV1866 @ SY6235 @ SV252 ) @ SV252 )
| ~ ( c_lessequals @ SV1109 @ SV1866 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4009]) ).
thf(4827,plain,
! [SV1867: $i,SV1110: $i,SV253: $i] :
( ( ! [SY6236: $i] :
( ~ ( class_Orderings_Olinorder @ SV253 )
| ( c_lessequals @ SV1110 @ SV1867 @ SV253 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY6236 @ SV1110 @ SV253 ) @ SV1867 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4010]) ).
thf(4828,plain,
! [SV1868: $i,SV1111: $i,SV254: $i] :
( ( ! [SY6237: $i] :
( ~ ( class_Orderings_Olinorder @ SV254 )
| ( c_lessequals @ SV1111 @ SV1868 @ SV254 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1111 @ SY6237 @ SV254 ) @ SV1868 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4011]) ).
thf(4829,plain,
! [SV1869: $i,SV1112: $i,SV255: $i] :
( ( ( c_lessequals @ SV255 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1112 ) @ SV1869 ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1869 @ tc_nat ) @ SV1112 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4012]) ).
thf(4830,plain,
! [SV1870: $i,SV1113: $i,SV256: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV256 @ SV1113 @ tc_nat ) @ SV1870 @ tc_nat )
| ~ ( c_lessequals @ SV256 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1870 ) @ SV1113 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4013]) ).
thf(4831,plain,
! [SV1871: $i,SV1114: $i,SV257: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV257 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ ( c_Power_Opower__class_Opower @ SV1114 @ SV1871 @ SV257 ) @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV1114 @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4014]) ).
thf(4832,plain,
! [SV1872: $i,SV1115: $i,SV258: $i] :
( ( ! [SY6238: $i] :
( ~ ( class_Orderings_Olinorder @ SV258 )
| ( c_HOL_Oord__class_Oless @ SV1115 @ SV1872 @ SV258 )
| ( c_HOL_Oord__class_Oless @ SV1115 @ SY6238 @ SV258 )
| ~ ( c_HOL_Oord__class_Oless @ SV1115 @ ( c_Orderings_Oord__class_Omax @ SY6238 @ SV1872 @ SV258 ) @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4015]) ).
thf(4833,plain,
! [SV1873: $i,SV1118: $i,SV261: $i] :
( ( ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV261 ) ) @ SV1118 ) @ SV1873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_InductTermi_OIT @ SV1118 )
| ~ ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV261 @ SV1118 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4018]) ).
thf(4834,plain,
! [SV1874: $i,SV1119: $i,SV262: $i] :
( ( ! [SY6239: $i] :
( ( c_List_Ofoldl @ SV262 @ SV1119 @ ( c_List_Olist_ONil @ SV1874 ) @ SY6239 @ SV1874 )
= SV1119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4019]) ).
thf(4835,plain,
! [SV1875: $i,SV1120: $i,SV263: $i] :
( ( ! [SY6240: $i] :
( ( c_Nat_Onat_Onat__case @ SV263 @ SV1120 @ ( c_Suc @ SV1875 ) @ SY6240 )
= ( hAPP @ SV1120 @ SV1875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4020]) ).
thf(4836,plain,
! [SV1876: $i,SV1121: $i,SV264: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV264 ) @ ( c_HOL_Otimes__class_Otimes @ SV1121 @ SV1121 @ SV264 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1876 @ SV1876 @ SV264 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4021]) ).
thf(4837,plain,
! [SV1877: $i,SV1122: $i,SV265: $i] :
( ( ! [SY6241: $i,SY6242: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV265 @ SV1122 @ tc_nat ) @ SV1877 @ tc_nat ) ) @ SY6241 ) @ SY6242 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV265 @ SV1877 @ tc_nat ) ) @ SY6241 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV1877 @ tc_nat ) ) @ SY6242 ) @ tc_nat )
| ~ ( c_lessequals @ SV1122 @ SV265 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4022]) ).
thf(4838,plain,
! [SV1878: $i,SV1123: $i,SV266: $i] :
( ( ! [SY6243: $i,SY6244: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV266 @ SV1123 @ tc_nat ) ) @ SV1878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY6243 @ SV1123 @ tc_nat ) ) @ SY6244 ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV266 @ SY6243 @ tc_nat ) @ SV1123 @ tc_nat ) ) @ SV1878 ) @ SY6244 @ tc_nat )
| ~ ( c_lessequals @ SY6243 @ SV266 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4023]) ).
thf(4839,plain,
! [SV1879: $i,SV1124: $i,SV267: $i] :
( ( ! [SY6245: $i,SY6246: $i] :
( ( c_lessequals @ SV267 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1124 @ SV1879 @ tc_nat ) @ SY6245 @ tc_nat ) ) @ SY6246 ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1879 @ SY6245 @ tc_nat ) ) @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1124 @ SY6245 @ tc_nat ) ) @ SY6246 ) @ tc_nat )
| ~ ( c_lessequals @ SV1879 @ SV1124 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4024]) ).
thf(4840,plain,
! [SV1880: $i,SV1125: $i,SV268: $i] :
( ( ! [SY6247: $i,SY6248: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SV1125 @ tc_nat ) ) @ SV1880 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY6247 @ SV1125 @ tc_nat ) ) @ SY6248 ) @ tc_nat )
| ~ ( c_lessequals @ SV1880 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6247 @ SV268 @ tc_nat ) @ SV1125 @ tc_nat ) ) @ SY6248 ) @ tc_nat )
| ~ ( c_lessequals @ SV268 @ SY6247 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4025]) ).
thf(4841,plain,
! [SV1881: $i,SV1126: $i,SV269: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV269 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SV1126 @ SV1881 @ tc_nat ) @ SV269 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1126 @ SV269 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1881 @ SV269 ) @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4026]) ).
thf(4842,plain,
! [SV1882: $i,SV1127: $i,SV270: $i] :
( ( ! [SY6249: $i] :
( ~ ( class_Orderings_Olinorder @ SV270 )
| ( c_HOL_Oord__class_Oless @ SV1127 @ SV1882 @ SV270 )
| ( c_HOL_Oord__class_Oless @ SY6249 @ SV1882 @ SV270 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY6249 @ SV1127 @ SV270 ) @ SV1882 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4027]) ).
thf(4843,plain,
! [SV1883: $i,SV1129: $i,SV272: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV272 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1129 ) @ SV1883 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
| ~ ( c_HOL_Oord__class_Oless @ SV1883 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
| ~ ( c_lessequals @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4029]) ).
thf(4844,plain,
! [SV1884: $i,SV1130: $i,SV273: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV273 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV1130 ) @ SV1884 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
| ~ ( c_lessequals @ SV1884 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
| ~ ( c_HOL_Oord__class_Oless @ SV1130 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4030]) ).
thf(4845,plain,
! [SV1131: $i,SV274: $i] :
( ( ( SV274 = SV1131 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV274 @ SV1131 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV274 @ ( c_Suc @ SV1131 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4031]) ).
thf(4846,plain,
! [SV1132: $i,SV275: $i] :
( ( ( SV275 = SV1132 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1132 @ ( c_Suc @ SV275 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1132 @ SV275 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4032]) ).
thf(4847,plain,
! [SV1133: $i,SV276: $i] :
( ( ( SV276 = SV1133 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV276 @ ( c_Suc @ SV1133 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV276 @ SV1133 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4033]) ).
thf(4848,plain,
! [SV277: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV277 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ SV277 ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ SV277 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV277 ) @ SV277 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4034]) ).
thf(4849,plain,
! [SV1885: $i,SV1134: $i,SV278: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV278 ) @ SV1134 ) @ SV1885 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV278 ) @ ( c_HOL_Ominus__class_Ominus @ SV1134 @ SV1885 @ tc_nat ) ) )
| ~ ( c_lessequals @ SV1885 @ SV1134 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4035]) ).
thf(4850,plain,
! [SV1886: $i,SV1135: $i,SV279: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV279 ) @ SV1135 ) @ SV1886 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV279 @ SV1886 @ tc_nat ) ) @ SV1135 ) )
| ~ ( c_lessequals @ SV1886 @ SV279 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4036]) ).
thf(4851,plain,
! [SV1887: $i,SV1136: $i,SV280: $i] :
( ( ! [SY6250: $i,SY6251: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV280 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1136 @ SV1887 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SY6250 @ SY6251 @ SV280 ) @ SV280 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1136 @ SY6250 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SV1887 @ SY6251 @ SV280 ) @ SV280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4037]) ).
thf(4852,plain,
! [SV1888: $i,SV1137: $i,SV281: $i] :
( ( ! [SY6252: $i,SY6253: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV281 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1137 @ SV1888 @ SV281 ) @ ( c_HOL_Otimes__class_Otimes @ SY6252 @ SY6253 @ SV281 ) @ SV281 )
= ( c_HOL_Otimes__class_Otimes @ SV1137 @ ( c_HOL_Otimes__class_Otimes @ SV1888 @ ( c_HOL_Otimes__class_Otimes @ SY6252 @ SY6253 @ SV281 ) @ SV281 ) @ SV281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4038]) ).
thf(4853,plain,
! [SV1889: $i,SV1138: $i,SV282: $i] :
( ( ! [SY6254: $i,SY6255: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV282 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1138 @ SV1889 @ SV282 ) @ ( c_HOL_Otimes__class_Otimes @ SY6254 @ SY6255 @ SV282 ) @ SV282 )
= ( c_HOL_Otimes__class_Otimes @ SY6254 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1138 @ SV1889 @ SV282 ) @ SY6255 @ SV282 ) @ SV282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4039]) ).
thf(4854,plain,
! [SV1890: $i,SV1139: $i,SV283: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_HOL_Ominus__class_Ominus @ SV1139 @ SV1890 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV283 ) @ SV1890 ) @ SV1139 @ tc_nat ) )
| ~ ( c_lessequals @ SV1890 @ SV1139 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4040]) ).
thf(4855,plain,
! [SV1891: $i,SV1140: $i,SV284: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV284 @ SV1140 @ tc_nat ) @ SV1891 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV284 @ SV1891 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4041]) ).
thf(4856,plain,
! [SV1892: $i,SV1141: $i,SV285: $i] :
( ( ! [SY6256: $i] :
( ( c_Type_Otype_Otype__rec @ SV285 @ SV1141 @ ( c_Type_Otype_OAtom @ SV1892 ) @ SY6256 )
= ( hAPP @ SV285 @ SV1892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4042]) ).
thf(4857,plain,
! [SV1893: $i,SV1142: $i,SV286: $i] :
( ( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV286 @ SV1142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1893 @ SV1142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( c_Lambda_Obeta @ SV286 @ SV1893 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4043]) ).
thf(4858,plain,
! [SV1894: $i,SV1144: $i,SV288: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV288 )
| ( c_HOL_Oord__class_Oless @ SV1144 @ SV1894 @ SV288 )
| ( c_lessequals @ SV1894 @ SV1144 @ SV288 )
| ~ ( c_lessequals @ SV1144 @ SV1894 @ SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4045]) ).
thf(4859,plain,
! [SV1145: $i,SV291: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV291 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1145 @ SV1145 @ SV291 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4048]) ).
thf(4860,plain,
! [SV1146: $i,SV292: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV292 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1146 @ SV1146 @ SV292 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4049]) ).
thf(4861,plain,
! [SV1147: $i,SV293: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV293 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1147 @ SV1147 @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4050]) ).
thf(4862,plain,
! [SV1148: $i,SV294: $i] :
( ( ( ~ ( c_lessequals @ SV294 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1148 ) @ SV294 ) @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1148 ) @ SV294 ) @ SV294 @ tc_nat )
= SV1148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4051]) ).
thf(4863,plain,
! [SV1149: $i,SV295: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV295 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1149 @ SV1149 @ SV295 )
= SV1149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4052]) ).
thf(4864,plain,
! [SV1895: $i,SV1151: $i,SV297: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV297 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV297 ) @ SV1151 ) @ SV1895 ) @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1895 @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1151 @ SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4054]) ).
thf(4865,plain,
! [SV1896: $i,SV1156: $i,SV302: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV302 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV1156 @ SV1896 @ SV302 ) @ SV302 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV302 ) @ SV1156 ) @ ( c_List_Olistsum @ SV1896 @ SV302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4059]) ).
thf(4866,plain,
! [SV1897: $i,SV1157: $i,SV303: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV1157 @ SV1897 @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV1897 @ SV1157 @ SV303 )
| ( SV1897 = SV1157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4060]) ).
thf(4867,plain,
! [SV1898: $i,SV1158: $i,SV304: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV304 )
| ( SV1158 = SV1898 )
| ( c_HOL_Oord__class_Oless @ SV1898 @ SV1158 @ SV304 )
| ( c_HOL_Oord__class_Oless @ SV1158 @ SV1898 @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4061]) ).
thf(4868,plain,
! [SV1159: $i,SV305: $i] :
( ( ( SV305 = SV1159 )
= $true )
| ( ( ~ ( c_lessequals @ SV1159 @ SV305 @ tc_nat )
| ~ ( c_lessequals @ SV305 @ SV1159 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4062]) ).
thf(4869,plain,
! [SV1160: $i,SV306: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV306 @ SV1160 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1160 @ SV306 @ tc_nat )
| ( SV1160 = SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4063]) ).
thf(4870,plain,
! [SV1899: $i,SV1161: $i,SV307: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV307 @ SV1161 ) @ SV1899 ) )
| ( c_HOL_Oord__class_Oless @ SV1161 @ SV1899 @ tc_nat )
| ( SV1899 = SV1161 )
| ( c_HOL_Oord__class_Oless @ SV1899 @ SV1161 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4064]) ).
thf(4871,plain,
! [SV1900: $i,SV1162: $i,SV308: $i] :
( ( ! [SY6257: $i,SY6258: $i] :
( ( SV308 = SV1162 )
| ~ ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY6257 ) @ SY6258 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1162 )
| ~ ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY6257 ) @ SY6258 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4065]) ).
thf(4872,plain,
! [SV1163: $i,SV309: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV309 @ SV1163 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1163 @ SV309 @ tc_nat )
| ( SV1163 = SV309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4066]) ).
thf(4873,plain,
! [SV1901: $i,SV1164: $i,SV310: $i] :
( ( ~ ( class_Orderings_Oorder @ SV310 )
| ( SV1164 = SV1901 )
| ~ ( c_lessequals @ SV1901 @ SV1164 @ SV310 )
| ~ ( c_lessequals @ SV1164 @ SV1901 @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4067]) ).
thf(4874,plain,
! [SV1902: $i,SV1165: $i,SV311: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV311 )
| ( c_HOL_Oord__class_Oless @ SV1165 @ SV1902 @ SV311 )
| ( c_HOL_Oord__class_Oless @ SV1902 @ SV1165 @ SV311 )
| ( SV1902 = SV1165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4068]) ).
thf(4875,plain,
! [SV1903: $i,SV1166: $i,SV312: $i] :
( ( ~ ( class_Orderings_Oorder @ SV312 )
| ( SV1166 = SV1903 )
| ~ ( c_lessequals @ SV1903 @ SV1166 @ SV312 )
| ~ ( c_lessequals @ SV1166 @ SV1903 @ SV312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4069]) ).
thf(4876,plain,
! [SV1904: $i,SV1167: $i,SV313: $i] :
( ( ~ ( class_Orderings_Oorder @ SV313 )
| ( SV1167 = SV1904 )
| ~ ( c_lessequals @ SV1167 @ SV1904 @ SV313 )
| ~ ( c_lessequals @ SV1904 @ SV1167 @ SV313 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4070]) ).
thf(4877,plain,
! [SV1905: $i,SV1168: $i,SV314: $i] :
( ( ! [SY6259: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV314 @ SV1168 @ SV1905 ) @ ( c_List_Oreplicate @ SY6259 @ SV1168 @ SV1905 ) @ SV1905 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY6259 @ SV1168 @ SV1905 ) @ ( c_List_Oreplicate @ SV314 @ SV1168 @ SV1905 ) @ SV1905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4071]) ).
thf(4878,plain,
! [SV1906: $i,SV1169: $i,SV315: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV315 )
| ( c_HOL_Oord__class_Oless @ SV1169 @ SV1906 @ SV315 )
| ( SV1906 = SV1169 )
| ( c_HOL_Oord__class_Oless @ SV1906 @ SV1169 @ SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4072]) ).
thf(4879,plain,
! [SV1907: $i,SV1170: $i,SV316: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV316 )
| ( SV1170 = SV1907 )
| ( c_HOL_Oord__class_Oless @ SV1170 @ SV1907 @ SV316 )
| ( c_HOL_Oord__class_Oless @ SV1907 @ SV1170 @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4073]) ).
thf(4880,plain,
! [SV1908: $i,SV1171: $i,SV317: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV317 )
| ( c_lessequals @ SV1171 @ SV1908 @ SV317 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1908 @ SV317 ) @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4074]) ).
thf(4881,plain,
! [SV1909: $i,SV1172: $i,SV318: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV318 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1172 @ SV1909 @ SV318 ) @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV318 )
| ~ ( c_lessequals @ SV1172 @ SV1909 @ SV318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4075]) ).
thf(4882,plain,
! [SV1173: $i,SV319: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV319 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1173 @ SV1173 @ SV319 )
= SV1173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4076]) ).
thf(4883,plain,
! [SV1910: $i,SV1174: $i,SV320: $i] :
( ( ! [SY6260: $i,SY6261: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV1174 ) @ SV1910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SY6260 ) @ SY6261 ) @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SV1910 @ SY6261 @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SY6260 @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4077]) ).
thf(4884,plain,
! [SV1911: $i,SV1175: $i,SV321: $i] :
( ( ! [SY6262: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV1175 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1911 ) @ SY6262 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1175 @ SY6262 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV321 @ SV1911 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4078]) ).
thf(4885,plain,
! [SV1176: $i,SV322: $i] :
( ( ( c_lessequals @ SV322 @ SV1176 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV322 @ SV1176 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4079]) ).
thf(4886,plain,
! [SV1177: $i,SV323: $i] :
( ( ( c_lessequals @ SV323 @ SV1177 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV323 @ SV1177 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4080]) ).
thf(4887,plain,
! [SV1912: $i,SV1178: $i,SV324: $i] :
( ( ~ ( class_Orderings_Oorder @ SV324 )
| ( c_lessequals @ SV1178 @ SV1912 @ SV324 )
| ~ ( c_HOL_Oord__class_Oless @ SV1178 @ SV1912 @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4081]) ).
thf(4888,plain,
! [SV1913: $i,SV1179: $i,SV325: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV325 )
| ( c_lessequals @ SV1179 @ SV1913 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV1179 @ SV1913 @ SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4082]) ).
thf(4889,plain,
! [SV1914: $i,SV1180: $i,SV326: $i] :
( ( ! [SY6263: $i] :
( ~ ( class_Orderings_Olinorder @ SV326 )
| ( c_HOL_Oord__class_Oless @ SV1180 @ SV1914 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ SV1180 @ ( c_Orderings_Oord__class_Omin @ SV1914 @ SY6263 @ SV326 ) @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4083]) ).
thf(4890,plain,
! [SV1915: $i,SV1181: $i,SV327: $i] :
( ( ! [SY6264: $i] :
( ~ ( class_Orderings_Olinorder @ SV327 )
| ( c_HOL_Oord__class_Oless @ SV1181 @ SV1915 @ SV327 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_Orderings_Oord__class_Omin @ SY6264 @ SV1915 @ SV327 ) @ SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4084]) ).
thf(4891,plain,
! [SV1916: $i,SV1182: $i,SV328: $i] :
( ( ! [SY6265: $i] :
( ~ ( class_Orderings_Olinorder @ SV328 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1182 @ SV1916 @ SV328 ) @ SY6265 @ SV328 )
| ~ ( c_HOL_Oord__class_Oless @ SV1182 @ SY6265 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4085]) ).
thf(4892,plain,
! [SV1917: $i,SV1183: $i,SV329: $i] :
( ( ! [SY6266: $i] :
( ~ ( class_Orderings_Olinorder @ SV329 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1183 @ SV1917 @ SV329 ) @ SY6266 @ SV329 )
| ~ ( c_HOL_Oord__class_Oless @ SV1917 @ SY6266 @ SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4086]) ).
thf(4893,plain,
! [SV1918: $i,SV1184: $i,SV330: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV330 @ SV1184 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1918 @ SV1184 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV330 @ SV1918 @ tc_nat ) )
| ~ ( c_lessequals @ SV1184 @ SV1918 @ tc_nat )
| ~ ( c_lessequals @ SV1184 @ SV330 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4087]) ).
thf(4894,plain,
! [SV1919: $i,SV1185: $i,SV331: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV331 @ SV1185 @ tc_nat ) @ SV1919 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV331 @ SV1919 @ tc_nat ) @ SV1185 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4088]) ).
thf(4895,plain,
! [SV1920: $i,SV1186: $i,SV332: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV332 ) @ SV1186 ) @ SV1920 ) @ SV332 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1920 @ SV332 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1186 @ SV332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4089]) ).
thf(4896,plain,
! [SV1921: $i,SV1187: $i,SV333: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV333 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV333 ) @ SV1187 ) @ SV1921 ) @ SV333 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1921 @ SV333 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1187 @ SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4090]) ).
thf(4897,plain,
! [SV1922: $i,SV1188: $i,SV334: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV334 @ SV1188 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1922 @ SV1188 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1188 @ SV334 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV334 @ SV1922 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4091]) ).
thf(4898,plain,
! [SV1923: $i,SV1189: $i,SV335: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV335 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1189 @ SV1923 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
| ~ ( c_lessequals @ SV1923 @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV1189 @ SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4092]) ).
thf(4899,plain,
! [SV1924: $i,SV1190: $i,SV336: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV336 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1190 @ SV1924 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV1924 @ SV336 )
| ~ ( c_lessequals @ SV1190 @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4093]) ).
thf(4900,plain,
! [SV1925: $i,SV1191: $i,SV337: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV337 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1191 @ SV1925 @ SV337 ) @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
| ~ ( c_lessequals @ SV1925 @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV1191 @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4094]) ).
thf(4901,plain,
! [SV1926: $i,SV1192: $i,SV338: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV338 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1192 @ SV1926 @ SV338 ) @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV1926 @ SV338 )
| ~ ( c_lessequals @ SV1192 @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4095]) ).
thf(4902,plain,
! [SV1927: $i,SV1193: $i,SV339: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV339 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1193 @ SV1927 @ SV339 ) @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
| ~ ( c_lessequals @ SV1927 @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV1193 @ SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4096]) ).
thf(4903,plain,
! [SV1928: $i,SV1194: $i,SV340: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV340 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1928 @ SV340 ) @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV1928 @ SV340 )
| ~ ( c_lessequals @ SV1194 @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4097]) ).
thf(4904,plain,
! [SV1929: $i,SV1195: $i,SV341: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV341 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1195 @ SV1929 @ SV341 ) @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
| ~ ( c_lessequals @ SV1195 @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV1929 @ SV341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4098]) ).
thf(4905,plain,
! [SV1196: $i,SV342: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV342 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1196 @ SV1196 @ SV342 ) @ ( c_HOL_Ozero__class_Ozero @ SV342 ) @ SV342 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4099]) ).
thf(4906,plain,
! [SV1930: $i,SV1197: $i,SV343: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV343 ) @ SV1197 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV343 ) @ SV1930 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1197 @ SV1930 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4100]) ).
thf(4907,plain,
! [SV1931: $i,SV1198: $i,SV344: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV344 @ SV1198 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1931 ) @ SV344 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1931 ) @ SV1198 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4101]) ).
thf(4908,plain,
! [SV1199: $i,SV345: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV345 ) @ SV1199 @ tc_nat )
= $true )
| ( ( ( ( c_Suc @ SV345 )
= SV1199 )
| ~ ( c_HOL_Oord__class_Oless @ SV345 @ SV1199 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4102]) ).
thf(4909,plain,
! [SV1200: $i,SV346: $i] :
( ( ( ~ ( c_lessequals @ SV346 @ SV1200 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV1200 ) @ SV346 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4103]) ).
thf(4910,plain,
! [SV1201: $i,SV347: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV347 ) @ SV1201 @ tc_nat )
= $true )
| ( ( c_lessequals @ SV1201 @ SV347 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4104]) ).
thf(4911,plain,
! [SV1932: $i,SV1202: $i,SV348: $i] :
( ( ! [SY6267: $i] :
( ( c_List_Olist_OCons @ SV348 @ ( c_List_Oappend @ SV1202 @ SV1932 @ SY6267 ) @ SY6267 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV348 @ SV1202 @ SY6267 ) @ SV1932 @ SY6267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4105]) ).
thf(4912,plain,
! [SV1933: $i,SV1203: $i,SV349: $i] :
( ( ! [SY6268: $i] :
( ( c_List_Olist_OCons @ SV349 @ ( c_List_Oappend @ SV1203 @ SV1933 @ SY6268 ) @ SY6268 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV349 @ SV1203 @ SY6268 ) @ SV1933 @ SY6268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4106]) ).
thf(4913,plain,
! [SV1934: $i,SV1204: $i,SV350: $i] :
( ( ! [SY6269: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV350 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ ( c_Orderings_Oord__class_Omin @ SV1204 @ SV1934 @ SV350 ) ) @ SY6269 )
= ( c_Orderings_Oord__class_Omin @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV1204 ) @ SY6269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV1934 ) @ SY6269 ) @ SV350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4107]) ).
thf(4914,plain,
! [SV1935: $i,SV1205: $i,SV351: $i] :
( ( ( c_lessequals @ SV351 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1205 ) @ SV351 ) @ SV1935 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1935 @ SV1205 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4108]) ).
thf(4915,plain,
! [SV1936: $i,SV1206: $i,SV352: $i] :
( ( ! [SY6270: $i,SY6271: $i,SY6272: $i,SY6273: $i,SY6274: $i,SY6275: $i] :
( ( ( hAPP @ ( hAPP @ SV352 @ ( hAPP @ ( hAPP @ SV1206 @ SV1936 ) @ SY6270 ) ) @ SY6271 )
= ( hAPP @ ( hAPP @ SV1206 @ ( hAPP @ ( hAPP @ SV352 @ SV1936 ) @ SY6271 ) ) @ ( hAPP @ ( hAPP @ SV352 @ SY6270 ) @ SY6271 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6272 @ SV1206 @ SV352 @ SY6273 @ SY6274 @ SY6275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4109]) ).
thf(4916,plain,
! [SV1937: $i,SV1207: $i,SV353: $i] :
( ( ! [SY6276: $i,SY6277: $i,SY6278: $i,SY6279: $i,SY6280: $i,SY6281: $i] :
( ( ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ ( hAPP @ ( hAPP @ SV1937 @ SY6276 ) @ SY6277 ) )
= ( hAPP @ ( hAPP @ SV1937 @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SY6276 ) ) @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SY6277 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1937 @ SV353 @ SY6278 @ SY6279 @ SY6280 @ SY6281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4110]) ).
thf(4917,plain,
! [SV1938: $i,SV1208: $i,SV354: $i] :
( ( ! [SY6282: $i,SY6283: $i,SY6284: $i,SY6285: $i,SY6286: $i] :
( ( ( hAPP @ ( hAPP @ SV354 @ SV1208 ) @ SV1938 )
= ( hAPP @ ( hAPP @ SV354 @ SV1938 ) @ SV1208 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6282 @ SV354 @ SY6283 @ SY6284 @ SY6285 @ SY6286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4111]) ).
thf(4918,plain,
! [SV1939: $i,SV1209: $i,SV355: $i] :
( ( ! [SY6287: $i,SY6288: $i,SY6289: $i,SY6290: $i,SY6291: $i,SY6292: $i] :
( ( ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ ( hAPP @ ( hAPP @ SV355 @ SV1939 ) @ SY6287 ) )
= ( hAPP @ ( hAPP @ SV355 @ ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ SV1939 ) ) @ SY6287 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6288 @ SV355 @ SY6289 @ SY6290 @ SY6291 @ SY6292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4112]) ).
thf(4919,plain,
! [SV1940: $i,SV1210: $i,SV356: $i] :
( ( ! [SY6293: $i,SY6294: $i,SY6295: $i,SY6296: $i] :
( ( ( hAPP @ ( hAPP @ SV356 @ SV1210 ) @ SV1940 )
= SV1940 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6293 @ SV356 @ SY6294 @ SY6295 @ SV1210 @ SY6296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4113]) ).
thf(4920,plain,
! [SV1941: $i,SV1211: $i,SV357: $i] :
( ( ! [SY6297: $i,SY6298: $i,SY6299: $i,SY6300: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV1211 ) @ SV1941 )
= SV1211 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6297 @ SV357 @ SY6298 @ SV1211 @ SY6299 @ SY6300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4114]) ).
thf(4921,plain,
! [SV1942: $i,SV1212: $i,SV358: $i] :
( ( ! [SY6301: $i,SY6302: $i,SY6303: $i,SY6304: $i,SY6305: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV1212 ) @ SV1942 )
= ( hAPP @ ( hAPP @ SV358 @ SV1942 ) @ SV1212 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV358 @ SY6301 @ SY6302 @ SY6303 @ SY6304 @ SY6305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4115]) ).
thf(4922,plain,
! [SV1943: $i,SV1213: $i,SV359: $i] :
( ( ! [SY6306: $i,SY6307: $i,SY6308: $i,SY6309: $i,SY6310: $i,SY6311: $i] :
( ( ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ ( hAPP @ ( hAPP @ SV359 @ SV1943 ) @ SY6306 ) )
= ( hAPP @ ( hAPP @ SV359 @ ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ SV1943 ) ) @ SY6306 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV359 @ SY6307 @ SY6308 @ SY6309 @ SY6310 @ SY6311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4116]) ).
thf(4923,plain,
! [SV1944: $i,SV1214: $i,SV360: $i] :
( ( ! [SY6312: $i,SY6313: $i,SY6314: $i,SY6315: $i] :
( ( ( hAPP @ ( hAPP @ SV360 @ SV1214 ) @ SV1944 )
= SV1944 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV360 @ SY6312 @ SY6313 @ SV1214 @ SY6314 @ SY6315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4117]) ).
thf(4924,plain,
! [SV1945: $i,SV1215: $i,SV361: $i] :
( ( ! [SY6316: $i,SY6317: $i,SY6318: $i,SY6319: $i,SY6320: $i,SY6321: $i] :
( ( ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ ( hAPP @ ( hAPP @ SV361 @ SV1945 ) @ SY6316 ) )
= ( hAPP @ ( hAPP @ SV361 @ ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ SV1945 ) ) @ SY6316 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV361 @ SY6317 @ SY6318 @ SY6319 @ SY6320 @ SY6321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4118]) ).
thf(4925,plain,
! [SV1946: $i,SV1216: $i,SV362: $i] :
( ( ! [SY6322: $i,SY6323: $i,SY6324: $i,SY6325: $i,SY6326: $i] :
( ( ( hAPP @ ( hAPP @ SV362 @ SV1216 ) @ SV1946 )
= ( hAPP @ ( hAPP @ SV362 @ SV1946 ) @ SV1216 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV362 @ SY6322 @ SY6323 @ SY6324 @ SY6325 @ SY6326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4119]) ).
thf(4926,plain,
! [SV1947: $i,SV1217: $i,SV363: $i] :
( ( ! [SY6327: $i,SY6328: $i,SY6329: $i,SY6330: $i,SY6331: $i,SY6332: $i] :
( ( ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV1947 ) ) @ SY6327 )
= ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SY6327 ) ) @ SV1947 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV363 @ SY6328 @ SY6329 @ SY6330 @ SY6331 @ SY6332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4120]) ).
thf(4927,plain,
! [SV1948: $i,SV1218: $i,SV364: $i] :
( ( ! [SY6333: $i,SY6334: $i,SY6335: $i,SY6336: $i,SY6337: $i,SY6338: $i] :
( ( ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ SY6333 ) )
= ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ SY6333 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV364 @ SY6334 @ SY6335 @ SY6336 @ SY6337 @ SY6338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4121]) ).
thf(4928,plain,
! [SV1949: $i,SV1219: $i,SV365: $i] :
( ( ! [SY6339: $i,SY6340: $i,SY6341: $i,SY6342: $i,SY6343: $i,SY6344: $i] :
( ( ( hAPP @ ( hAPP @ SV365 @ ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ SV1949 ) ) @ SY6339 )
= ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ ( hAPP @ ( hAPP @ SV365 @ SV1949 ) @ SY6339 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV365 @ SY6340 @ SY6341 @ SY6342 @ SY6343 @ SY6344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4122]) ).
thf(4929,plain,
! [SV1950: $i,SV1220: $i,SV366: $i] :
( ( ! [SY6345: $i,SY6346: $i,SY6347: $i,SY6348: $i,SY6349: $i,SY6350: $i,SY6351: $i] :
( ( ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV1950 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SY6345 ) @ SY6346 ) )
= ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SY6345 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV1950 ) @ SY6346 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV366 @ SY6347 @ SY6348 @ SY6349 @ SY6350 @ SY6351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4123]) ).
thf(4930,plain,
! [SV1951: $i,SV1221: $i,SV367: $i] :
( ( ! [SY6352: $i,SY6353: $i,SY6354: $i,SY6355: $i,SY6356: $i,SY6357: $i] :
( ( ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ SY6352 ) )
= ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ SY6352 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6353 @ SV367 @ SY6354 @ SY6355 @ SY6356 @ SY6357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4124]) ).
thf(4931,plain,
! [SV1952: $i,SV1222: $i,SV368: $i] :
( ( ! [SY6358: $i,SY6359: $i,SY6360: $i,SY6361: $i,SY6362: $i,SY6363: $i] :
( ( ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ ( hAPP @ ( hAPP @ SV368 @ SV1952 ) @ SY6358 ) )
= ( hAPP @ ( hAPP @ SV368 @ ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ SV1952 ) ) @ SY6358 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6359 @ SV368 @ SY6360 @ SY6361 @ SY6362 @ SY6363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4125]) ).
thf(4932,plain,
! [SV1953: $i,SV1223: $i,SV369: $i] :
( ( ! [SY6364: $i,SY6365: $i,SY6366: $i,SY6367: $i,SY6368: $i,SY6369: $i] :
( ( ( hAPP @ ( hAPP @ SV369 @ ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ SV1953 ) ) @ SY6364 )
= ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ ( hAPP @ ( hAPP @ SV369 @ SV1953 ) @ SY6364 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6365 @ SV369 @ SY6366 @ SY6367 @ SY6368 @ SY6369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4126]) ).
thf(4933,plain,
! [SV1954: $i,SV1224: $i,SV370: $i] :
( ( ! [SY6370: $i,SY6371: $i,SY6372: $i,SY6373: $i,SY6374: $i,SY6375: $i] :
( ( ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV1954 ) ) @ SY6370 )
= ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SY6370 ) ) @ SV1954 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6371 @ SV370 @ SY6372 @ SY6373 @ SY6374 @ SY6375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4127]) ).
thf(4934,plain,
! [SV1955: $i,SV1225: $i,SV371: $i] :
( ( ! [SY6376: $i,SY6377: $i,SY6378: $i,SY6379: $i,SY6380: $i,SY6381: $i,SY6382: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ ( hAPP @ ( hAPP @ SV371 @ SY6376 ) @ SY6377 ) )
= ( hAPP @ ( hAPP @ SV371 @ SY6376 ) @ ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ SY6377 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6378 @ SV371 @ SY6379 @ SY6380 @ SY6381 @ SY6382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4128]) ).
thf(4935,plain,
! [SV1956: $i,SV1226: $i,SV372: $i] :
( ( ! [SY6383: $i,SY6384: $i,SY6385: $i,SY6386: $i,SY6387: $i,SY6388: $i,SY6389: $i] :
( ( ( hAPP @ ( hAPP @ SV372 @ ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ SV1956 ) ) @ ( hAPP @ ( hAPP @ SV372 @ SY6383 ) @ SY6384 ) )
= ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ ( hAPP @ ( hAPP @ SV372 @ SV1956 ) @ ( hAPP @ ( hAPP @ SV372 @ SY6383 ) @ SY6384 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6385 @ SV372 @ SY6386 @ SY6387 @ SY6388 @ SY6389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4129]) ).
thf(4936,plain,
! [SV1957: $i,SV1227: $i,SV373: $i] :
( ( ! [SY6390: $i,SY6391: $i,SY6392: $i,SY6393: $i,SY6394: $i,SY6395: $i,SY6396: $i] :
( ( ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV1957 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SY6390 ) @ SY6391 ) )
= ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SY6390 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV1957 ) @ SY6391 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6392 @ SV373 @ SY6393 @ SY6394 @ SY6395 @ SY6396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4130]) ).
thf(4937,plain,
! [SV1958: $i,SV1228: $i,SV374: $i] :
( ( ! [SY6397: $i,SY6398: $i,SY6399: $i,SY6400: $i] :
( ( ( hAPP @ ( hAPP @ SV374 @ SV1228 ) @ SV1958 )
= SV1228 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6397 @ SV374 @ SY6398 @ SY6399 @ SV1958 @ SY6400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4131]) ).
thf(4938,plain,
! [SV1959: $i,SV1229: $i,SV375: $i] :
( ( ! [SY6401: $i,SY6402: $i,SY6403: $i,SY6404: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV1229 ) @ SV1959 )
= SV1959 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6401 @ SV375 @ SY6402 @ SY6403 @ SV1229 @ SY6404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4132]) ).
thf(4939,plain,
! [SV1960: $i,SV1230: $i,SV376: $i] :
( ( ! [SY6405: $i,SY6406: $i,SY6407: $i,SY6408: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ SV1230 ) @ SV1960 )
= SV1960 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6405 @ SV376 @ SY6406 @ SV1960 @ SY6407 @ SY6408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4133]) ).
thf(4940,plain,
! [SV1961: $i,SV1231: $i,SV377: $i] :
( ( ! [SY6409: $i,SY6410: $i,SY6411: $i,SY6412: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SV1231 ) @ SV1961 )
= SV1231 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6409 @ SV377 @ SY6410 @ SV1231 @ SY6411 @ SY6412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4134]) ).
thf(4941,plain,
! [SV1962: $i,SV1232: $i,SV378: $i] :
( ( ! [SY6413: $i,SY6414: $i,SY6415: $i,SY6416: $i,SY6417: $i,SY6418: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ ( hAPP @ ( hAPP @ SV1232 @ SV1962 ) @ SY6413 ) ) @ SY6414 )
= ( hAPP @ ( hAPP @ SV1232 @ ( hAPP @ ( hAPP @ SV378 @ SV1962 ) @ SY6414 ) ) @ ( hAPP @ ( hAPP @ SV378 @ SY6413 ) @ SY6414 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1232 @ SV378 @ SY6415 @ SY6416 @ SY6417 @ SY6418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4135]) ).
thf(4942,plain,
! [SV1963: $i,SV1233: $i,SV379: $i] :
( ( ! [SY6419: $i,SY6420: $i,SY6421: $i,SY6422: $i,SY6423: $i] :
( ( ( hAPP @ ( hAPP @ SV379 @ SV1233 ) @ SV1963 )
= ( hAPP @ ( hAPP @ SV379 @ SV1963 ) @ SV1233 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6419 @ SV379 @ SY6420 @ SY6421 @ SY6422 @ SY6423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4136]) ).
thf(4943,plain,
! [SV1964: $i,SV1234: $i,SV380: $i] :
( ( ! [SY6424: $i,SY6425: $i,SY6426: $i,SY6427: $i] :
( ( ( hAPP @ ( hAPP @ SV380 @ SV1234 ) @ SV1964 )
= SV1234 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV380 @ SY6424 @ SY6425 @ SV1964 @ SY6426 @ SY6427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4137]) ).
thf(4944,plain,
! [SV1965: $i,SV1235: $i,SV381: $i] :
( ( ! [SY6428: $i,SY6429: $i,SY6430: $i,SY6431: $i] :
( ( ( hAPP @ ( hAPP @ SV381 @ SV1235 ) @ SV1965 )
= SV1965 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV381 @ SY6428 @ SY6429 @ SV1235 @ SY6430 @ SY6431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4138]) ).
thf(4945,plain,
! [SV1966: $i,SV1236: $i,SV382: $i] :
( ( ! [SY6432: $i,SY6433: $i,SY6434: $i,SY6435: $i] :
( ( ( hAPP @ ( hAPP @ SV382 @ SV1236 ) @ SV1236 )
= ( hAPP @ ( hAPP @ SV1966 @ ( hAPP @ ( hAPP @ SV382 @ SY6432 ) @ SY6432 ) ) @ SV1236 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV382 @ SV1966 @ SY6433 @ SY6434 @ SY6432 @ SY6435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4139]) ).
thf(4946,plain,
! [SV1967: $i,SV1237: $i,SV383: $i] :
( ( ! [SY6436: $i,SY6437: $i,SY6438: $i,SY6439: $i,SY6440: $i] :
( ( ( hAPP @ ( hAPP @ SV383 @ SV1237 ) @ ( hAPP @ ( hAPP @ SV1967 @ SY6436 ) @ SV1237 ) )
= ( hAPP @ ( hAPP @ SV1967 @ ( hAPP @ ( hAPP @ SV383 @ SY6436 ) @ SY6437 ) ) @ SV1237 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV383 @ SV1967 @ SY6438 @ SY6439 @ SY6437 @ SY6440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4140]) ).
thf(4947,plain,
! [SV1968: $i,SV1238: $i,SV384: $i] :
( ( ! [SY6441: $i,SY6442: $i,SY6443: $i,SY6444: $i,SY6445: $i] :
( ( ( hAPP @ ( hAPP @ SV384 @ ( hAPP @ ( hAPP @ SV1238 @ SV1968 ) @ SY6441 ) ) @ SY6441 )
= ( hAPP @ ( hAPP @ SV1238 @ ( hAPP @ ( hAPP @ SV384 @ SV1968 ) @ SY6442 ) ) @ SY6441 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV384 @ SV1238 @ SY6443 @ SY6444 @ SY6442 @ SY6445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4141]) ).
thf(4948,plain,
! [SV1969: $i,SV1239: $i,SV385: $i] :
( ( ! [SY6446: $i,SY6447: $i,SY6448: $i,SY6449: $i,SY6450: $i,SY6451: $i] :
( ( ( hAPP @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ SV1239 @ SV1969 ) @ SY6446 ) ) @ ( hAPP @ ( hAPP @ SV1239 @ SY6447 ) @ SY6446 ) )
= ( hAPP @ ( hAPP @ SV1239 @ ( hAPP @ ( hAPP @ SV385 @ SV1969 ) @ SY6447 ) ) @ SY6446 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV385 @ SV1239 @ SY6448 @ SY6449 @ SY6450 @ SY6451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4142]) ).
thf(4949,plain,
! [SV1970: $i,SV1240: $i,SV386: $i] :
( ( ! [SY6452: $i] :
( ~ ( hBOOL @ ( hAPP @ SV386 @ ( c_Type_Otype_Otype__case @ SV1240 @ SV1970 @ ( c_Type_Otype_OAtom @ SY6452 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV386 @ ( hAPP @ SV1240 @ SY6452 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4143]) ).
thf(4950,plain,
! [SV1971: $i,SV1241: $i,SV387: $i] :
( ( ! [SY6453: $i] :
( ~ ( hBOOL @ ( hAPP @ SV387 @ ( c_Type_Otype_Otype__case @ SV1241 @ SV1971 @ ( c_Type_Otype_OAtom @ SY6453 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV387 @ ( hAPP @ SV1241 @ SY6453 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4144]) ).
thf(4951,plain,
! [SV1972: $i,SV1242: $i,SV388: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV388 ) @ SV1242 @ tc_nat ) @ ( c_Suc @ SV1972 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV388 @ SV1242 @ tc_nat ) @ SV1972 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4145]) ).
thf(4952,plain,
! [SV1973: $i,SV1243: $i,SV389: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV389 ) @ SV1243 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV389 ) @ SV1973 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1243 @ SV1973 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4146]) ).
thf(4953,plain,
! [SV1974: $i,SV1244: $i,SV390: $i] :
( ( ( c_lessequals @ SV390 @ SV1244 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1974 ) @ SV390 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1974 ) @ SV1244 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4147]) ).
thf(4954,plain,
! [SV1975: $i,SV1245: $i,SV391: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV391 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV391 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV391 ) @ ( c_HOL_Otimes__class_Otimes @ SV1245 @ SV1245 @ SV391 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1975 @ SV1975 @ SV391 ) ) @ SV391 )
| ( SV1245
= ( c_HOL_Ozero__class_Ozero @ SV391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4148]) ).
thf(4955,plain,
! [SV1976: $i,SV1246: $i,SV392: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV392 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV392 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV392 ) @ ( c_HOL_Otimes__class_Otimes @ SV1246 @ SV1246 @ SV392 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1976 @ SV1976 @ SV392 ) ) @ SV392 )
| ( SV1976
= ( c_HOL_Ozero__class_Ozero @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4149]) ).
thf(4956,plain,
! [SV393: $i] :
( ( ( c_InductTermi_OIT @ SV393 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4150]) ).
thf(4957,plain,
! [SV1977: $i,SV1247: $i,SV394: $i] :
( ( ! [SY6454: $i,SY6455: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV394 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1247 ) @ SV1977 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SY6454 ) @ SY6455 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1247 ) @ SY6454 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1977 ) @ SY6455 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4151]) ).
thf(4958,plain,
! [SV1978: $i,SV1248: $i,SV395: $i] :
( ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV395 ) @ SV1248 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV395 ) @ SV1978 ) )
| ~ ( c_Lambda_Obeta @ SV1248 @ SV1978 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4152]) ).
thf(4959,plain,
! [SV1979: $i,SV1249: $i,SV396: $i] :
( ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV396 ) @ SV1249 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1979 ) @ SV1249 ) )
| ~ ( c_Lambda_Obeta @ SV396 @ SV1979 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4153]) ).
thf(4960,plain,
! [SV1250: $i,SV397: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV397 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1250 @ SV397 ) @ ( c_HOL_Ozero__class_Ozero @ SV397 ) @ SV397 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4154]) ).
thf(4961,plain,
! [SV1980: $i,SV1251: $i,SV398: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV398 )
| ( ( c_Orderings_Oord__class_Omax @ SV1251 @ SV1980 @ SV398 )
= ( c_Orderings_Oord__class_Omax @ SV1980 @ SV1251 @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4155]) ).
thf(4962,plain,
! [SV1981: $i,SV1252: $i,SV400: $i] :
( ( ! [SY6456: $i] :
( ( c_List_Odrop @ SV400 @ ( c_List_Oreplicate @ SV1252 @ SV1981 @ SY6456 ) @ SY6456 )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ SV1252 @ SV400 @ tc_nat ) @ SV1981 @ SY6456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4156]) ).
thf(4963,plain,
! [SV1982: $i,SV1253: $i,SV401: $i] :
( ( ! [SY6457: $i] :
( ~ ( class_Orderings_Olinorder @ SV401 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV1253 @ SV1982 @ SV401 ) @ ( c_Orderings_Oord__class_Omin @ SV1253 @ SY6457 @ SV401 ) @ SV401 ) @ ( c_Orderings_Oord__class_Omin @ SV1253 @ ( c_Orderings_Oord__class_Omax @ SV1982 @ SY6457 @ SV401 ) @ SV401 ) @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4157]) ).
thf(4964,plain,
! [SV1983: $i,SV1255: $i,SV404: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV404 )
| ( ( c_Orderings_Oord__class_Omax @ SV1255 @ ( c_Orderings_Oord__class_Omin @ SV1255 @ SV1983 @ SV404 ) @ SV404 )
= SV1255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4159]) ).
thf(4965,plain,
! [SV1984: $i,SV1256: $i,SV406: $i] :
( ( ! [SY6458: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV406 )
| ( c_HOL_Oord__class_Oless @ SV1256 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1256 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV1984 @ SV406 ) @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SY6458 @ SV406 ) @ SV406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4160]) ).
thf(4966,plain,
! [SV1985: $i,SV1257: $i,SV407: $i] :
( ( ! [SY6459: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV407 )
| ( c_HOL_Oord__class_Oless @ SV1257 @ SV1985 @ SV407 )
| ( c_HOL_Oord__class_Oless @ SV1985 @ SV1257 @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY6459 @ SV1985 @ SV407 ) @ ( c_HOL_Otimes__class_Otimes @ SY6459 @ SV1257 @ SV407 ) @ SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4161]) ).
thf(4967,plain,
! [SV1986: $i,SV1258: $i,SV408: $i] :
( ( ! [SY6460: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV408 )
| ( c_HOL_Oord__class_Oless @ SV1258 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV1258 @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1986 @ SV1258 @ SV408 ) @ ( c_HOL_Otimes__class_Otimes @ SY6460 @ SV1258 @ SV408 ) @ SV408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4162]) ).
thf(4968,plain,
! [SV1987: $i,SV1259: $i,SV409: $i] :
( ( ! [SY6461: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV409 )
| ( c_HOL_Oord__class_Oless @ SV1259 @ SV1987 @ SV409 )
| ( c_HOL_Oord__class_Oless @ SV1987 @ SV1259 @ SV409 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1987 @ SY6461 @ SV409 ) @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SY6461 @ SV409 ) @ SV409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4163]) ).
thf(4969,plain,
! [SV1260: $i,SV410: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV410 @ ( c_HOL_Ominus__class_Ominus @ SV410 @ SV1260 @ tc_nat ) @ tc_nat )
= SV1260 )
= $true )
| ( ( ~ ( c_lessequals @ SV1260 @ SV410 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4164]) ).
thf(4970,plain,
! [SV1261: $i,SV411: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV411 ) @ SV1261 )
= ( c_Lambda_OdB_OVar @ SV411 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV411 @ SV1261 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4165]) ).
thf(4971,plain,
! [SV1262: $i,SV412: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV412 ) @ SV1262 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4166]) ).
thf(4972,plain,
! [SV1988: $i,SV1263: $i,SV413: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV413 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV1263 @ SV1988 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV413 ) @ SV1988 ) @ ( c_Suc @ SV1263 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV1988 @ SV1263 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4167]) ).
thf(4973,plain,
! [SV1989: $i,SV1264: $i,SV414: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV414 )
| ( c_HOL_Oord__class_Oless @ SV1264 @ SV1989 @ SV414 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1264 @ SV1989 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4168]) ).
thf(4974,plain,
! [SV1990: $i,SV1265: $i,SV415: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV415 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SV1990 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 )
| ~ ( c_HOL_Oord__class_Oless @ SV1265 @ SV1990 @ SV415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4169]) ).
thf(4975,plain,
! [SV1991: $i,SV1266: $i,SV416: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV416 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1266 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1991 @ SV416 ) @ SV416 )
| ~ ( c_HOL_Oord__class_Oless @ SV1266 @ SV1991 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4170]) ).
thf(4976,plain,
! [SV1992: $i,SV1267: $i,SV417: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV417 )
| ( c_HOL_Oord__class_Oless @ SV1267 @ SV1992 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1267 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1992 @ SV417 ) @ SV417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4171]) ).
thf(4977,plain,
! [SV1993: $i,SV1268: $i,SV420: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV420 ) @ SV1268 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1993 @ SV1268 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV420 @ SV1993 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4172]) ).
thf(4978,plain,
! [SV1994: $i,SV1269: $i,SV421: $i] :
( ( ! [SY6462: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV1269 ) @ SV1994 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SY6462 ) @ SV1994 ) @ SV421 )
| ~ ( c_lessequals @ SV1269 @ SY6462 @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4173]) ).
thf(4979,plain,
! [SV1995: $i,SV1270: $i,SV422: $i] :
( ( ! [SY6463: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
| ( c_lessequals @ SV1270 @ SV1995 @ SV422 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1270 ) @ SY6463 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1995 ) @ SY6463 ) @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4174]) ).
thf(4980,plain,
! [SV1996: $i,SV1271: $i,SV423: $i] :
( ( ! [SY6464: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV423 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SV1996 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SY6464 ) @ SV423 )
| ~ ( c_lessequals @ SV1996 @ SY6464 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4175]) ).
thf(4981,plain,
! [SV1997: $i,SV1272: $i,SV424: $i] :
( ( ! [SY6465: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
| ( c_lessequals @ SV1272 @ SV1997 @ SV424 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SY6465 ) @ SV1272 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SY6465 ) @ SV1997 ) @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4176]) ).
thf(4982,plain,
! [SV1998: $i,SV1273: $i,SV425: $i] :
( ( ! [SY6466: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV425 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV1273 ) @ SV1998 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SY6466 ) @ SV1998 ) @ SV425 )
| ~ ( c_lessequals @ SV1273 @ SY6466 @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4177]) ).
thf(4983,plain,
! [SV1999: $i,SV1274: $i,SV426: $i] :
( ( ! [SY6467: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV426 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SV1999 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SY6467 ) @ SV426 )
| ~ ( c_lessequals @ SV1999 @ SY6467 @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4178]) ).
thf(4984,plain,
! [SV2000: $i,SV1275: $i,SV427: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV427 ) @ SV1275 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2000 ) @ SV1275 ) @ tc_nat )
| ~ ( c_lessequals @ SV427 @ SV2000 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4179]) ).
thf(4985,plain,
! [SV2001: $i,SV1276: $i,SV428: $i] :
( ( ( c_lessequals @ SV428 @ SV1276 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2001 ) @ SV428 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2001 ) @ SV1276 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4180]) ).
thf(4986,plain,
! [SV2002: $i,SV1277: $i,SV429: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV429 ) @ SV1277 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV429 ) @ SV2002 ) @ tc_nat )
| ~ ( c_lessequals @ SV1277 @ SV2002 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4181]) ).
thf(4987,plain,
! [SV1278: $i,SV430: $i] :
( ( ( ~ ( c_lessequals @ SV430 @ SV1278 @ tc_nat ) )
= $true )
| ( ( SV1278
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1278 @ SV430 @ tc_nat ) ) @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4182]) ).
thf(4988,plain,
! [SV1279: $i,SV431: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV431 ) @ ( c_HOL_Ominus__class_Ominus @ SV1279 @ SV431 @ tc_nat ) )
= SV1279 )
= $true )
| ( ( ~ ( c_lessequals @ SV431 @ SV1279 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4183]) ).
thf(4989,plain,
! [SV1280: $i,SV432: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV432 @ SV1280 @ tc_nat ) ) @ SV1280 )
= SV432 )
= $true )
| ( ( ~ ( c_lessequals @ SV1280 @ SV432 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4184]) ).
thf(4990,plain,
! [SV2003: $i,SV1281: $i,SV433: $i] :
( ( ! [SY6468: $i,SY6469: $i,SY6470: $i,SY6471: $i,SY6472: $i] :
( ( ( hAPP @ ( hAPP @ SV433 @ SV1281 ) @ ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ SY6468 ) )
= ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ ( c_Suc @ SY6468 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6469 @ SV433 @ SV2003 @ SY6470 @ SY6471 @ SY6472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4185]) ).
thf(4991,plain,
! [SV2004: $i,SV1282: $i,SV434: $i] :
( ( ! [SY6473: $i,SY6474: $i,SY6475: $i,SY6476: $i,SY6477: $i] :
( ( ( hAPP @ ( hAPP @ SV434 @ ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ SY6473 ) ) @ SV2004 )
= ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ ( c_Suc @ SY6473 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6474 @ SV434 @ SV1282 @ SY6475 @ SY6476 @ SY6477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4186]) ).
thf(4992,plain,
! [SV2005: $i,SV1283: $i,SV435: $i] :
( ( ! [SY6478: $i,SY6479: $i,SY6480: $i,SY6481: $i,SY6482: $i] :
( ( ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ ( c_Suc @ SV2005 ) )
= ( hAPP @ ( hAPP @ SY6478 @ SV1283 ) @ ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ SV2005 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6479 @ SY6478 @ SV435 @ SY6480 @ SY6481 @ SY6482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4187]) ).
thf(4993,plain,
! [SV2006: $i,SV1284: $i,SV436: $i] :
( ( ! [SY6483: $i,SY6484: $i,SY6485: $i,SY6486: $i,SY6487: $i] :
( ( ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ ( c_Suc @ SV2006 ) )
= ( hAPP @ ( hAPP @ SY6483 @ SV1284 ) @ ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ SV2006 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6484 @ SY6483 @ SV436 @ SY6485 @ SY6486 @ SY6487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4188]) ).
thf(4994,plain,
! [SV2007: $i,SV1285: $i,SV437: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV437 @ SV1285 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2007 @ SV437 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2007 @ SV1285 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4189]) ).
thf(4995,plain,
! [SV2008: $i,SV1286: $i,SV438: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV438 @ SV1286 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV438 @ SV2008 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1286 @ SV2008 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4190]) ).
thf(4996,plain,
! [SV2009: $i,SV1287: $i,SV439: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV439 ) @ ( c_HOL_Ominus__class_Ominus @ SV1287 @ SV2009 @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV439 ) @ SV1287 ) @ SV2009 @ tc_nat ) )
| ~ ( c_lessequals @ SV2009 @ SV1287 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4191]) ).
thf(4997,plain,
! [SV2010: $i,SV1288: $i,SV440: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV440 @ SV1288 @ tc_nat ) ) @ SV2010 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV440 ) @ SV2010 ) @ SV1288 @ tc_nat ) )
| ~ ( c_lessequals @ SV1288 @ SV440 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4192]) ).
thf(4998,plain,
! [SV2011: $i,SV1289: $i,SV441: $i] :
( ( ! [SY6488: $i] :
( ( c_List_Odrop @ SV441 @ ( c_List_Odrop @ SV1289 @ SV2011 @ SY6488 ) @ SY6488 )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV441 ) @ SV1289 ) @ SV2011 @ SY6488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4193]) ).
thf(4999,plain,
! [SV2012: $i,SV1290: $i,SV442: $i] :
( ( ! [SY6489: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV442 )
| ( c_lessequals @ SV1290 @ SV2012 @ SV442 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV442 ) @ SV2012 @ SV442 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1290 @ ( c_Suc @ SY6489 ) @ SV442 ) @ ( c_Power_Opower__class_Opower @ SV2012 @ ( c_Suc @ SY6489 ) @ SV442 ) @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4194]) ).
thf(5000,plain,
! [SV2013: $i,SV1291: $i,SV443: $i] :
( ( ! [SY6490: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV443 ) @ SV1291 ) @ SV2013 @ SY6490 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV443 @ SV2013 @ SY6490 ) @ ( c_List_Oreplicate @ SV1291 @ SV2013 @ SY6490 ) @ SY6490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4195]) ).
thf(5001,plain,
! [SV2014: $i,SV1292: $i,SV444: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV444 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1292 @ ( c_HOL_Otimes__class_Otimes @ SV1292 @ SV2014 @ SV444 ) @ SV444 )
= ( c_HOL_Otimes__class_Otimes @ SV1292 @ SV2014 @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4196]) ).
thf(5002,plain,
! [SV1293: $i,SV445: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV445 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV445 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1293 @ SV445 ) @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1293 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4197]) ).
thf(5003,plain,
! [SV1294: $i,SV446: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV446 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1294 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1294 @ SV446 ) @ SV446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4198]) ).
thf(5004,plain,
! [SV2015: $i,SV1295: $i,SV447: $i] :
( ( ! [SY6491: $i,SY6492: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SY6491 @ SY6492 @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
| ~ ( c_lessequals @ SV2015 @ SY6492 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SY6491 @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4199]) ).
thf(5005,plain,
! [SV2016: $i,SV1296: $i,SV448: $i] :
( ( ! [SY6493: $i,SY6494: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SY6493 @ SY6494 @ SV448 ) @ SV448 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ SV2016 @ SY6494 @ SV448 )
| ~ ( c_lessequals @ SV1296 @ SY6493 @ SV448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4200]) ).
thf(5006,plain,
! [SV2017: $i,SV1297: $i,SV449: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV449 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1297 @ ( c_Power_Opower__class_Opower @ SV1297 @ SV2017 @ SV449 ) @ SV449 )
= ( c_Power_Opower__class_Opower @ SV1297 @ ( c_Suc @ SV2017 ) @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4201]) ).
thf(5007,plain,
! [SV2018: $i,SV1298: $i,SV450: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV450 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1298 @ SV2018 @ SV450 ) @ SV1298 @ SV450 )
= ( c_Power_Opower__class_Opower @ SV1298 @ ( c_Suc @ SV2018 ) @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4202]) ).
thf(5008,plain,
! [SV2019: $i,SV1299: $i,SV451: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV451 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV1299 @ SV451 )
| ( c_lessequals @ SV1299 @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1299 @ SV451 ) @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4203]) ).
thf(5009,plain,
! [SV2020: $i,SV1300: $i,SV452: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV452 )
| ( c_lessequals @ SV1300 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
| ( c_lessequals @ SV2020 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1300 @ SV2020 @ SV452 ) @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4204]) ).
thf(5010,plain,
! [SV2021: $i,SV1301: $i,SV453: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV453 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV1301 @ SV453 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV2021 @ SV453 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1301 @ SV453 ) @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4205]) ).
thf(5011,plain,
! [SV2022: $i,SV1302: $i,SV454: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV454 )
| ( c_lessequals @ SV1302 @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV1302 @ SV454 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1302 @ SV2022 @ SV454 ) @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4206]) ).
thf(5012,plain,
! [SV2023: $i,SV1303: $i,SV455: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV455 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1303 @ SV2023 @ SV455 ) @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SV1303 @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV2023 @ SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4207]) ).
thf(5013,plain,
! [SV2024: $i,SV1304: $i,SV456: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV456 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1304 @ SV2024 @ SV456 ) @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV2024 @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1304 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4208]) ).
thf(5014,plain,
! [SV2025: $i,SV1305: $i,SV457: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV457 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1305 @ SV2025 @ SV457 ) @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV2025 @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SV1305 @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4209]) ).
thf(5015,plain,
! [SV1306: $i,SV458: $i] :
( ( ( c_lessequals @ SV458 @ SV1306 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV458 ) @ SV1306 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4210]) ).
thf(5016,plain,
! [SV1307: $i,SV459: $i] :
( ( ( c_lessequals @ SV459 @ ( c_Suc @ SV1307 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV459 @ SV1307 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4211]) ).
thf(5017,plain,
! [SV2026: $i,SV1308: $i,SV460: $i] :
( ( ! [SY6495: $i] :
( ( c_Type_Otypings @ SV460 @ SV1308 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV2026 @ SV460 @ SY6495 @ SV1308 ) )
| ~ ( c_Type_Otyping @ SV460 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY6495 @ SV1308 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4212]) ).
thf(5018,plain,
! [SV1309: $i,SV461: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV461 @ ( c_HOL_Otimes__class_Otimes @ SV1309 @ SV461 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1309 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV461 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4213]) ).
thf(5019,plain,
! [SV1310: $i,SV462: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV462 @ ( c_HOL_Otimes__class_Otimes @ SV462 @ SV1310 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1310 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV462 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4214]) ).
thf(5020,plain,
! [SV2027: $i,SV1311: $i,SV464: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV464 @ SV1311 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SV2027 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1311 @ SV2027 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV2027 @ SV1311 @ tc_nat )
| ~ ( c_lessequals @ SV2027 @ SV464 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4216]) ).
thf(5021,plain,
! [SV2028: $i,SV1312: $i,SV465: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV465 @ SV1312 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV2028 @ SV1312 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV465 @ SV2028 @ tc_nat )
| ~ ( c_lessequals @ SV1312 @ SV2028 @ tc_nat )
| ~ ( c_lessequals @ SV1312 @ SV465 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4217]) ).
thf(5022,plain,
! [SV2029: $i,SV1313: $i,SV466: $i] :
( ( ! [SY6496: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV466 )
| ( c_HOL_Oord__class_Oless @ SV1313 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ SV2029 ) @ SY6496 ) @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ SV1313 @ SY6496 @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV2029 @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4218]) ).
thf(5023,plain,
! [SV2030: $i,SV1314: $i,SV467: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV467 ) @ SV1314 @ SV2030 )
= ( c_Lambda_OdB_OVar @ SV467 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV467 @ SV2030 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4219]) ).
thf(5024,plain,
! [SV2031: $i,SV1315: $i,SV468: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV468 @ ( c_Lambda_OdB_OVar @ SV1315 ) @ SV2031 ) )
| ~ ( c_InductTermi_OIT @ SV468 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4220]) ).
thf(5025,plain,
! [SV1316: $i,SV469: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV469 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV469 ) @ SV1316 ) @ SV1316 ) @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1316 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4221]) ).
thf(5026,plain,
! [SV1317: $i,SV470: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV470 ) )
= $true )
| ( ( ( c_lessequals @ SV1317 @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV470 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV470 ) @ SV1317 ) @ SV1317 ) @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV470 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4222]) ).
thf(5027,plain,
! [SV1318: $i,SV471: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV471 ) @ SV1318 ) @ SV471 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4223]) ).
thf(5028,plain,
! [SV1319: $i,SV472: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV472 ) @ SV1319 ) @ SV1319 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4224]) ).
thf(5029,plain,
! [SV2032: $i,SV1320: $i,SV473: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV473 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1320 @ SV2032 @ tc_nat ) @ SV473 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1320 @ SV473 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV2032 @ SV473 ) @ SV473 ) )
| ~ ( c_lessequals @ SV2032 @ SV1320 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4225]) ).
thf(5030,plain,
! [SV2033: $i,SV1321: $i,SV474: $i] :
( ( ! [SY6497: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV474 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1321 @ SV2033 @ SV474 ) @ ( c_HOL_Otimes__class_Otimes @ SY6497 @ SV2033 @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SV2033 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SY6497 @ SV1321 @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4226]) ).
thf(5031,plain,
! [SV2034: $i,SV1322: $i,SV475: $i] :
( ( ! [SY6498: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV475 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2034 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SY6498 @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SY6498 @ SV2034 @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4227]) ).
thf(5032,plain,
! [SV2035: $i,SV1323: $i,SV476: $i] :
( ( ! [SY6499: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ SV476 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1323 @ SV2035 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SY6499 @ SV2035 @ SV476 ) @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV2035 @ SV476 )
| ~ ( c_lessequals @ SV1323 @ SY6499 @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4228]) ).
thf(5033,plain,
! [SV2036: $i,SV1324: $i,SV477: $i] :
( ( ! [SY6500: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ SV477 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2036 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SY6500 @ SV477 ) @ SV477 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV477 ) @ SV1324 @ SV477 )
| ~ ( c_lessequals @ SV2036 @ SY6500 @ SV477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4229]) ).
thf(5034,plain,
! [SV2037: $i,SV1325: $i,SV478: $i] :
( ( ! [SY6501: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ SV478 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2037 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SY6501 @ SV478 ) @ SV478 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV478 ) @ SV1325 @ SV478 )
| ~ ( c_lessequals @ SV2037 @ SY6501 @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4230]) ).
thf(5035,plain,
! [SV2038: $i,SV1326: $i,SV479: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV479 ) @ ( c_List_Olist_OCons @ SV1326 @ SV2038 @ SV479 ) @ SV479 )
= ( c_List_Olist_OCons @ SV1326 @ SV2038 @ SV479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4231]) ).
thf(5036,plain,
! [SV2039: $i,SV1327: $i,SV480: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV480 ) @ SV1327 ) @ SV2039 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV480 @ ( c_HOL_Ominus__class_Ominus @ SV2039 @ SV1327 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4232]) ).
thf(5037,plain,
! [SV2040: $i,SV1328: $i,SV481: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV481 @ ( c_HOL_Ominus__class_Ominus @ SV1328 @ SV2040 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SV2040 ) @ SV1328 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4233]) ).
thf(5038,plain,
! [SV2041: $i,SV1329: $i,SV482: $i] :
( ( ! [SY6502: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV482 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SV1329 ) @ SV2041 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SY6502 ) @ SV2041 ) @ SV482 )
| ~ ( c_HOL_Oord__class_Oless @ SV1329 @ SY6502 @ SV482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4234]) ).
thf(5039,plain,
! [SV2042: $i,SV1330: $i,SV483: $i] :
( ( ! [SY6503: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV483 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SV1330 ) @ SV2042 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SY6503 ) @ SV2042 ) @ SV483 )
| ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SY6503 @ SV483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4235]) ).
thf(5040,plain,
! [SV2043: $i,SV1331: $i,SV484: $i] :
( ( ! [SY6504: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV484 )
| ( c_HOL_Oord__class_Oless @ SV1331 @ SV2043 @ SV484 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV1331 ) @ SY6504 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV2043 ) @ SY6504 ) @ SV484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4236]) ).
thf(5041,plain,
! [SV2044: $i,SV1332: $i,SV485: $i] :
( ( ! [SY6505: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV485 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SV2044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SY6505 ) @ SV485 )
| ~ ( c_HOL_Oord__class_Oless @ SV2044 @ SY6505 @ SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4237]) ).
thf(5042,plain,
! [SV2045: $i,SV1333: $i,SV486: $i] :
( ( ! [SY6506: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV486 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SV2045 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SY6506 ) @ SV486 )
| ~ ( c_HOL_Oord__class_Oless @ SV2045 @ SY6506 @ SV486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4238]) ).
thf(5043,plain,
! [SV2046: $i,SV1334: $i,SV487: $i] :
( ( ! [SY6507: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV487 )
| ( c_HOL_Oord__class_Oless @ SV1334 @ SV2046 @ SV487 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SY6507 ) @ SV1334 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SY6507 ) @ SV2046 ) @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4239]) ).
thf(5044,plain,
! [SV2047: $i,SV1335: $i,SV488: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV488 ) @ SV1335 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2047 ) @ SV1335 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV488 @ SV2047 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4240]) ).
thf(5045,plain,
! [SV2048: $i,SV1336: $i,SV489: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV489 @ SV1336 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2048 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2048 ) @ SV1336 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4241]) ).
thf(5046,plain,
! [SV2049: $i,SV1337: $i,SV490: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV490 ) @ SV1337 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV490 ) @ SV2049 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1337 @ SV2049 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4242]) ).
thf(5047,plain,
! [SV1338: $i,SV491: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV491 @ SV1338 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1338 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV491 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4243]) ).
thf(5048,plain,
! [SV2050: $i,SV1339: $i,SV492: $i] :
( ( ! [SY6508: $i] :
( ~ ( class_Orderings_Oorder @ SV492 )
| ( c_lessequals @ SV1339 @ SV2050 @ SV492 )
| ~ ( c_lessequals @ SV1339 @ SY6508 @ SV492 )
| ~ ( c_lessequals @ SY6508 @ SV2050 @ SV492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4244]) ).
thf(5049,plain,
! [SV2051: $i,SV1340: $i,SV493: $i] :
( ( ! [SY6509: $i] :
( ~ ( class_Orderings_Oorder @ SV493 )
| ( c_HOL_Oord__class_Oless @ SV1340 @ SV2051 @ SV493 )
| ~ ( c_lessequals @ SV1340 @ SY6509 @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SY6509 @ SV2051 @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4245]) ).
thf(5050,plain,
! [SV2052: $i,SV1341: $i,SV494: $i] :
( ( ! [SY6510: $i] :
( ~ ( class_Orderings_Oorder @ SV494 )
| ( c_HOL_Oord__class_Oless @ SV1341 @ SV2052 @ SV494 )
| ~ ( c_HOL_Oord__class_Oless @ SV1341 @ SY6510 @ SV494 )
| ~ ( c_lessequals @ SY6510 @ SV2052 @ SV494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4246]) ).
thf(5051,plain,
! [SV2053: $i,SV1342: $i,SV495: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV495 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1342 ) @ SV2053 ) @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
| ~ ( c_lessequals @ SV2053 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
| ~ ( c_lessequals @ SV1342 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4247]) ).
thf(5052,plain,
! [SV2054: $i,SV1343: $i,SV496: $i] :
( ( ! [SY6511: $i] :
( ~ ( class_Orderings_Opreorder @ SV496 )
| ( c_lessequals @ SV1343 @ SV2054 @ SV496 )
| ~ ( c_lessequals @ SY6511 @ SV2054 @ SV496 )
| ~ ( c_lessequals @ SV1343 @ SY6511 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4248]) ).
thf(5053,plain,
! [SV2055: $i,SV1344: $i,SV498: $i] :
( ( ( c_lessequals @ SV498 @ SV1344 @ tc_nat )
| ~ ( c_lessequals @ SV2055 @ SV1344 @ tc_nat )
| ~ ( c_lessequals @ SV498 @ SV2055 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4249]) ).
thf(5054,plain,
! [SV1346: $i,SV501: $i] :
( ( ( SV501
= ( c_Suc @ SV1346 ) )
= $true )
| ( ( ( c_lessequals @ SV501 @ SV1346 @ tc_nat )
| ~ ( c_lessequals @ SV501 @ ( c_Suc @ SV1346 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4251]) ).
thf(5055,plain,
! [SV1347: $i,SV503: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV503 @ SV1347 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1347 @ ( c_Suc @ SV503 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4253]) ).
thf(5056,plain,
! [SV1348: $i,SV504: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV504 @ ( c_Suc @ SV1348 ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1348 @ SV504 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4254]) ).
thf(5057,plain,
! [SV2056: $i,SV1349: $i,SV505: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV1349 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2056 @ SV1349 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV505 @ SV2056 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1349 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4255]) ).
thf(5058,plain,
! [SV2057: $i,SV1350: $i,SV506: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV1350 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV2057 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1350 @ SV2057 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV506 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4256]) ).
thf(5059,plain,
! [SV2058: $i,SV1351: $i,SV507: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SV1351 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SV2058 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV507 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1351 @ SV2058 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4257]) ).
thf(5060,plain,
! [SV2059: $i,SV1352: $i,SV508: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV508 @ SV1352 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2059 @ SV1352 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1352 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV508 @ SV2059 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4258]) ).
thf(5061,plain,
! [SV2060: $i,SV1353: $i,SV509: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV509 @ SV1353 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2060 @ SV509 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2060 @ SV1353 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2060 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4259]) ).
thf(5062,plain,
! [SV2061: $i,SV1354: $i,SV510: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SV1354 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SV2061 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1354 @ SV2061 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV510 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4260]) ).
thf(5063,plain,
! [SV2062: $i,SV1355: $i,SV511: $i] :
( ( ! [SY6512: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV511 )
| ( c_HOL_Oord__class_Oless @ SV1355 @ SV2062 @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY6512 @ SV2062 @ SV511 ) @ ( c_HOL_Otimes__class_Otimes @ SY6512 @ SV1355 @ SV511 ) @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ SY6512 @ ( c_HOL_Ozero__class_Ozero @ SV511 ) @ SV511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4261]) ).
thf(5064,plain,
! [SV2063: $i,SV1356: $i,SV512: $i] :
( ( ! [SY6513: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV512 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2063 @ SV512 ) @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SY6513 @ SV512 ) @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SY6513 @ SV2063 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SV1356 @ ( c_HOL_Ozero__class_Ozero @ SV512 ) @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4262]) ).
thf(5065,plain,
! [SV2064: $i,SV1357: $i,SV513: $i] :
( ( ! [SY6514: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV513 )
| ( c_HOL_Oord__class_Oless @ SV1357 @ SV2064 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY6514 @ SV1357 @ SV513 ) @ ( c_HOL_Otimes__class_Otimes @ SY6514 @ SV2064 @ SV513 ) @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV513 ) @ SY6514 @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4263]) ).
thf(5066,plain,
! [SV2065: $i,SV1358: $i,SV514: $i] :
( ( ! [SY6515: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV514 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2065 @ SV514 ) @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SY6515 @ SV514 ) @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ SV2065 @ SY6515 @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SV1358 @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4264]) ).
thf(5067,plain,
! [SV2066: $i,SV1359: $i,SV515: $i] :
( ( ! [SY6516: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV515 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2066 @ SV515 ) @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SY6516 @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SV1359 @ ( c_HOL_Ozero__class_Ozero @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SY6516 @ SV2066 @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4265]) ).
thf(5068,plain,
! [SV2067: $i,SV1360: $i,SV516: $i] :
( ( ! [SY6517: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV516 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2067 @ SV516 ) @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SY6517 @ SV516 ) @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV516 ) @ SV1360 @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ SV2067 @ SY6517 @ SV516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4266]) ).
thf(5069,plain,
! [SV2068: $i,SV1361: $i,SV517: $i] :
( ( ! [SY6518: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV517 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2068 @ SV517 ) @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SY6518 @ SV517 ) @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ SV2068 @ SY6518 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1361 @ SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4267]) ).
thf(5070,plain,
! [SV2069: $i,SV1362: $i,SV518: $i] :
( ( ! [SY6519: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV518 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2069 @ SV518 ) @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SY6519 @ SV518 ) @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SY6519 @ SV2069 @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SV1362 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4268]) ).
thf(5071,plain,
! [SV2070: $i,SV1363: $i,SV519: $i] :
( ( ! [SY6520: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV519 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1363 @ SV2070 @ SV519 ) @ ( c_HOL_Otimes__class_Otimes @ SY6520 @ SV2070 @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SV2070 @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SY6520 @ SV1363 @ SV519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4269]) ).
thf(5072,plain,
! [SV2071: $i,SV1364: $i,SV520: $i] :
( ( ! [SY6521: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV520 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1364 @ SV2071 @ SV520 ) @ ( c_HOL_Otimes__class_Otimes @ SY6521 @ SV2071 @ SV520 ) @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV2071 @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ SV1364 @ SY6521 @ SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4270]) ).
thf(5073,plain,
! [SV2072: $i,SV1365: $i,SV521: $i] :
( ( ! [SY6522: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV521 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1365 @ SV2072 @ SV521 ) @ ( c_HOL_Otimes__class_Otimes @ SY6522 @ SV2072 @ SV521 ) @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ SV1365 @ SY6522 @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV521 ) @ SV2072 @ SV521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4271]) ).
thf(5074,plain,
! [SV2073: $i,SV1366: $i,SV522: $i] :
( ( ! [SY6523: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV522 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1366 @ SV2073 @ SV522 ) @ ( c_HOL_Otimes__class_Otimes @ SY6523 @ SV2073 @ SV522 ) @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SY6523 @ SV1366 @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SV2073 @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4272]) ).
thf(5075,plain,
! [SV2074: $i,SV1367: $i,SV523: $i] :
( ( ! [SY6524: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV523 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2074 @ SV523 ) @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SY6524 @ SV523 ) @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV1367 @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ SV2074 @ SY6524 @ SV523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4273]) ).
thf(5076,plain,
! [SV2075: $i,SV1368: $i,SV524: $i] :
( ( ( c_List_Olist_OCons @ SV524 @ SV1368 @ SV2075 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV2075 ) @ ( c_List_Olist_OCons @ SV524 @ SV1368 @ SV2075 ) @ SV2075 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4274]) ).
thf(5077,plain,
! [SV2076: $i,SV1369: $i,SV525: $i] :
( ( ! [SY6525: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV525 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ ( c_Orderings_Oord__class_Omax @ SV1369 @ SV2076 @ SV525 ) ) @ SY6525 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ SV1369 ) @ SY6525 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ SV2076 ) @ SY6525 ) @ SV525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4275]) ).
thf(5078,plain,
! [SV1370: $i,SV526: $i] :
( ( ( c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV526 ) @ ( c_Lambda_OdB_OVar @ SV1370 ) ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4276]) ).
thf(5079,plain,
! [SV2077: $i,SV1371: $i,SV527: $i] :
( ( ! [SY6526: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV527 @ SV1371 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2077 @ SY6526 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1371 @ SY6526 @ tc_nat )
| ~ ( c_lessequals @ SV527 @ SV2077 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4277]) ).
thf(5080,plain,
! [SV2078: $i,SV1372: $i,SV529: $i] :
( ( ! [SY6527: $i,SY6528: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV529 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SY6527 @ SY6528 @ SV529 ) @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SY6527 @ SV529 )
| ~ ( c_lessequals @ SV2078 @ SY6528 @ SV529 )
| ~ ( c_lessequals @ SV1372 @ SY6527 @ SV529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4278]) ).
thf(5081,plain,
! [SV2079: $i,SV1373: $i,SV530: $i] :
( ( ! [SY6529: $i,SY6530: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV530 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SY6529 @ SY6530 @ SV530 ) @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
| ~ ( c_lessequals @ SV2079 @ SY6530 @ SV530 )
| ~ ( c_lessequals @ SV1373 @ SY6529 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4279]) ).
thf(5082,plain,
! [SV2080: $i,SV1374: $i,SV531: $i] :
( ( ! [SY6531: $i] :
( ~ ( class_Orderings_Olinorder @ SV531 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV1374 @ SV2080 @ SV531 ) @ SY6531 @ SV531 )
= ( c_Orderings_Oord__class_Omax @ SV1374 @ ( c_Orderings_Oord__class_Omax @ SV2080 @ SY6531 @ SV531 ) @ SV531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4280]) ).
thf(5083,plain,
! [SV2081: $i,SV1375: $i,SV532: $i] :
( ( ! [SY6532: $i] :
( ~ ( class_Orderings_Olinorder @ SV532 )
| ( ( c_Orderings_Oord__class_Omax @ SV1375 @ ( c_Orderings_Oord__class_Omax @ SV2081 @ SY6532 @ SV532 ) @ SV532 )
= ( c_Orderings_Oord__class_Omax @ SV2081 @ ( c_Orderings_Oord__class_Omax @ SV1375 @ SY6532 @ SV532 ) @ SV532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4281]) ).
thf(5084,plain,
! [SV2082: $i,SV1376: $i,SV534: $i] :
( ( ! [SY6533: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV534 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV534 ) @ ( c_HOL_Otimes__class_Otimes @ SV1376 @ SV2082 @ SV534 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY6533 @ SV2082 @ SV534 ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV534 ) @ SV1376 ) @ SY6533 ) @ SV2082 @ SV534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4282]) ).
thf(5085,plain,
! [SV1377: $i,SV535: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV535 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV535 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1377 @ SV535 ) @ SV535 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4283]) ).
thf(5086,plain,
! [SV1378: $i,SV536: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV536 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1378 @ SV536 ) @ SV536 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4284]) ).
thf(5087,plain,
! [SV537: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV537 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV537 ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV537 ) ) @ SV537 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4285]) ).
thf(5088,plain,
! [SV1379: $i,SV538: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV538 ) @ ( c_Lambda_OdB_OAbs @ SV1379 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV538 @ SV1379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4286]) ).
thf(5089,plain,
! [SV2083: $i,SV1380: $i,SV539: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV539 )
| ( ( c_Orderings_Oord__class_Omax @ SV1380 @ ( c_Orderings_Oord__class_Omax @ SV1380 @ SV2083 @ SV539 ) @ SV539 )
= ( c_Orderings_Oord__class_Omax @ SV1380 @ SV2083 @ SV539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4287]) ).
thf(5090,plain,
! [SV2084: $i,SV1381: $i,SV540: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV540 @ SV1381 @ SV2084 ) @ ( c_List_Olist_OCons @ SV1381 @ ( c_List_Olist_ONil @ SV2084 ) @ SV2084 ) @ SV2084 )
= ( c_List_Olist_OCons @ SV1381 @ ( c_List_Oreplicate @ SV540 @ SV1381 @ SV2084 ) @ SV2084 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4288]) ).
thf(5091,plain,
! [SV2085: $i,SV1382: $i,SV541: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV541 )
| ( c_lessequals @ SV1382 @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV541 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV1382 @ SV541 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV2085 @ SV541 ) @ SV541 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4289]) ).
thf(5092,plain,
! [SV2086: $i,SV1383: $i,SV542: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV542 )
| ( c_lessequals @ SV1383 @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV542 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV2086 @ SV542 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ ( c_HOL_Otimes__class_Otimes @ SV2086 @ SV1383 @ SV542 ) @ SV542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4290]) ).
thf(5093,plain,
! [SV2087: $i,SV1384: $i,SV543: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV543 )
| ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV543 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV2087 @ SV543 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ ( c_HOL_Otimes__class_Otimes @ SV1384 @ SV2087 @ SV543 ) @ SV543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4291]) ).
thf(5094,plain,
! [SV2088: $i,SV1385: $i,SV544: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV544 )
| ( c_lessequals @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV544 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV1385 @ SV544 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ ( c_HOL_Otimes__class_Otimes @ SV2088 @ SV1385 @ SV544 ) @ SV544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4292]) ).
thf(5095,plain,
! [SV2089: $i,SV1388: $i,SV547: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV547 )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV547 ) @ SV1388 ) @ SV2089 ) @ SV2089 @ SV547 )
= SV1388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4295]) ).
thf(5096,plain,
! [SV2090: $i,SV1389: $i,SV548: $i] :
( ( ! [SY6534: $i,SY6535: $i,SY6536: $i] :
( ( c_List_Ofoldl @ SV548 @ SV1389 @ ( c_List_Oappend @ SV2090 @ SY6534 @ SY6535 ) @ SY6536 @ SY6535 )
= ( c_List_Ofoldl @ SV548 @ ( c_List_Ofoldl @ SV548 @ SV1389 @ SV2090 @ SY6536 @ SY6535 ) @ SY6534 @ SY6536 @ SY6535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4296]) ).
thf(5097,plain,
! [SV2091: $i,SV1390: $i,SV549: $i] :
( ( ! [SY6537: $i] :
( ( c_Type_Otype_Otype__case @ SV549 @ SV1390 @ ( c_Type_Otype_OAtom @ SV2091 ) @ SY6537 )
= ( hAPP @ SV549 @ SV2091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4297]) ).
thf(5098,plain,
! [SV2092: $i,SV1391: $i,SV550: $i] :
( ( ! [SY6538: $i,SY6539: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV550 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV1391 ) @ SV2092 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SY6538 ) @ SY6539 ) @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SV2092 @ SY6539 @ SV550 )
| ~ ( c_lessequals @ SV1391 @ SY6538 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4298]) ).
thf(5099,plain,
! [SV2093: $i,SV1392: $i,SV551: $i] :
( ( ! [SY6540: $i,SY6541: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV551 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV1392 ) @ SV2093 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SY6540 ) @ SY6541 ) @ SV551 )
| ~ ( c_lessequals @ SV2093 @ SY6541 @ SV551 )
| ~ ( c_HOL_Oord__class_Oless @ SV1392 @ SY6540 @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4299]) ).
thf(5100,plain,
! [SV1393: $i,SV552: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV552 ) @ ( c_Suc @ SV1393 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV552 @ SV1393 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4300]) ).
thf(5101,plain,
! [SV1394: $i,SV553: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV553 @ SV1394 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV553 ) @ ( c_Suc @ SV1394 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4301]) ).
thf(5102,plain,
! [SV1395: $i,SV554: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV554 ) @ ( c_Suc @ SV1395 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV554 @ SV1395 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4302]) ).
thf(5103,plain,
! [SV1396: $i,SV555: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV555 ) @ SV1396 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1396 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4303]) ).
thf(5104,plain,
! [SV1397: $i,SV556: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV556 ) @ SV1397 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV556 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4304]) ).
thf(5105,plain,
! [SV1398: $i,SV557: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV557 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV557 ) @ SV1398 @ SV557 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV557 ) @ SV1398 ) @ SV1398 ) @ SV557 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4305]) ).
thf(5106,plain,
! [SV1399: $i,SV558: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV558 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV558 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV558 ) @ SV1399 ) @ SV1399 ) @ SV558 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV558 ) @ SV1399 @ SV558 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4306]) ).
thf(5107,plain,
! [SV2094: $i,SV1400: $i,SV559: $i] :
( ( ( SV559
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV559 @ SV1400 @ SV2094 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV559 @ SV1400 @ SV2094 ) ) )
| ~ ( c_Type_Otyping @ SV1400 @ ( c_Lambda_OdB_OAbs @ SV2094 ) @ SV559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4307]) ).
thf(5108,plain,
! [SV1401: $i,SV560: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV560 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV560 ) @ SV1401 @ SV560 )
= ( c_HOL_Ozero__class_Ozero @ SV560 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4308]) ).
thf(5109,plain,
! [SV1402: $i,SV561: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV561 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV1402 @ SV561 )
= ( c_HOL_Ozero__class_Ozero @ SV561 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4309]) ).
thf(5110,plain,
! [SV1403: $i,SV562: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV562 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1403 @ ( c_HOL_Ozero__class_Ozero @ SV562 ) @ SV562 )
= ( c_HOL_Ozero__class_Ozero @ SV562 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4310]) ).
thf(5111,plain,
! [SV1404: $i,SV563: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV563 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV563 ) @ SV1404 @ SV563 )
= ( c_HOL_Ozero__class_Ozero @ SV563 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4311]) ).
thf(5112,plain,
! [SV1405: $i,SV564: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV564 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1405 @ ( c_HOL_Ozero__class_Ozero @ SV564 ) @ SV564 )
= ( c_HOL_Ozero__class_Ozero @ SV564 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4312]) ).
thf(5113,plain,
! [SV1406: $i,SV565: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV565 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1406 @ ( c_HOL_Ozero__class_Ozero @ SV565 ) @ SV565 )
= ( c_HOL_Ozero__class_Ozero @ SV565 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4313]) ).
thf(5114,plain,
! [SV1407: $i,SV566: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV566 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV566 ) @ SV1407 @ SV566 )
= ( c_HOL_Ozero__class_Ozero @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4314]) ).
thf(5115,plain,
! [SV1408: $i,SV567: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV567 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV567 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1408 @ SV1408 @ SV567 )
= ( c_HOL_Ozero__class_Ozero @ SV567 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4315]) ).
thf(5116,plain,
! [SV1409: $i,SV568: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV568 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1409 @ SV1409 @ SV568 )
= ( c_HOL_Ozero__class_Ozero @ SV568 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4316]) ).
thf(5117,plain,
! [SV1410: $i,SV569: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV569 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1410 @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SV569 )
= SV1410 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4317]) ).
thf(5118,plain,
! [SV1411: $i,SV570: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV570 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1411 @ SV1411 @ SV570 )
= ( c_HOL_Ozero__class_Ozero @ SV570 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4318]) ).
thf(5119,plain,
! [SV1412: $i,SV571: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV571 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1412 @ SV1412 @ SV571 )
= ( c_HOL_Ozero__class_Ozero @ SV571 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4319]) ).
thf(5120,plain,
! [SV572: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV572 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV572 ) @ ( c_HOL_Ozero__class_Ozero @ SV572 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV572 ) )
= ( c_HOL_Ozero__class_Ozero @ SV572 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4320]) ).
thf(5121,plain,
! [SV1413: $i,SV573: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV573 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV573 ) @ ( c_HOL_Ozero__class_Ozero @ SV573 ) ) @ SV1413 )
= SV1413 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4321]) ).
thf(5122,plain,
! [SV1414: $i,SV574: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV574 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV574 ) @ ( c_HOL_Ozero__class_Ozero @ SV574 ) ) @ SV1414 )
= SV1414 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4322]) ).
thf(5123,plain,
! [SV1415: $i,SV575: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV575 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV575 )
| ( SV1415
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1415 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4323]) ).
thf(5124,plain,
! [SV1416: $i,SV576: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV576 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SV1416 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) )
= SV1416 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4324]) ).
thf(5125,plain,
! [SV1417: $i,SV577: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV577 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV577 ) @ ( c_HOL_Ozero__class_Ozero @ SV577 ) ) @ SV1417 )
= SV1417 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4325]) ).
thf(5126,plain,
! [SV1418: $i,SV578: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV578 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV578 ) @ SV1418 ) @ ( c_HOL_Ozero__class_Ozero @ SV578 ) )
= SV1418 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4326]) ).
thf(5127,plain,
! [SV1419: $i,SV579: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV579 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV579 ) @ SV1419 ) @ ( c_HOL_Ozero__class_Ozero @ SV579 ) )
= SV1419 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4327]) ).
thf(5128,plain,
! [SV1420: $i,SV580: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV580 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV580 ) @ ( c_HOL_Ozero__class_Ozero @ SV580 ) ) @ SV1420 )
= SV1420 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4328]) ).
thf(5129,plain,
! [SV1423: $i,SV584: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV584 ) )
= $true )
| ( ( c_lessequals @ SV1423 @ SV1423 @ SV584 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4332]) ).
thf(5130,plain,
! [SV1424: $i,SV585: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV585 ) )
= $true )
| ( ( c_lessequals @ SV1424 @ SV1424 @ SV585 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4333]) ).
thf(5131,plain,
! [SV2095: $i,SV1425: $i,SV586: $i] :
( ( ! [SY6542: $i] :
( ~ ( class_Orderings_Opreorder @ SV586 )
| ( c_HOL_Oord__class_Oless @ SV1425 @ SV2095 @ SV586 )
| ~ ( c_HOL_Oord__class_Oless @ SY6542 @ SV2095 @ SV586 )
| ~ ( c_lessequals @ SV1425 @ SY6542 @ SV586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4334]) ).
thf(5132,plain,
! [SV2096: $i,SV1426: $i,SV587: $i] :
( ( ! [SY6543: $i] :
( ~ ( class_Orderings_Opreorder @ SV587 )
| ( c_HOL_Oord__class_Oless @ SV1426 @ SV2096 @ SV587 )
| ~ ( c_lessequals @ SY6543 @ SV2096 @ SV587 )
| ~ ( c_HOL_Oord__class_Oless @ SV1426 @ SY6543 @ SV587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4335]) ).
thf(5133,plain,
! [SV2097: $i,SV1427: $i,SV588: $i] :
( ( ! [SY6544: $i,SY6545: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV588 )
| ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SY6544 ) @ SV588 )
| ~ ( c_lessequals @ SY6545 @ SY6544 @ SV588 )
| ~ ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SY6545 ) @ SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4336]) ).
thf(5134,plain,
! [SV2098: $i,SV1429: $i,SV590: $i] :
( ( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV590 @ SV1429 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV2098 @ SV1429 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV590 @ SV2098 @ tc_nat ) @ SV1429 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4338]) ).
thf(5135,plain,
! [SV2099: $i,SV1430: $i,SV591: $i] :
( ( ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1430 @ SV2099 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ominus__class_Ominus @ SV1430 @ SV2099 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4339]) ).
thf(5136,plain,
! [SV1431: $i,SV592: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV592 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1431 @ SV1431 @ SV592 )
= SV1431 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4340]) ).
thf(5137,plain,
! [SV2100: $i,SV1432: $i,SV593: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV593 @ SV1432 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1432 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV593 @ SV2100 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV593 @ SV2100 ) )
| ( hBOOL @ ( hAPP @ SV593 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4341]) ).
thf(5138,plain,
! [SV2101: $i,SV1433: $i,SV594: $i] :
( ( ! [SY6546: $i,SY6547: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SY6546 @ SY6547 @ SV594 ) @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV2101 @ SY6547 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SY6546 @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4342]) ).
thf(5139,plain,
! [SV1434: $i,SV595: $i] :
( ( ( SV595 = SV1434 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV595 @ ( c_Suc @ SV1434 ) @ tc_nat )
| ~ ( c_lessequals @ SV1434 @ SV595 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4343]) ).
thf(5140,plain,
! [SV2102: $i,SV1435: $i,SV596: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV596 @ SV1435 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2102 @ SV1435 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV596 @ SV2102 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4344]) ).
thf(5141,plain,
! [SV2103: $i,SV1436: $i,SV597: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV597 @ SV1436 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV597 @ SV2103 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1436 @ SV2103 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4345]) ).
thf(5142,plain,
! [SV2104: $i,SV1437: $i,SV598: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV598 @ SV1437 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV598 @ SV2104 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1437 @ SV2104 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4346]) ).
thf(5143,plain,
! [SV2105: $i,SV1438: $i,SV599: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV599 @ SV1438 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2105 @ SV1438 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV599 @ SV2105 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4347]) ).
thf(5144,plain,
! [SV2106: $i,SV1439: $i,SV600: $i] :
( ( ! [SY6548: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV600 @ SV1439 @ SV2106 ) @ ( c_List_Olist_OCons @ SV1439 @ SY6548 @ SV2106 ) @ SV2106 )
= ( c_List_Olist_OCons @ SV1439 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV600 @ SV1439 @ SV2106 ) @ SY6548 @ SV2106 ) @ SV2106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4348]) ).
thf(5145,plain,
! [SV1440: $i,SV601: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV601 @ SV1440 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1440 @ SV601 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4349]) ).
thf(5146,plain,
! [SV1441: $i,SV602: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV602 @ SV1441 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1441 @ SV602 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4350]) ).
thf(5147,plain,
! [SV1442: $i,SV603: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV603 @ SV1442 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV603 ) @ SV1442 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4351]) ).
thf(5148,plain,
! [SV1443: $i,SV604: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV604 @ ( c_Suc @ SV1443 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV604 @ SV1443 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4352]) ).
thf(5149,plain,
! [SV605: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV605 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV605 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV605 ) @ ( c_HOL_Ozero__class_Ozero @ SV605 ) @ SV605 ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV605 ) @ ( c_HOL_Ozero__class_Ozero @ SV605 ) @ SV605 ) )
= ( c_HOL_Ozero__class_Ozero @ SV605 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4353]) ).
thf(5150,plain,
! [SV2107: $i,SV1444: $i,SV606: $i] :
( ( ! [SY6549: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV606 )
| ( c_HOL_Oord__class_Oless @ SV1444 @ ( c_HOL_Ozero__class_Ozero @ SV606 ) @ SV606 )
| ( c_HOL_Oord__class_Oless @ SV2107 @ SY6549 @ SV606 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2107 @ SV1444 @ SV606 ) @ ( c_HOL_Otimes__class_Otimes @ SY6549 @ SV1444 @ SV606 ) @ SV606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4354]) ).
thf(5151,plain,
! [SV2108: $i,SV1445: $i,SV607: $i] :
( ( ! [SY6550: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV607 )
| ( c_HOL_Oord__class_Oless @ SV1445 @ SV2108 @ SV607 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV607 ) @ SY6550 @ SV607 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2108 @ SY6550 @ SV607 ) @ ( c_HOL_Otimes__class_Otimes @ SV1445 @ SY6550 @ SV607 ) @ SV607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4355]) ).
thf(5152,plain,
! [SV2109: $i,SV1446: $i,SV608: $i] :
( ( ! [SY6551: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV608 )
| ( c_HOL_Oord__class_Oless @ SV1446 @ ( c_HOL_Ozero__class_Ozero @ SV608 ) @ SV608 )
| ( c_HOL_Oord__class_Oless @ SV2109 @ SY6551 @ SV608 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2109 @ SV608 ) @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SY6551 @ SV608 ) @ SV608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4356]) ).
thf(5153,plain,
! [SV2110: $i,SV1447: $i,SV609: $i] :
( ( ! [SY6552: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV609 )
| ( c_HOL_Oord__class_Oless @ SV1447 @ SV2110 @ SV609 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV609 ) @ SY6552 @ SV609 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY6552 @ SV2110 @ SV609 ) @ ( c_HOL_Otimes__class_Otimes @ SY6552 @ SV1447 @ SV609 ) @ SV609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4357]) ).
thf(5154,plain,
! [SV2111: $i,SV1448: $i,SV610: $i] :
( ( ! [SY6553: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV610 ) @ SV1448 ) @ SV2111 @ SY6553 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV610 @ SV2111 @ SY6553 ) ) @ ( c_Lambda_Osubst @ SV1448 @ SV2111 @ SY6553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4358]) ).
thf(5155,plain,
! [SV611: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV611 @ tc_nat )
= $false )
| ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV611 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV611 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4359]) ).
thf(5156,plain,
! [SV2112: $i,SV1449: $i,SV612: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV612 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1449 ) @ SV2112 ) @ SV612 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV612 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1449 @ SV612 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV2112 @ SV612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4360]) ).
thf(5157,plain,
! [SV1450: $i,SV613: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV613 @ SV1450 @ tc_nat ) @ SV613 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV613 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1450 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4361]) ).
thf(5158,plain,
! [SV2113: $i,SV1451: $i,SV614: $i] :
( ( ! [SY6554: $i] :
( ~ ( class_Orderings_Olinorder @ SV614 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1451 @ ( c_Orderings_Oord__class_Omin @ SV2113 @ SY6554 @ SV614 ) @ SV614 ) @ ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1451 @ SV2113 @ SV614 ) @ ( c_Orderings_Oord__class_Omax @ SV1451 @ SY6554 @ SV614 ) @ SV614 ) @ SV614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4362]) ).
thf(5159,plain,
! [SV2114: $i,SV1452: $i,SV615: $i] :
( ( ! [SY6555: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV615 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV1452 @ SV2114 @ SV615 ) @ SY6555 @ SV615 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1452 @ SY6555 @ SV615 ) @ ( c_Power_Opower__class_Opower @ SV2114 @ SY6555 @ SV615 ) @ SV615 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4363]) ).
thf(5160,plain,
! [SV2115: $i,SV1453: $i,SV616: $i] :
( ( ! [SY6556: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV616 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV1453 @ SV2115 @ SV616 ) @ SY6556 @ SV616 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1453 @ SY6556 @ SV616 ) @ ( c_Power_Opower__class_Opower @ SV2115 @ SY6556 @ SV616 ) @ SV616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4364]) ).
thf(5161,plain,
! [SV2116: $i,SV1454: $i,SV617: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV617 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SV1454 @ SV2116 @ SV617 ) @ SV617 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ ( c_List_Olistsum @ SV1454 @ SV617 ) ) @ ( c_List_Olistsum @ SV2116 @ SV617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4365]) ).
thf(5162,plain,
! [SV1455: $i,SV618: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV618 ) @ ( c_HOL_Ominus__class_Ominus @ SV1455 @ SV618 @ tc_nat ) )
= SV1455 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1455 @ SV618 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4366]) ).
thf(5163,plain,
! [SV1456: $i,SV619: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV619 @ ( c_Suc @ SV1456 ) @ tc_nat ) @ SV619 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV619 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4367]) ).
thf(5164,plain,
! [SV2117: $i,SV1457: $i,SV620: $i] :
( ( ! [SY6557: $i] :
( ~ ( class_Orderings_Olinorder @ SV620 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV1457 @ SV2117 @ SV620 ) @ SY6557 @ SV620 )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1457 @ SY6557 @ SV620 ) @ ( c_Orderings_Oord__class_Omax @ SV2117 @ SY6557 @ SV620 ) @ SV620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4368]) ).
thf(5165,plain,
! [SV2118: $i,SV1458: $i,SV621: $i] :
( ( ! [SY6558: $i] :
( ~ ( class_Orderings_Olinorder @ SV621 )
| ( ( c_Orderings_Oord__class_Omax @ SV1458 @ ( c_Orderings_Oord__class_Omin @ SV2118 @ SY6558 @ SV621 ) @ SV621 )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1458 @ SV2118 @ SV621 ) @ ( c_Orderings_Oord__class_Omax @ SV1458 @ SY6558 @ SV621 ) @ SV621 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4369]) ).
thf(5166,plain,
! [SV2119: $i,SV1459: $i,SV622: $i] :
( ( ! [SY6559: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV622 )
| ( ( c_Power_Opower__class_Opower @ SV1459 @ ( c_HOL_Otimes__class_Otimes @ SV2119 @ SY6559 @ tc_nat ) @ SV622 )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV1459 @ SV2119 @ SV622 ) @ SY6559 @ SV622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4370]) ).
thf(5167,plain,
! [SV2120: $i,SV1460: $i,SV623: $i] :
( ( ~ ( class_Orderings_Oorder @ SV623 )
| ( c_HOL_Oord__class_Oless @ SV1460 @ SV2120 @ SV623 )
| ( SV2120 = SV1460 )
| ~ ( c_lessequals @ SV1460 @ SV2120 @ SV623 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4371]) ).
thf(5168,plain,
! [SV2121: $i,SV1461: $i,SV624: $i] :
( ( ~ ( class_Orderings_Oorder @ SV624 )
| ( c_HOL_Oord__class_Oless @ SV1461 @ SV2121 @ SV624 )
| ~ ( c_lessequals @ SV1461 @ SV2121 @ SV624 )
| ( SV2121 = SV1461 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4372]) ).
thf(5169,plain,
! [SV1462: $i,SV625: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV625 @ SV1462 @ tc_nat )
= $true )
| ( ( ( SV625 = SV1462 )
| ~ ( c_lessequals @ SV625 @ SV1462 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4373]) ).
thf(5170,plain,
! [SV1463: $i,SV626: $i] :
( ( ( SV626 = SV1463 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV626 @ SV1463 @ tc_nat )
| ~ ( c_lessequals @ SV626 @ SV1463 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4374]) ).
thf(5171,plain,
! [SV1464: $i,SV627: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV627 @ SV1464 @ tc_nat )
= $true )
| ( ( ( SV627 = SV1464 )
| ~ ( c_lessequals @ SV627 @ SV1464 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4375]) ).
thf(5172,plain,
! [SV2122: $i,SV1465: $i,SV628: $i] :
( ( ~ ( class_Orderings_Oorder @ SV628 )
| ( SV1465 = SV2122 )
| ( c_HOL_Oord__class_Oless @ SV1465 @ SV2122 @ SV628 )
| ~ ( c_lessequals @ SV1465 @ SV2122 @ SV628 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4376]) ).
thf(5173,plain,
! [SV2123: $i,SV1466: $i,SV629: $i] :
( ( ~ ( class_Orderings_Oorder @ SV629 )
| ( c_HOL_Oord__class_Oless @ SV1466 @ SV2123 @ SV629 )
| ( SV1466 = SV2123 )
| ~ ( c_lessequals @ SV1466 @ SV2123 @ SV629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4377]) ).
thf(5174,plain,
! [SV2124: $i,SV1467: $i,SV630: $i] :
( ( ~ ( class_Orderings_Oorder @ SV630 )
| ( c_HOL_Oord__class_Oless @ SV1467 @ SV2124 @ SV630 )
| ( SV1467 = SV2124 )
| ~ ( c_lessequals @ SV1467 @ SV2124 @ SV630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4378]) ).
thf(5175,plain,
! [SV2125: $i,SV1468: $i,SV631: $i] :
( ( ~ ( class_Orderings_Oorder @ SV631 )
| ( c_HOL_Oord__class_Oless @ SV1468 @ SV2125 @ SV631 )
| ~ ( c_lessequals @ SV1468 @ SV2125 @ SV631 )
| ( SV1468 = SV2125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4379]) ).
thf(5176,plain,
! [SV2126: $i,SV1469: $i,SV632: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV632 )
| ( SV1469 = SV2126 )
| ~ ( c_lessequals @ SV1469 @ SV2126 @ SV632 )
| ( c_HOL_Oord__class_Oless @ SV1469 @ SV2126 @ SV632 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4380]) ).
thf(5177,plain,
! [SV2127: $i,SV1470: $i,SV633: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV633 )
| ( SV1470 = SV2127 )
| ( c_HOL_Oord__class_Oless @ SV1470 @ SV2127 @ SV633 )
| ~ ( c_lessequals @ SV1470 @ SV2127 @ SV633 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4381]) ).
thf(5178,plain,
! [SV2128: $i,SV1471: $i,SV634: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV634 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ ( c_HOL_Otimes__class_Otimes @ SV1471 @ SV2128 @ SV634 ) @ SV634 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV2128 @ SV634 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV1471 @ SV634 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4382]) ).
thf(5179,plain,
! [SV2129: $i,SV1472: $i,SV635: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV635 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ ( c_HOL_Otimes__class_Otimes @ SV1472 @ SV2129 @ SV635 ) @ SV635 )
| ~ ( c_lessequals @ SV2129 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 )
| ~ ( c_lessequals @ SV1472 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4383]) ).
thf(5180,plain,
! [SV2130: $i,SV1473: $i,SV636: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV636 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ ( c_HOL_Otimes__class_Otimes @ SV1473 @ SV2130 @ SV636 ) @ SV636 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV2130 @ SV636 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV1473 @ SV636 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4384]) ).
thf(5181,plain,
! [SV1474: $i,SV637: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV637 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV637 ) @ ( c_HOL_Otimes__class_Otimes @ SV1474 @ SV1474 @ SV637 ) @ SV637 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4385]) ).
thf(5182,plain,
! [SV2131: $i,SV1475: $i,SV638: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV638 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ ( c_HOL_Otimes__class_Otimes @ SV1475 @ SV2131 @ SV638 ) @ SV638 )
| ~ ( c_lessequals @ SV2131 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 )
| ~ ( c_lessequals @ SV1475 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4386]) ).
thf(5183,plain,
! [SV2132: $i,SV1476: $i,SV639: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV639 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ ( c_HOL_Otimes__class_Otimes @ SV1476 @ SV2132 @ SV639 ) @ SV639 )
| ~ ( c_lessequals @ SV2132 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 )
| ~ ( c_lessequals @ SV1476 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4387]) ).
thf(5184,plain,
! [SV2133: $i,SV1477: $i,SV640: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV640 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ ( c_HOL_Otimes__class_Otimes @ SV1477 @ SV2133 @ SV640 ) @ SV640 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV2133 @ SV640 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV1477 @ SV640 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4388]) ).
thf(5185,plain,
! [SV1478: $i,SV642: $i] :
( ( ( c_lessequals @ SV642 @ SV1478 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV642 ) @ ( c_Suc @ SV1478 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4389]) ).
thf(5186,plain,
! [SV1479: $i,SV643: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV643 ) @ ( c_Suc @ SV1479 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV643 @ SV1479 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4390]) ).
thf(5187,plain,
! [SV2134: $i,SV1480: $i,SV644: $i] :
( ( ! [SY6560: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV644 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1480 @ SV2134 @ SV644 ) @ SY6560 @ SV644 )
= ( c_HOL_Otimes__class_Otimes @ SV1480 @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SY6560 @ SV644 ) @ SV644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4391]) ).
thf(5188,plain,
! [SV2135: $i,SV1481: $i,SV645: $i] :
( ( ! [SY6561: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV645 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1481 @ SV2135 @ SV645 ) @ SY6561 @ SV645 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1481 @ SY6561 @ SV645 ) @ SV2135 @ SV645 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4392]) ).
thf(5189,plain,
! [SV2136: $i,SV1482: $i,SV646: $i] :
( ( ! [SY6562: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV646 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1482 @ SV2136 @ SV646 ) @ SY6562 @ SV646 )
= ( c_HOL_Otimes__class_Otimes @ SV1482 @ ( c_HOL_Otimes__class_Otimes @ SV2136 @ SY6562 @ SV646 ) @ SV646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4393]) ).
thf(5190,plain,
! [SV2137: $i,SV1483: $i,SV647: $i] :
( ( ! [SY6563: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV647 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1483 @ ( c_HOL_Otimes__class_Otimes @ SV2137 @ SY6563 @ SV647 ) @ SV647 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1483 @ SV2137 @ SV647 ) @ SY6563 @ SV647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4394]) ).
thf(5191,plain,
! [SV2138: $i,SV1484: $i,SV648: $i] :
( ( ! [SY6564: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV648 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1484 @ ( c_HOL_Otimes__class_Otimes @ SV2138 @ SY6564 @ SV648 ) @ SV648 )
= ( c_HOL_Otimes__class_Otimes @ SV2138 @ ( c_HOL_Otimes__class_Otimes @ SV1484 @ SY6564 @ SV648 ) @ SV648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4395]) ).
thf(5192,plain,
! [SV2139: $i,SV1485: $i,SV649: $i] :
( ( ! [SY6565: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV649 @ SV1485 @ SV2139 ) @ SY6565 @ SV2139 )
= ( c_List_Oappend @ SV649 @ ( c_List_Oappend @ SV1485 @ SY6565 @ SV2139 ) @ SV2139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4396]) ).
thf(5193,plain,
! [SV2140: $i,SV1486: $i,SV650: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV650 @ SV1486 @ tc_nat ) @ SV2140 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV650 @ ( c_HOL_Otimes__class_Otimes @ SV1486 @ SV2140 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4397]) ).
thf(5194,plain,
! [SV2141: $i,SV1487: $i,SV651: $i] :
( ( ! [SY6566: $i] :
( ( c_List_Oappend @ SV651 @ ( c_List_Oappend @ SV1487 @ SV2141 @ SY6566 ) @ SY6566 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV651 @ SV1487 @ SY6566 ) @ SV2141 @ SY6566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4398]) ).
thf(5195,plain,
! [SV2142: $i,SV1488: $i,SV652: $i] :
( ( ! [SY6567: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV652 @ SV1488 @ SV2142 ) @ SY6567 @ SV2142 )
= ( c_List_Oappend @ SV652 @ ( c_List_Oappend @ SV1488 @ SY6567 @ SV2142 ) @ SV2142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4399]) ).
thf(5196,plain,
! [SV2143: $i,SV1489: $i,SV653: $i] :
( ( ! [SY6568: $i] :
( ( c_List_Oappend @ SV653 @ ( c_List_Oappend @ SV1489 @ SV2143 @ SY6568 ) @ SY6568 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV653 @ SV1489 @ SY6568 ) @ SV2143 @ SY6568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4400]) ).
thf(5197,plain,
! [SV2144: $i,SV1490: $i,SV654: $i] :
( ( ! [SY6569: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV654 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1490 @ ( c_HOL_Otimes__class_Otimes @ SV2144 @ SY6569 @ SV654 ) @ SV654 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1490 @ SV2144 @ SV654 ) @ SY6569 @ SV654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4401]) ).
thf(5198,plain,
! [SV2145: $i,SV1491: $i,SV655: $i] :
( ( ! [SY6570: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV655 )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV655 ) @ SV1491 ) @ SV2145 ) @ SY6570 @ SV655 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV655 ) @ ( c_HOL_Otimes__class_Otimes @ SV1491 @ SY6570 @ SV655 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SY6570 @ SV655 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4402]) ).
thf(5199,plain,
! [SV2146: $i,SV1492: $i,SV656: $i] :
( ( ! [SY6571: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV656 )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV656 ) @ SV1492 ) @ SV2146 ) @ SY6571 @ SV656 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV656 ) @ ( c_HOL_Otimes__class_Otimes @ SV1492 @ SY6571 @ SV656 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2146 @ SY6571 @ SV656 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4403]) ).
thf(5200,plain,
! [SV2147: $i,SV1493: $i,SV657: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV657 ) @ SV1493 ) @ SV2147 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV657 @ SV2147 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1493 @ SV2147 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4404]) ).
thf(5201,plain,
! [SV2148: $i,SV1494: $i,SV658: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1494 ) @ SV2148 ) @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV658 @ SV1494 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV658 @ SV2148 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4405]) ).
thf(5202,plain,
! [SV2149: $i,SV1495: $i,SV659: $i] :
( ( ! [SY6572: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV659 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1495 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV659 ) @ SV2149 ) @ SY6572 ) @ SV659 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV659 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV2149 @ SV659 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SY6572 @ SV659 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4406]) ).
thf(5203,plain,
! [SV2150: $i,SV1496: $i,SV660: $i] :
( ( ~ ( class_Orderings_Oorder @ SV660 )
| ~ ( c_HOL_Oord__class_Oless @ SV1496 @ SV2150 @ SV660 )
| ~ ( c_HOL_Oord__class_Oless @ SV2150 @ SV1496 @ SV660 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4407]) ).
thf(5204,plain,
! [SV2151: $i,SV1497: $i,SV661: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV661 )
| ~ ( c_HOL_Oord__class_Oless @ SV1497 @ SV2151 @ SV661 )
| ~ ( c_HOL_Oord__class_Oless @ SV2151 @ SV1497 @ SV661 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4408]) ).
thf(5205,plain,
! [SV1498: $i,SV662: $i] :
( ( ( c_lessequals @ SV662 @ SV1498 @ tc_nat )
= $true )
| ( ( c_lessequals @ SV1498 @ SV662 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4409]) ).
thf(5206,plain,
! [SV2152: $i,SV1499: $i,SV663: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV663 )
| ( c_lessequals @ SV1499 @ SV2152 @ SV663 )
| ( c_lessequals @ SV2152 @ SV1499 @ SV663 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4410]) ).
thf(5207,plain,
! [SV2153: $i,SV1500: $i,SV664: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV664 )
| ~ ( c_HOL_Oord__class_Oless @ SV1500 @ SV2153 @ SV664 )
| ~ ( c_HOL_Oord__class_Oless @ SV2153 @ SV1500 @ SV664 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4411]) ).
thf(5208,plain,
! [SV2154: $i,SV1501: $i,SV665: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV665 )
| ~ ( c_HOL_Oord__class_Oless @ SV1501 @ SV2154 @ SV665 )
| ~ ( c_HOL_Oord__class_Oless @ SV2154 @ SV1501 @ SV665 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4412]) ).
thf(5209,plain,
! [SV2155: $i,SV1502: $i,SV666: $i] :
( ( ( c_Nat_Onat_Onat__rec @ SV666 @ SV1502 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2155 )
= SV666 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4413]) ).
thf(5210,plain,
! [SV1503: $i,SV667: $i] :
( ( ( hBOOL @ ( hAPP @ SV667 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV667 @ SV1503 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV667 @ SV1503 ) )
| ( hBOOL @ ( hAPP @ SV667 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4414]) ).
thf(5211,plain,
! [SV668: $i] :
( ( ( c_lessequals @ SV668 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false )
| ( ( SV668
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4415]) ).
thf(5212,plain,
! [SV1504: $i,SV669: $i] :
( ( ( hBOOL @ ( hAPP @ SV669 @ SV1504 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV669 @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ SV669 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV669 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4416]) ).
thf(5213,plain,
! [SV2156: $i,SV1505: $i,SV672: $i] :
( ( ( c_Nat_Onat_Onat__case @ SV672 @ SV1505 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2156 )
= SV672 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4417]) ).
thf(5214,plain,
! [SV2157: $i,SV1506: $i,SV673: $i] :
( ( ( c_Nat_Onat_Onat__case @ SV673 @ SV1506 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2157 )
= SV673 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4418]) ).
thf(5215,plain,
! [SV1507: $i,SV678: $i] :
( ( ( hBOOL @ ( hAPP @ SV678 @ SV1507 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV678 @ ( v_sko__List__Xreplicate__Xinduct__1 @ SV678 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV678 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4419]) ).
thf(5216,plain,
! [SV2158: $i,SV1508: $i,SV679: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV679 @ ( c_Nat_Onat_Onat__case @ SV1508 @ SV2158 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV679 @ SV1508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4420]) ).
thf(5217,plain,
! [SV1509: $i,SV680: $i] :
( ( ( hBOOL @ ( hAPP @ SV680 @ SV1509 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV680 @ ( v_sko__Nat__Xnat__Xinducts__1 @ SV680 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV680 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4421]) ).
thf(5218,plain,
! [SV1510: $i,SV683: $i] :
( ( ( hBOOL @ ( hAPP @ SV683 @ SV1510 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV683 @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV683 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV683 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4422]) ).
thf(5219,plain,
! [SV1511: $i,SV686: $i] :
( ( ( hBOOL @ ( hAPP @ SV686 @ SV1511 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV686 @ ( v_sko__List__Xupt__Xinduct__1 @ SV686 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV686 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4425]) ).
thf(5220,plain,
! [SV1513: $i,SV689: $i] :
( ( ( hBOOL @ ( hAPP @ SV689 @ SV1513 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV689 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV689 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV689 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4427]) ).
thf(5221,plain,
! [SV2159: $i,SV1514: $i,SV692: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV692 @ SV1514 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2159 @ SV1514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4428]) ).
thf(5222,plain,
! [SV2160: $i,SV1515: $i,SV698: $i] :
( ( ! [SY6573: $i,SY6574: $i,SY6575: $i,SY6576: $i] :
( ( ( hAPP @ ( hAPP @ SV698 @ SV1515 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV2160 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6573 @ SY6574 @ SV698 @ SY6575 @ SV2160 @ SY6576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4429]) ).
thf(5223,plain,
! [SV1516: $i,SV699: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV699 ) )
= $true )
| ( ( ( c_List_Olistsum @ SV1516 @ SV699 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV699 ) @ SV1516 @ ( c_HOL_Ozero__class_Ozero @ SV699 ) @ SV699 @ SV699 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4430]) ).
thf(5224,plain,
! [SV1517: $i,SV700: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV700 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV700 ) @ ( c_HOL_Ozero__class_Ozero @ SV700 ) @ SV1517 @ SV700 @ SV700 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV700 ) @ SV1517 @ ( c_HOL_Ozero__class_Ozero @ SV700 ) @ SV700 @ SV700 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4431]) ).
thf(5225,plain,
! [SV2161: $i,SV1518: $i,SV701: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV701 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SV1518 @ SV2161 @ SV701 @ SV701 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SV1518 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SV2161 @ ( c_HOL_Ozero__class_Ozero @ SV701 ) @ SV701 @ SV701 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4432]) ).
thf(5226,plain,
! [SV2162: $i,SV1519: $i,SV702: $i] :
( ( ! [SY6577: $i] :
( ( c_Type_Otyping @ SV702 @ SV1519 @ SV2162 )
| ~ ( c_Lambda_Obeta @ SY6577 @ SV1519 )
| ~ ( c_Type_Otyping @ SV702 @ SY6577 @ SV2162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4433]) ).
thf(5227,plain,
! [SV2163: $i,SV1520: $i,SV703: $i] :
( ( ( ( hAPP @ SV703 @ SV1520 )
= SV2163 )
| ~ ( c_Type_Otyping @ SV703 @ ( c_Lambda_OdB_OVar @ SV1520 ) @ SV2163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4434]) ).
thf(5228,plain,
! [SV2164: $i,SV1522: $i,SV705: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV705 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV705 @ SV1522 ) @ tc_Type_Otype ) @ SV1522 @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV705 @ SV1522 ) )
| ~ ( c_Type_Otyping @ SV705 @ ( c_Lambda_OdB_OAbs @ SV1522 ) @ SV2164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4436]) ).
thf(5229,plain,
! [SV2165: $i,SV1523: $i,SV706: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV706 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV1523 @ SV706 @ SV2165 ) @ tc_Type_Otype ) @ SV2165 @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV1523 @ SV706 @ SV2165 ) )
| ~ ( c_Type_Otyping @ SV706 @ ( c_Lambda_OdB_OAbs @ SV2165 ) @ SV1523 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4437]) ).
thf(5230,plain,
! [SV2166: $i,SV1524: $i,SV707: $i] :
( ( ! [SY6578: $i] :
( ( c_Type_Otyping @ SV707 @ SV1524 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV2166 @ SV707 @ SV1524 @ SY6578 ) ) @ SV2166 ) )
| ~ ( c_Type_Otyping @ SV707 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1524 ) @ SY6578 ) @ SV2166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4438]) ).
thf(5231,plain,
! [SV2167: $i,SV1525: $i,SV708: $i] :
( ( ! [SY6579: $i,SY6580: $i] :
( ( c_Type_Otype_Otype__rec @ SV708 @ SV1525 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2167 ) @ SY6579 ) @ SY6580 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV1525 @ SV2167 ) @ SY6579 ) @ ( c_Type_Otype_Otype__rec @ SV708 @ SV1525 @ SV2167 @ SY6580 ) ) @ ( c_Type_Otype_Otype__rec @ SV708 @ SV1525 @ SY6579 @ SY6580 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4439]) ).
thf(5232,plain,
! [SV2168: $i,SV1526: $i,SV709: $i] :
( ( ! [SY6581: $i,SY6582: $i] :
( ( c_Type_Otype_Otype__case @ SV709 @ SV1526 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2168 ) @ SY6581 ) @ SY6582 )
= ( hAPP @ ( hAPP @ SV1526 @ SV2168 ) @ SY6581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4440]) ).
thf(5233,plain,
! [SV2169: $i,SV1527: $i,SV710: $i] :
( ( ! [SY6583: $i,SY6584: $i] :
( ~ ( hBOOL @ ( hAPP @ SV710 @ ( c_Type_Otype_Otype__case @ SV1527 @ SV2169 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY6583 ) @ SY6584 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV710 @ ( hAPP @ ( hAPP @ SV2169 @ SY6583 ) @ SY6584 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4441]) ).
thf(5234,plain,
! [SV2170: $i,SV1528: $i,SV711: $i] :
( ( ! [SY6585: $i,SY6586: $i] :
( ~ ( hBOOL @ ( hAPP @ SV711 @ ( c_Type_Otype_Otype__case @ SV1528 @ SV2170 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY6585 ) @ SY6586 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV711 @ ( hAPP @ ( hAPP @ SV2170 @ SY6585 ) @ SY6586 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4442]) ).
thf(5235,plain,
! [SV2171: $i,SV1529: $i,SV712: $i] :
( ( ! [SY6587: $i,SY6588: $i,SY6589: $i] :
( ( c_List_Ofoldr @ SV712 @ ( c_List_Olist_OCons @ SV1529 @ SV2171 @ SY6587 ) @ SY6588 @ SY6587 @ SY6589 )
= ( hAPP @ ( hAPP @ SV712 @ SV1529 ) @ ( c_List_Ofoldr @ SV712 @ SV2171 @ SY6588 @ SY6587 @ SY6589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4443]) ).
thf(5236,plain,
! [SV2172: $i,SV1530: $i,SV713: $i] :
( ( ! [SY6590: $i,SY6591: $i,SY6592: $i] :
( ( c_List_Ofoldr @ SV713 @ ( c_List_Oappend @ SV1530 @ SV2172 @ SY6590 ) @ SY6591 @ SY6590 @ SY6592 )
= ( c_List_Ofoldr @ SV713 @ SV1530 @ ( c_List_Ofoldr @ SV713 @ SV2172 @ SY6591 @ SY6590 @ SY6592 ) @ SY6590 @ SY6592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4444]) ).
thf(5237,plain,
! [SV2173: $i,SV1531: $i,SV714: $i] :
( ( ! [SY6593: $i] :
( ( c_List_Ofoldr @ SV714 @ ( c_List_Olist_ONil @ SV1531 ) @ SV2173 @ SV1531 @ SY6593 )
= SV2173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4445]) ).
thf(5238,plain,
! [SV1532: $i,SV715: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ SV715 @ SV1532 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV715 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4446]) ).
thf(5239,plain,
! [SV2174: $i,SV1533: $i,SV716: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV716 ) @ SV1533 ) @ SV2174 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV716 @ SV2174 ) ) @ ( c_Lambda_Olift @ SV1533 @ SV2174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4447]) ).
thf(5240,plain,
! [SV2175: $i,SV1534: $i,SV717: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV717 @ SV1534 ) @ SV2175 @ SV1534 )
= SV717 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4448]) ).
thf(5241,plain,
! [SV2176: $i,SV1535: $i,SV718: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV718 @ SV1535 ) @ ( c_Lambda_Olift @ SV2176 @ SV1535 ) )
| ~ ( c_Lambda_Obeta @ SV718 @ SV2176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4449]) ).
thf(5242,plain,
! [SV2177: $i,SV1536: $i,SV719: $i] :
( ( ! [SY6594: $i,SY6595: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV719 @ SV1536 @ SV2177 @ SY6594 ) @ SY6595 )
= ( hAPP @ SV719 @ SY6595 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY6595 @ SV1536 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4450]) ).
thf(5243,plain,
! [SV2178: $i,SV1537: $i,SV720: $i] :
( ( ! [SY6596: $i] :
( ( c_Type_Otyping @ SV720 @ SV1537 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV2178 @ SV720 @ SV1537 @ SY6596 ) @ SV2178 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV720 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1537 @ SY6596 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4451]) ).
thf(5244,plain,
! [SV2179: $i,SV1538: $i,SV721: $i] :
( ( ! [SY6597: $i,SY6598: $i] :
( ( c_Type_Otyping @ SV721 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1538 @ SV2179 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY6597 )
| ~ ( c_Type_Otypings @ SV721 @ SV2179 @ SY6598 )
| ~ ( c_Type_Otyping @ SV721 @ SV1538 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY6598 @ SY6597 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4452]) ).
thf(5245,plain,
! [SV2180: $i,SV1539: $i,SV722: $i] :
( ( ! [SY6599: $i] :
( ( c_Type_Otyping @ SV722 @ SV1539 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV2180 @ SV722 @ SV1539 @ SY6599 ) @ SV2180 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV722 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1539 @ SY6599 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4453]) ).
thf(5246,plain,
! [SV1540: $i,SV723: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV723 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV723 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV723 )
| ~ ( class_Power_Opower @ SV723 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV723 ) @ SV1540 @ SV723 )
= ( c_HOL_Ozero__class_Ozero @ SV723 ) )
| ( SV1540
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4454]) ).
thf(5247,plain,
! [SV1541: $i,SV724: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV724 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV724 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV724 ) @ SV1541 @ SV724 )
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1541
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4455]) ).
thf(5248,plain,
! [SV725: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV725 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV725 )
= ( c_HOL_Ozero__class_Ozero @ SV725 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4456]) ).
thf(5249,plain,
! [SV2181: $i,SV1542: $i,SV726: $i] :
( ( ! [SY6600: $i,SY6601: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ SV726 @ SV1542 @ SV2181 @ SY6600 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY6601 @ SY6600 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV726 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY6601 @ SY6600 ) @ ( c_Suc @ SV1542 ) @ SV2181 @ SY6600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4457]) ).
thf(5250,plain,
! [SV2182: $i,SV1543: $i,SV727: $i] :
( ( ! [SY6602: $i,SY6603: $i] :
( ( c_Type_Otyping @ SV727 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1543 ) @ SV2182 ) @ SY6602 )
| ~ ( c_Type_Otyping @ SV727 @ SV2182 @ SY6603 )
| ~ ( c_Type_Otyping @ SV727 @ SV1543 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY6603 ) @ SY6602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4458]) ).
thf(5251,plain,
! [SV2183: $i,SV1544: $i,SV728: $i] :
( ( ! [SY6604: $i,SY6605: $i,SY6606: $i] :
( ~ ( c_Type_Otyping @ SV728 @ SV1544 @ SV2183 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV728 @ SY6604 @ SV2183 @ tc_Type_Otype ) @ SY6605 @ SY6606 )
| ( c_Type_Otyping @ SV728 @ ( c_Lambda_Osubst @ SY6605 @ SV1544 @ SY6604 ) @ SY6606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4459]) ).
thf(5252,plain,
! [SV2184: $i,SV1545: $i,SV729: $i] :
( ( ! [SY6607: $i] :
( ( c_Type_Otyping @ SV729 @ ( c_Lambda_OdB_OAbs @ SV1545 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2184 ) @ SY6607 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV729 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2184 @ tc_Type_Otype ) @ SV1545 @ SY6607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4460]) ).
thf(5253,plain,
! [SV2185: $i,SV1546: $i,SV730: $i] :
( ( ! [SY6608: $i,SY6609: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV730 @ SV1546 @ SV2185 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY6608 @ SV1546 ) @ SY6609 )
| ~ ( c_Type_Otyping @ SV730 @ SY6608 @ SY6609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4461]) ).
thf(5254,plain,
! [SV2186: $i,SV1547: $i,SV731: $i] :
( ( ! [SY6610: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV731 @ SV1547 @ SV2186 @ SY6610 ) @ SV1547 )
= SV2186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4462]) ).
thf(5255,plain,
! [SV1548: $i,SV732: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV732 @ SV1548 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV1548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4463]) ).
thf(5256,plain,
! [SV1549: $i,SV733: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV733 @ SV1549 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV1549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4464]) ).
thf(5257,plain,
! [SV1550: $i,SV734: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV734 @ SV1550 ) )
= $true )
| ( ( ~ ( class_Orderings_Obot @ SV1550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4465]) ).
thf(5258,plain,
! [SV2187: $i,SV1552: $i,SV736: $i] :
( ( ( SV736 = SV1552 )
| ~ ( c_fequal @ SV736 @ SV1552 @ SV2187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4467]) ).
thf(5259,plain,
! [SV2188: $i,SV1553: $i,SV737: $i] :
( ( ! [SY6611: $i,SY6612: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV737 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1553 @ SV2188 @ SV737 )
!= ( c_HOL_Ominus__class_Ominus @ SY6611 @ SY6612 @ SV737 ) )
| ( c_lessequals @ SV2188 @ SV1553 @ SV737 )
| ~ ( c_lessequals @ SY6612 @ SY6611 @ SV737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4468]) ).
thf(5260,plain,
! [SV2189: $i,SV1554: $i,SV738: $i] :
( ( ! [SY6613: $i,SY6614: $i] :
( ( ( c_List_Olist_OCons @ SV738 @ SV1554 @ SV2189 )
!= ( c_List_Olist_OCons @ SY6613 @ SY6614 @ SV2189 ) )
| ( SV738 = SY6613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4469]) ).
thf(5261,plain,
! [SV2190: $i,SV1555: $i,SV739: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV739 @ SV1555 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV739 @ SV2190 @ tc_nat ) )
| ( SV1555 = SV2190 )
| ( SV739
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4470]) ).
thf(5262,plain,
! [SV2191: $i,SV1556: $i,SV740: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV740 ) @ SV1556 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV740 ) @ SV2191 ) )
| ( SV1556 = SV2191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4471]) ).
thf(5263,plain,
! [SV2192: $i,SV1557: $i,SV741: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV741 ) @ SV1557 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV741 ) @ SV2192 ) )
| ( SV1557 = SV2192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4472]) ).
thf(5264,plain,
! [SV2193: $i,SV1558: $i,SV742: $i] :
( ( ! [SY6615: $i,SY6616: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV1558 @ tc_nat ) ) @ SV2193 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY6615 @ SV1558 @ tc_nat ) ) @ SY6616 ) )
| ~ ( c_lessequals @ SY6615 @ SV742 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV742 @ SY6615 @ tc_nat ) @ SV1558 @ tc_nat ) ) @ SV2193 )
= SY6616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4473]) ).
thf(5265,plain,
! [SV2194: $i,SV1559: $i,SV743: $i] :
( ( ( ( c_List_Oappend @ SV743 @ SV1559 @ SV2194 )
!= SV743 )
| ( SV1559
= ( c_List_Olist_ONil @ SV2194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4474]) ).
thf(5266,plain,
! [SV2195: $i,SV1560: $i,SV744: $i] :
( ( ! [SY6617: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV744 ) @ SV1560 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV2195 ) @ SY6617 ) )
| ( SV744 = SV2195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4475]) ).
thf(5267,plain,
! [SV2196: $i,SV1561: $i,SV745: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1561 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV2196 @ SV1561 @ tc_nat ) )
| ( SV1561
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV745 = SV2196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4476]) ).
thf(5268,plain,
! [SV1562: $i,SV746: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV746 )
!= ( c_Lambda_OdB_OAbs @ SV1562 ) )
= $true )
| ( ( SV746 = SV1562 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4477]) ).
thf(5269,plain,
! [SV2197: $i,SV1563: $i,SV747: $i] :
( ( ! [SY6618: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV747 ) @ SV1563 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV2197 ) @ SY6618 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1563 = SY6618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4478]) ).
thf(5270,plain,
! [SV2198: $i,SV1564: $i,SV748: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV748 ) @ SV1564 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV748 ) @ SV2198 @ tc_nat ) )
| ( SV1564 = SV2198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4479]) ).
thf(5271,plain,
! [SV1565: $i,SV749: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV749 ) @ SV1565 ) )
= $true )
| ( ( ( SV1565
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1565
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4480]) ).
thf(5272,plain,
! [SV2199: $i,SV1566: $i,SV750: $i] :
( ( ! [SY6619: $i,SY6620: $i,SY6621: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV750 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV1566 @ SV2199 @ SV750 ) ) @ SY6619 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SY6620 @ SV2199 @ SV750 ) ) @ SY6621 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ SY6620 @ SV750 ) @ SV2199 @ SV750 ) ) @ SY6619 )
= SY6621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4481]) ).
thf(5273,plain,
! [SV2200: $i,SV1567: $i,SV751: $i] :
( ( ! [SY6622: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV751 ) ) @ SV1567 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2200 ) @ SY6622 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4482]) ).
thf(5274,plain,
! [SV1568: $i,SV752: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV752 ) @ SV1568 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1568
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4483]) ).
thf(5275,plain,
! [SV1569: $i,SV753: $i] :
( ( ( SV753
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV753 ) @ SV1569 ) )
= $true )
| ( ( SV1569
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4484]) ).
thf(5276,plain,
! [SV2201: $i,SV1570: $i,SV754: $i] :
( ( ! [SY6623: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV754 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SV1570 ) @ SV2201 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SY6623 ) @ SV2201 ) )
| ( SV1570 = SY6623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4485]) ).
thf(5277,plain,
! [SV2202: $i,SV1571: $i,SV755: $i] :
( ( ( ( c_List_Olist_ONil @ SV755 )
!= ( c_List_Oappend @ SV1571 @ SV2202 @ SV755 ) )
| ( SV2202
= ( c_List_Olist_ONil @ SV755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4486]) ).
thf(5278,plain,
! [SV1572: $i,SV756: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV756 ) @ SV1572 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV1572
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1572
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4487]) ).
thf(5279,plain,
! [SV1573: $i,SV757: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV757 ) @ SV1573 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV757
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1573
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4488]) ).
thf(5280,plain,
! [SV2203: $i,SV1574: $i,SV758: $i] :
( ( ! [SY6624: $i] :
( ( ( c_List_Oappend @ SV758 @ SV1574 @ SV2203 )
!= ( c_List_Oappend @ SY6624 @ SV1574 @ SV2203 ) )
| ( SV758 = SY6624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4489]) ).
thf(5281,plain,
! [SV2204: $i,SV1575: $i,SV759: $i] :
( ( ! [SY6625: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1575 ) @ SV2204 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SY6625 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SV2204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4490]) ).
thf(5282,plain,
! [SV2205: $i,SV1576: $i,SV760: $i] :
( ( ! [SY6626: $i,SY6627: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV760 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV2205 @ SV760 )
!= ( c_HOL_Ominus__class_Ominus @ SY6626 @ SY6627 @ SV760 ) )
| ( c_HOL_Oord__class_Oless @ SY6626 @ SY6627 @ SV760 )
| ~ ( c_HOL_Oord__class_Oless @ SV1576 @ SV2205 @ SV760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4491]) ).
thf(5283,plain,
! [SV2206: $i,SV1577: $i,SV761: $i] :
( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV761 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1577 @ SV2206 @ SV761 )
!= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
| ( SV1577
= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
| ( SV2206
= ( c_HOL_Ozero__class_Ozero @ SV761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4492]) ).
thf(5284,plain,
! [SV2207: $i,SV1578: $i,SV762: $i] :
( ( SV762
!= ( c_List_Olist_OCons @ SV1578 @ SV762 @ SV2207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4493]) ).
thf(5285,plain,
! [SV2208: $i,SV1579: $i,SV763: $i] :
( ( ! [SY6628: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV763 )
| ( ( c_Power_Opower__class_Opower @ SV1579 @ SV2208 @ SV763 )
!= ( c_Power_Opower__class_Opower @ SY6628 @ SV2208 @ SV763 ) )
| ( SV1579 = SY6628 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2208 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SY6628 @ SV763 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4494]) ).
thf(5286,plain,
! [SV2209: $i,SV1580: $i,SV764: $i] :
( ( ! [SY6629: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV764 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SV2209 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SY6629 ) )
| ( SV2209 = SY6629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4495]) ).
thf(5287,plain,
! [SV1581: $i,SV765: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV765 ) @ SV1581 ) )
= $true )
| ( ( ( SV765
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV765
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4496]) ).
thf(5288,plain,
! [SV2210: $i,SV1582: $i,SV766: $i] :
( ( ! [SY6630: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV766 ) @ SV1582 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2210 ) @ SY6630 ) )
| ( SV1582 = SY6630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4497]) ).
thf(5289,plain,
! [SV1583: $i,SV768: $i] :
( ( ( c_Lambda_OdB_OVar @ SV768 )
= ( c_Lambda_OdB_OAbs @ SV1583 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4499]) ).
thf(5290,plain,
! [SV2211: $i,SV1584: $i,SV769: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV769 ) @ SV1584 )
!= ( c_Lambda_OdB_OAbs @ SV2211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4500]) ).
thf(5291,plain,
! [SV1585: $i,SV770: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV770 @ SV1585 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV770
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4501]) ).
thf(5292,plain,
! [SV2212: $i,SV1586: $i,SV771: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV771 ) @ SV1586 )
!= ( c_Type_Otype_OAtom @ SV2212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4502]) ).
thf(5293,plain,
! [SV2213: $i,SV1587: $i,SV772: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV772 @ SV1587 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV2213 @ SV1587 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV772 = SV2213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4503]) ).
thf(5294,plain,
! [SV2214: $i,SV1588: $i,SV773: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV773 )
| ~ ( class_Int_Onumber__ring @ SV773 )
| ( SV1588
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV773 ) @ SV1588 ) @ SV2214 ) )
| ( SV2214
= ( c_HOL_Ozero__class_Ozero @ SV773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4504]) ).
thf(5295,plain,
! [SV2215: $i,SV1589: $i,SV774: $i] :
( ( ! [SY6631: $i,SY6632: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV774 )
| ~ ( class_Int_Onumber__ring @ SV774 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SY6631 @ SV774 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SY6632 @ SV774 ) ) )
| ( SY6631 = SY6632 )
| ( SV2215
= ( c_HOL_Ozero__class_Ozero @ SV774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4505]) ).
thf(5296,plain,
! [SV2216: $i,SV1590: $i,SV775: $i] :
( ( ! [SY6633: $i,SY6634: $i] :
( ( ( c_List_Oreplicate @ SV775 @ SV1590 @ SV2216 )
!= ( c_List_Oreplicate @ SY6633 @ SY6634 @ SV2216 ) )
| ( SV775 = SY6633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4506]) ).
thf(5297,plain,
! [SV1591: $i,SV776: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV776 ) @ SV1591 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV1591
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV776
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4507]) ).
thf(5298,plain,
! [SV2217: $i,SV1592: $i,SV778: $i] :
( ( ! [SY6635: $i,SY6636: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV778 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1592 @ SV2217 @ SV778 )
!= ( c_HOL_Ominus__class_Ominus @ SY6635 @ SY6636 @ SV778 ) )
| ( c_HOL_Oord__class_Oless @ SV1592 @ SV2217 @ SV778 )
| ~ ( c_HOL_Oord__class_Oless @ SY6635 @ SY6636 @ SV778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4509]) ).
thf(5299,plain,
! [SV2218: $i,SV1593: $i,SV779: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV779 )
| ( ( c_Orderings_Oord__class_Omax @ SV1593 @ SV2218 @ SV779 )
!= SV2218 )
| ( c_lessequals @ SV1593 @ SV2218 @ SV779 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4510]) ).
thf(5300,plain,
! [SV2219: $i,SV1594: $i,SV780: $i] :
( ( ! [SY6637: $i,SY6638: $i] :
( ( ( c_List_Oappend @ SV780 @ ( c_List_Olist_OCons @ SV1594 @ ( c_List_Olist_ONil @ SV2219 ) @ SV2219 ) @ SV2219 )
!= ( c_List_Oappend @ SY6637 @ ( c_List_Olist_OCons @ SY6638 @ ( c_List_Olist_ONil @ SV2219 ) @ SV2219 ) @ SV2219 ) )
| ( SV1594 = SY6638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4511]) ).
thf(5301,plain,
! [SV1595: $i,SV781: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV781 ) @ SV1595 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV781
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4512]) ).
thf(5302,plain,
! [SV2220: $i,SV1596: $i,SV782: $i] :
( ( ! [SY6639: $i] :
( ( ( c_List_Oappend @ SV782 @ SV1596 @ SV2220 )
!= ( c_List_Oappend @ SV782 @ SY6639 @ SV2220 ) )
| ( SV1596 = SY6639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4513]) ).
thf(5303,plain,
! [SV2221: $i,SV1597: $i,SV783: $i] :
( ( ( c_Type_Otype_OAtom @ SV783 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1597 ) @ SV2221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4514]) ).
thf(5304,plain,
! [SV2222: $i,SV1598: $i,SV784: $i] :
( ( ! [SY6640: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SV1598 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2222 @ SY6640 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SY6640 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2222 @ SV1598 @ tc_nat ) ) )
| ( SV1598 = SY6640 )
| ( SV784 = SV2222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4515]) ).
thf(5305,plain,
! [SV2223: $i,SV1599: $i,SV786: $i] :
( ( ( ( c_List_Olist_ONil @ SV786 )
!= ( c_List_Oreplicate @ SV1599 @ SV2223 @ SV786 ) )
| ( SV1599
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4517]) ).
thf(5306,plain,
! [SV2224: $i,SV1600: $i,SV787: $i] :
( ( ! [SY6641: $i,SY6642: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV787 )
| ~ ( class_Int_Onumber__ring @ SV787 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2224 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY6641 @ SY6642 @ SV787 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SY6642 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY6641 @ SV2224 @ SV787 ) ) )
| ( SV2224 = SY6642 )
| ( SV1600 = SY6641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4518]) ).
thf(5307,plain,
! [SV1601: $i,SV788: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV788 @ SV1601 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV1601
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4519]) ).
thf(5308,plain,
! [SV2225: $i,SV1602: $i,SV789: $i] :
( ( ! [SY6643: $i,SY6644: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV789 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1602 @ SV2225 @ SV789 )
!= ( c_HOL_Ominus__class_Ominus @ SY6643 @ SY6644 @ SV789 ) )
| ( c_lessequals @ SY6644 @ SY6643 @ SV789 )
| ~ ( c_lessequals @ SV2225 @ SV1602 @ SV789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4520]) ).
thf(5309,plain,
! [SV2226: $i,SV1603: $i,SV790: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV790 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1603 @ SV2226 @ SV790 )
!= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
| ( SV2226
= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
| ( SV1603
= ( c_HOL_Ozero__class_Ozero @ SV790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4521]) ).
thf(5310,plain,
! [SV1604: $i,SV791: $i] :
( ( ( ( c_Suc @ SV791 )
!= ( c_Suc @ SV1604 ) )
= $true )
| ( ( SV791 = SV1604 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4522]) ).
thf(5311,plain,
! [SV1605: $i,SV792: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV792 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV792 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV792 )
| ~ ( class_Power_Opower @ SV792 )
| ( ( c_Power_Opower__class_Opower @ SV1605 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV792 )
!= ( c_HOL_Ozero__class_Ozero @ SV792 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4523]) ).
thf(5312,plain,
! [SV2227: $i,SV1606: $i,SV793: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV793 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV793 ) @ SV1606 ) @ SV2227 )
!= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV2227 @ SV793 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV1606 @ SV793 )
| ( SV1606
= ( c_HOL_Ozero__class_Ozero @ SV793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4524]) ).
thf(5313,plain,
! [SV2228: $i,SV1607: $i,SV794: $i] :
( ( ! [SY6645: $i] :
( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV794 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1607 ) @ SV2228 ) )
| ( hBOOL @ ( hAPP @ SV794 @ SY6645 ) )
| ( hBOOL @ ( hAPP @ SV794 @ SV1607 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4525]) ).
thf(5314,plain,
! [SV2229: $i,SV1608: $i,SV795: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV795 @ SV1608 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SV2229 @ SV1608 @ tc_nat ) )
| ~ ( c_lessequals @ SV1608 @ SV2229 @ tc_nat )
| ~ ( c_lessequals @ SV1608 @ SV795 @ tc_nat )
| ( SV795 = SV2229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4526]) ).
thf(5315,plain,
! [SV2230: $i,SV1609: $i,SV796: $i] :
( ( ! [SY6646: $i,SY6647: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV796 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SY6646 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SY6647 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ SY6646 )
= SY6647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4527]) ).
thf(5316,plain,
! [SV2231: $i,SV1610: $i,SV797: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV797 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV797 ) @ ( c_HOL_Otimes__class_Otimes @ SV1610 @ SV1610 @ SV797 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2231 @ SV2231 @ SV797 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV797 ) )
| ( SV2231
= ( c_HOL_Ozero__class_Ozero @ SV797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4528]) ).
thf(5317,plain,
! [SV2232: $i,SV1611: $i,SV798: $i] :
( ( ! [SY6648: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV798 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1611 @ SV1611 @ SV798 )
!= ( c_HOL_Ominus__class_Ominus @ SV2232 @ SY6648 @ SV798 ) )
| ( SV2232 = SY6648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4529]) ).
thf(5318,plain,
! [SV2233: $i,SV1612: $i,SV799: $i] :
( ( ! [SY6649: $i,SY6650: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV799 @ SV1612 @ tc_nat ) ) @ SV2233 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY6649 @ SV1612 @ tc_nat ) ) @ SY6650 ) )
| ~ ( c_lessequals @ SV799 @ SY6649 @ tc_nat )
| ( SV2233
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6649 @ SV799 @ tc_nat ) @ SV1612 @ tc_nat ) ) @ SY6650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4530]) ).
thf(5319,plain,
! [SV2234: $i,SV1613: $i,SV800: $i] :
( ( ! [SY6651: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV800 ) @ SV1613 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2234 ) @ SY6651 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV2234 @ SV1613 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV800 @ SY6651 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4531]) ).
thf(5320,plain,
! [SV2235: $i,SV1614: $i,SV801: $i] :
( ( ! [SY6652: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV801 ) @ SV1614 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV2235 ) @ SY6652 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV801 = SV2235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4532]) ).
thf(5321,plain,
! [SV2236: $i,SV1615: $i,SV802: $i] :
( ( ( ( c_List_Oappend @ SV802 @ SV1615 @ SV2236 )
!= ( c_List_Olist_ONil @ SV2236 ) )
| ( SV1615
= ( c_List_Olist_ONil @ SV2236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4533]) ).
thf(5322,plain,
! [SV2237: $i,SV1616: $i,SV803: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1616 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV803 @ SV2237 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV803 @ tc_nat )
| ( SV1616 = SV2237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4534]) ).
thf(5323,plain,
! [SV2238: $i,SV1617: $i,SV804: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV804 ) @ SV1617 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2238 ) @ SV1617 ) )
| ( SV804 = SV2238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4535]) ).
thf(5324,plain,
! [SV1618: $i,SV805: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV805 )
!= ( c_Lambda_OdB_OVar @ SV1618 ) )
= $true )
| ( ( SV805 = SV1618 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4536]) ).
thf(5325,plain,
! [SV2239: $i,SV1619: $i,SV806: $i] :
( ( ! [SY6653: $i,SY6654: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV806 )
| ~ ( class_Int_Onumber__ring @ SV806 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2239 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY6653 @ SY6654 @ SV806 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SY6654 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SY6653 @ SV2239 @ SV806 ) ) )
| ( SV2239 = SY6654 )
| ( SV1619 = SY6653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4537]) ).
thf(5326,plain,
! [SV2240: $i,SV1620: $i,SV807: $i] :
( ( ! [SY6655: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV807 ) @ SV1620 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2240 ) @ SY6655 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1620 = SY6655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4538]) ).
thf(5327,plain,
! [SV2241: $i,SV1621: $i,SV808: $i] :
( ( ! [SY6656: $i,SY6657: $i,SY6658: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV808 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV1621 @ SV2241 @ SV808 ) ) @ SY6656 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SY6657 @ SV2241 @ SV808 ) ) @ SY6658 ) )
| ( SY6656
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6657 @ SV1621 @ SV808 ) @ SV2241 @ SV808 ) ) @ SY6658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4539]) ).
thf(5328,plain,
! [SV2242: $i,SV1622: $i,SV809: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV809 @ SV1622 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV809 @ SV2242 @ tc_nat ) )
| ( SV809
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1622 = SV2242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4540]) ).
thf(5329,plain,
! [SV2243: $i,SV1623: $i,SV810: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV810 )
| ~ ( class_Int_Onumber__ring @ SV810 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1623 @ SV2243 @ SV810 )
!= ( c_HOL_Ozero__class_Ozero @ SV810 ) )
| ( SV1623 = SV2243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4541]) ).
thf(5330,plain,
! [SV1624: $i,SV811: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV811 @ SV1624 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV811 @ SV1624 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4542]) ).
thf(5331,plain,
! [SV2244: $i,SV1625: $i,SV812: $i] :
( ( ! [SY6659: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1625 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2244 @ SY6659 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SY6659 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2244 @ SV1625 @ tc_nat ) ) )
| ( SV1625 = SY6659 )
| ( SV812 = SV2244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4543]) ).
thf(5332,plain,
! [SV1626: $i,SV813: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV813 )
= ( c_Lambda_OdB_OVar @ SV1626 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4544]) ).
thf(5333,plain,
! [SV1627: $i,SV814: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV814 @ SV1627 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1627 @ SV814 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1627 = SV814 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4545]) ).
thf(5334,plain,
! [SV2245: $i,SV1628: $i,SV815: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV815 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1628 @ SV2245 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV815 )
= SV1628 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4546]) ).
thf(5335,plain,
! [SV2246: $i,SV1629: $i,SV816: $i] :
( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV816 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1629 @ SV2246 @ SV816 )
!= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
| ( SV2246
= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
| ( SV1629
= ( c_HOL_Ozero__class_Ozero @ SV816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4547]) ).
thf(5336,plain,
! [SV1630: $i,SV817: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV817 ) @ SV1630 )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV817
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV817
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4548]) ).
thf(5337,plain,
! [SV2247: $i,SV1631: $i,SV818: $i] :
( ( ! [SY6660: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV818 ) @ SV1631 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV2247 ) @ SY6660 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4549]) ).
thf(5338,plain,
! [SV2248: $i,SV1632: $i,SV819: $i] :
( ( ! [SY6661: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV819 ) @ SV1632 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2248 ) @ SY6661 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV819 = SV2248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4550]) ).
thf(5339,plain,
! [SV2249: $i,SV1633: $i,SV820: $i] :
( ( ! [SY6662: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV820 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SV2249 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SY6662 ) )
| ( SV2249 = SY6662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4551]) ).
thf(5340,plain,
! [SV2250: $i,SV1634: $i,SV821: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV821 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1634 @ SV821 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV2250 @ SV821 ) )
| ( SV1634 = SV2250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4552]) ).
thf(5341,plain,
! [SV2251: $i,SV1635: $i,SV822: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV822 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV822 ) @ ( c_HOL_Otimes__class_Otimes @ SV1635 @ SV1635 @ SV822 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2251 @ SV2251 @ SV822 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV822 ) )
| ( SV1635
= ( c_HOL_Ozero__class_Ozero @ SV822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4553]) ).
thf(5342,plain,
! [SV2252: $i,SV1636: $i,SV823: $i] :
( ( ! [SY6663: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV823 )
| ( ( c_Power_Opower__class_Opower @ SV1636 @ ( c_Suc @ SV2252 ) @ SV823 )
!= ( c_Power_Opower__class_Opower @ SY6663 @ ( c_Suc @ SV2252 ) @ SV823 ) )
| ( SV1636 = SY6663 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SY6663 @ SV823 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV1636 @ SV823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4554]) ).
thf(5343,plain,
! [SV2253: $i,SV1637: $i,SV824: $i] :
( ( ( ( c_List_Oappend @ SV824 @ SV1637 @ SV2253 )
!= SV1637 )
| ( SV824
= ( c_List_Olist_ONil @ SV2253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4555]) ).
thf(5344,plain,
! [SV2254: $i,SV1638: $i,SV825: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV825 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1638 ) @ SV2254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4556]) ).
thf(5345,plain,
! [SV2255: $i,SV1639: $i,SV826: $i] :
( ( ( SV826
!= ( c_List_Oappend @ SV1639 @ SV826 @ SV2255 ) )
| ( SV1639
= ( c_List_Olist_ONil @ SV2255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4557]) ).
thf(5346,plain,
! [SV1640: $i,SV827: $i] :
( ( ( ( c_Suc @ SV827 )
!= ( c_Suc @ SV1640 ) )
= $true )
| ( ( SV827 = SV1640 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4558]) ).
thf(5347,plain,
! [SV2256: $i,SV1641: $i,SV828: $i] :
( ( ( c_List_Olist_OCons @ SV828 @ SV1641 @ SV2256 )
!= ( c_List_Olist_ONil @ SV2256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4559]) ).
thf(5348,plain,
! [SV2257: $i,SV1642: $i,SV829: $i] :
( ( ( c_List_Olist_OCons @ SV829 @ SV1642 @ SV2257 )
!= ( c_List_Olist_ONil @ SV2257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4560]) ).
thf(5349,plain,
! [SV2258: $i,SV1643: $i,SV830: $i] :
( ( ! [SY6664: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV830 ) @ SV1643 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV2258 ) @ SY6664 ) )
| ( SV1643 = SY6664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4561]) ).
thf(5350,plain,
! [SV2259: $i,SV1644: $i,SV832: $i] :
( ( ! [SY6665: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV832 )
| ~ ( class_Int_Onumber__ring @ SV832 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2259 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SY6665 ) )
| ( SV2259 = SY6665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4563]) ).
thf(5351,plain,
! [SV2260: $i,SV1645: $i,SV833: $i] :
( ( ( ( c_List_Oreplicate @ SV833 @ SV1645 @ SV2260 )
!= ( c_List_Olist_ONil @ SV2260 ) )
| ( SV833
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4564]) ).
thf(5352,plain,
! [SV2261: $i,SV1646: $i,SV834: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV834 )
| ( ( c_Orderings_Oord__class_Omin @ SV1646 @ SV2261 @ SV834 )
!= SV1646 )
| ( c_lessequals @ SV1646 @ SV2261 @ SV834 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4565]) ).
thf(5353,plain,
! [SV1647: $i,SV835: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV835 @ SV1647 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( SV1647
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV835
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4566]) ).
thf(5354,plain,
! [SV2262: $i,SV1648: $i,SV836: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV836 @ SV1648 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV2262 ) )
| ( SV836
= ( c_Lambda_OdB_OAbs @ SV2262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4567]) ).
thf(5355,plain,
! [SV2263: $i,SV1649: $i,SV837: $i] :
( ( ! [SY6666: $i,SY6667: $i] :
( ( ( c_List_Oreplicate @ SV837 @ SV1649 @ SV2263 )
!= ( c_List_Oreplicate @ SY6666 @ SY6667 @ SV2263 ) )
| ( SV1649 = SY6667 )
| ( SV837
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4568]) ).
thf(5356,plain,
! [SV2264: $i,SV1650: $i,SV838: $i] :
( ( ! [SY6668: $i,SY6669: $i,SY6670: $i,SY6671: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SY6668 @ SY6669 ) )
| ~ ( c_Type_Otyping @ SY6670 @ SY6668 @ SV1650 )
| ~ ( c_InductTermi_OIT @ SY6668 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY6670 @ SY6669 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SY6671 )
| ~ ( c_InductTermi_OIT @ SV2264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4569]) ).
thf(5357,plain,
! [SV2265: $i,SV1651: $i,SV839: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV839 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV839 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV839 )
| ~ ( class_Power_Opower @ SV839 )
| ( ( c_Power_Opower__class_Opower @ SV1651 @ SV2265 @ SV839 )
!= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
| ( SV1651
= ( c_HOL_Ozero__class_Ozero @ SV839 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4570]) ).
thf(5358,plain,
! [SV2266: $i,SV1652: $i,SV840: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV840 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1652 @ SV2266 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV840 )
= SV1652 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4571]) ).
thf(5359,plain,
! [SV2267: $i,SV1653: $i,SV841: $i] :
( ( ! [SY6672: $i,SY6673: $i] :
( ( ( c_List_Oappend @ SV841 @ ( c_List_Olist_OCons @ SV1653 @ ( c_List_Olist_ONil @ SV2267 ) @ SV2267 ) @ SV2267 )
!= ( c_List_Oappend @ SY6672 @ ( c_List_Olist_OCons @ SY6673 @ ( c_List_Olist_ONil @ SV2267 ) @ SV2267 ) @ SV2267 ) )
| ( SV841 = SY6672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4572]) ).
thf(5360,plain,
! [SV2268: $i,SV1654: $i,SV842: $i] :
( ( ( SV842
!= ( c_List_Oappend @ SV842 @ SV1654 @ SV2268 ) )
| ( SV1654
= ( c_List_Olist_ONil @ SV2268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4573]) ).
thf(5361,plain,
! [SV2269: $i,SV1655: $i,SV843: $i] :
( ( ( c_Lambda_OdB_OVar @ SV843 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1655 ) @ SV2269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4574]) ).
thf(5362,plain,
! [SV1656: $i,SV845: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV845 ) @ SV1656 ) )
= $true )
| ( ( ( SV1656
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV845
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4576]) ).
thf(5363,plain,
! [SV2270: $i,SV1657: $i,SV846: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV846 )
| ( ( c_Power_Opower__class_Opower @ SV1657 @ SV2270 @ SV846 )
!= ( c_HOL_Ozero__class_Ozero @ SV846 ) )
| ( SV1657
= ( c_HOL_Ozero__class_Ozero @ SV846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4577]) ).
thf(5364,plain,
! [SV2271: $i,SV1658: $i,SV847: $i] :
( ( ( c_List_Olist_ONil @ SV847 )
!= ( c_List_Olist_OCons @ SV1658 @ SV2271 @ SV847 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4578]) ).
thf(5365,plain,
! [SV2272: $i,SV1659: $i,SV848: $i] :
( ( ! [SY6674: $i,SY6675: $i] :
( ( ( c_List_Olist_OCons @ SV848 @ SV1659 @ SV2272 )
!= ( c_List_Olist_OCons @ SY6674 @ SY6675 @ SV2272 ) )
| ( SV1659 = SY6675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4579]) ).
thf(5366,plain,
! [SV2273: $i,SV1660: $i,SV849: $i] :
( ( ( ( c_List_Olist_ONil @ SV849 )
!= ( c_List_Oappend @ SV1660 @ SV2273 @ SV849 ) )
| ( SV1660
= ( c_List_Olist_ONil @ SV849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4580]) ).
thf(5367,plain,
! [SV1661: $i,SV850: $i] :
( ( ( ( c_Type_Otype_OAtom @ SV850 )
!= ( c_Type_Otype_OAtom @ SV1661 ) )
= $true )
| ( ( SV850 = SV1661 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4581]) ).
thf(5368,plain,
! [SV1662: $i,SV851: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV851 ) @ SV1662 ) )
= $true )
| ( ( ( SV851
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1662
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4582]) ).
thf(5369,plain,
! [SV1663: $i,SV852: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV852 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV852 ) @ SV1663 ) @ SV1663 )
!= ( c_HOL_Ozero__class_Ozero @ SV852 ) )
| ( SV1663
= ( c_HOL_Ozero__class_Ozero @ SV852 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4583]) ).
thf(5370,plain,
! [SV2274: $i,SV1664: $i,SV853: $i] :
( ( ! [SY6676: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV853 ) @ SV1664 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2274 ) @ SY6676 ) )
| ( SV853 = SV2274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4584]) ).
thf(5371,plain,
! [SV2275: $i,SV1665: $i,SV854: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV854 ) @ SV1665 )
!= ( c_Lambda_OdB_OVar @ SV2275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4585]) ).
thf(5372,plain,
! [SV2276: $i,SV1666: $i,SV855: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV855 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV855 ) @ SV1666 ) @ SV2276 )
!= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV2276 @ SV855 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV1666 @ SV855 )
| ( SV2276
= ( c_HOL_Ozero__class_Ozero @ SV855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4586]) ).
thf(5373,plain,
! [SV2277: $i,SV1667: $i,SV856: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV856 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1667 @ SV2277 @ SV856 )
!= ( c_HOL_Ozero__class_Ozero @ SV856 ) )
| ( SV1667 = SV2277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4587]) ).
thf(5374,plain,
! [SV2278: $i,SV1668: $i,SV857: $i] :
( ( ( ( c_List_Oappend @ SV857 @ SV1668 @ SV2278 )
!= ( c_List_Olist_ONil @ SV2278 ) )
| ( SV857
= ( c_List_Olist_ONil @ SV2278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4588]) ).
thf(5375,plain,
! [SV2279: $i,SV1669: $i,SV858: $i] :
( ( ! [SY6677: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV858 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1669 @ SV2279 @ SV858 )
!= ( c_HOL_Ominus__class_Ominus @ SY6677 @ SY6677 @ SV858 ) )
| ( SV1669 = SV2279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4589]) ).
thf(5376,plain,
! [SV2280: $i,SV1670: $i,SV859: $i] :
( ( ( c_List_Olist_OCons @ SV859 @ SV1670 @ SV2280 )
!= SV1670 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4590]) ).
thf(5377,plain,
! [SV1671: $i,SV860: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV860 ) @ SV1671 )
!= SV860 )
= $true )
| ( ( SV1671
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4591]) ).
thf(5378,plain,
! [SV2281: $i,SV1672: $i,SV861: $i] :
( ( ! [SY6678: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SV2281 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SY6678 @ tc_nat ) ) )
| ( SV2281 = SY6678 )
| ( SV1672
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4592]) ).
thf(5379,plain,
! [SV2282: $i,SV1673: $i,SV863: $i] :
( ( ! [SY6679: $i,SY6680: $i,SY6681: $i,SY6682: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SY6679 @ SY6680 ) )
| ~ ( c_Type_Otyping @ SY6681 @ SY6679 @ SV863 )
| ~ ( c_InductTermi_OIT @ SY6679 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY6681 @ SY6680 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SY6682 )
| ~ ( c_InductTermi_OIT @ SV2282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4594]) ).
thf(5380,plain,
! [SV2283: $i,SV1674: $i,SV864: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV864 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1674 @ SV2283 @ SV864 )
!= ( c_HOL_Ozero__class_Ozero @ SV864 ) )
| ( SV1674 = SV2283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4595]) ).
thf(5381,plain,
! [SV2284: $i,SV1675: $i,SV865: $i,SV1: $i] :
( ( ! [SY6683: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1 @ SV865 @ tc_nat ) ) @ SV1675 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2284 @ SV865 @ tc_nat ) ) @ SY6683 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1675 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2284 @ SV1 @ tc_nat ) @ SV865 @ tc_nat ) ) @ SY6683 ) @ tc_nat )
| ~ ( c_lessequals @ SV1 @ SV2284 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4596]) ).
thf(5382,plain,
! [SV2285: $i,SV1676: $i,SV866: $i,SV2: $i] :
( ( ! [SY6684: $i] :
( ( c_HOL_Oord__class_Oless @ SV2 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV866 @ SV1676 @ tc_nat ) @ SV2285 @ tc_nat ) ) @ SY6684 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV2285 @ tc_nat ) ) @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV866 @ SV2285 @ tc_nat ) ) @ SY6684 ) @ tc_nat )
| ~ ( c_lessequals @ SV1676 @ SV866 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4597]) ).
thf(5383,plain,
! [SV2286: $i,SV1677: $i,SV867: $i,SV3: $i] :
( ( ! [SY6685: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV3 @ SV867 @ tc_nat ) ) @ SV1677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2286 @ SV867 @ tc_nat ) ) @ SY6685 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV3 @ SV2286 @ tc_nat ) @ SV867 @ tc_nat ) ) @ SV1677 ) @ SY6685 @ tc_nat )
| ~ ( c_lessequals @ SV2286 @ SV3 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4598]) ).
thf(5384,plain,
! [SV2287: $i,SV1678: $i,SV868: $i,SV4: $i] :
( ( ! [SY6686: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV868 @ tc_nat ) @ SV1678 @ tc_nat ) ) @ SV2287 ) @ SY6686 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV4 @ SV1678 @ tc_nat ) ) @ SV2287 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV868 @ SV1678 @ tc_nat ) ) @ SY6686 ) @ tc_nat )
| ~ ( c_lessequals @ SV868 @ SV4 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4599]) ).
thf(5385,plain,
! [SV2288: $i,SV1679: $i,SV869: $i,SV5: $i] :
( ( ! [SY6687: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV5 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV869 @ SV1679 @ SV5 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2288 @ SV869 @ SV5 ) @ SV1679 @ SV5 ) ) @ SY6687 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV2288 @ SV1679 @ SV5 ) ) @ SY6687 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4600]) ).
thf(5386,plain,
! [SV872: $i,SV8: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV8 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV8 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ ( c_Suc @ SV872 ) @ SV8 )
= ( c_HOL_Ozero__class_Ozero @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4601]) ).
thf(5387,plain,
! [SV2289: $i,SV1680: $i,SV873: $i,SV9: $i] :
( ( ! [SY6688: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV2289 @ SY6688 @ SV9 ) @ SV9 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV2289 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1680 @ SY6688 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV873 @ SV2289 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4602]) ).
thf(5388,plain,
! [SV874: $i,SV10: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV10 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV10 @ SV874 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4603]) ).
thf(5389,plain,
! [SV1681: $i,SV875: $i,SV11: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV11 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV875 @ SV1681 @ SV11 ) @ SV875 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4604]) ).
thf(5390,plain,
! [SV1682: $i,SV876: $i,SV12: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV12 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV876 @ SV1682 @ SV12 ) @ SV1682 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4605]) ).
thf(5391,plain,
! [SV2290: $i,SV1683: $i,SV877: $i,SV13: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV13 )
| ( c_lessequals @ SV877 @ ( c_Orderings_Oord__class_Omin @ SV1683 @ SV2290 @ SV13 ) @ SV13 )
| ~ ( c_lessequals @ SV877 @ SV2290 @ SV13 )
| ~ ( c_lessequals @ SV877 @ SV1683 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4606]) ).
thf(5392,plain,
! [SV2291: $i,SV1684: $i,SV878: $i,SV14: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV14 )
| ( c_lessequals @ SV878 @ ( c_Orderings_Oord__class_Omin @ SV1684 @ SV2291 @ SV14 ) @ SV14 )
| ~ ( c_lessequals @ SV878 @ SV2291 @ SV14 )
| ~ ( c_lessequals @ SV878 @ SV1684 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4607]) ).
thf(5393,plain,
! [SV2292: $i,SV1685: $i,SV879: $i,SV15: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV15 )
| ( c_lessequals @ SV879 @ ( c_Orderings_Oord__class_Omin @ SV1685 @ SV2292 @ SV15 ) @ SV15 )
| ~ ( c_lessequals @ SV879 @ SV2292 @ SV15 )
| ~ ( c_lessequals @ SV879 @ SV1685 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4608]) ).
thf(5394,plain,
! [SV2293: $i,SV1686: $i,SV880: $i,SV16: $i] :
( ( ! [SY6689: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV16 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SV880 @ SV1686 @ SV16 ) ) @ SV2293 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SY6689 @ SV1686 @ SV16 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV880 @ SY6689 @ SV16 ) @ SV1686 @ SV16 ) ) @ SV2293 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4609]) ).
thf(5395,plain,
! [SV1687: $i,SV881: $i,SV17: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV17 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SV881 @ SV1687 @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV881 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4610]) ).
thf(5396,plain,
! [SV882: $i,SV18: $i] :
( ( ( c_lessequals @ SV18 @ SV882 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV18 @ SV882 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4611]) ).
thf(5397,plain,
! [SV2294: $i,SV1688: $i,SV883: $i,SV19: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV19 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV883 @ SV1688 @ SV19 ) @ SV2294 @ SV19 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV883 @ SV2294 @ SV19 ) @ ( c_HOL_Ominus__class_Ominus @ SV1688 @ SV2294 @ SV19 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4612]) ).
thf(5398,plain,
! [SV2295: $i,SV1689: $i,SV884: $i,SV20: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV20 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV884 @ SV1689 @ SV20 ) @ SV2295 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SV1689 @ SV2295 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SV884 @ SV2295 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4613]) ).
thf(5399,plain,
! [SV1690: $i,SV885: $i,SV21: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV21 @ SV885 @ tc_nat ) ) @ SV1690 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV21 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV885 ) @ SV1690 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV885 @ SV21 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4614]) ).
thf(5400,plain,
! [SV2296: $i,SV1691: $i,SV886: $i,SV22: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV22 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV22 )
| ( c_HOL_Oord__class_Oless @ SV886 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1691 ) @ SV2296 ) @ SV22 )
| ~ ( c_lessequals @ SV886 @ SV2296 @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV1691 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4615]) ).
thf(5401,plain,
! [SV1692: $i,SV887: $i,SV23: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV23 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV887 ) @ SV1692 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV23 @ SV887 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1692 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4616]) ).
thf(5402,plain,
! [SV1693: $i,SV888: $i,SV24: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV24 ) )
= $true )
| ( ( ( c_lessequals @ SV888 @ SV1693 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV888 @ SV24 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1693 @ SV24 ) @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4617]) ).
thf(5403,plain,
! [SV1694: $i,SV889: $i,SV25: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV25 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV889 @ SV25 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1694 @ SV25 ) @ SV25 )
| ~ ( c_lessequals @ SV889 @ SV1694 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4618]) ).
thf(5404,plain,
! [SV2297: $i,SV1695: $i,SV890: $i,SV26: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV26 @ SV890 @ SV1695 ) @ ( c_Lambda_Osubst @ SV2297 @ SV890 @ SV1695 ) )
| ~ ( c_Lambda_Obeta @ SV26 @ SV2297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4619]) ).
thf(5405,plain,
! [SV2298: $i,SV1696: $i,SV891: $i,SV27: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV27 )
| ( c_HOL_Oord__class_Oless @ SV891 @ ( c_Orderings_Oord__class_Omin @ SV1696 @ SV2298 @ SV27 ) @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV2298 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV1696 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4620]) ).
thf(5406,plain,
! [SV2299: $i,SV1699: $i,SV894: $i,SV30: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV30 )
| ~ ( class_Int_Onumber__ring @ SV30 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV1699 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV2299 @ SV30 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV2299 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV1699 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4623]) ).
thf(5407,plain,
! [SV2300: $i,SV1700: $i,SV895: $i,SV31: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV31 )
| ~ ( class_Int_Onumber__ring @ SV31 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1700 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV2300 @ SV31 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV2300 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1700 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4624]) ).
thf(5408,plain,
! [SV897: $i,SV34: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV34 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV897 @ SV34 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV897 ) @ SV897 ) @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4626]) ).
thf(5409,plain,
! [SV898: $i,SV35: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV35 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV35 ) @ SV898 ) @ SV898 ) @ SV35 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV898 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4627]) ).
thf(5410,plain,
! [SV1701: $i,SV899: $i,SV36: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV36 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ SV899 @ ( c_Orderings_Oord__class_Omin @ SV899 @ SV1701 @ SV36 ) @ SV36 )
= ( c_Orderings_Oord__class_Omin @ SV899 @ SV1701 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4628]) ).
thf(5411,plain,
! [SV1702: $i,SV900: $i,SV37: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV37 ) @ SV900 @ SV1702 )
= ( c_Lambda_OdB_OVar @ SV37 ) )
= $true )
| ( ( ( SV37 = SV1702 )
| ( c_HOL_Oord__class_Oless @ SV1702 @ SV37 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4629]) ).
thf(5412,plain,
! [SV2301: $i,SV1703: $i,SV901: $i,SV38: $i] :
( ( ! [SY6690: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV38 @ SV901 @ tc_nat ) ) @ SV1703 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2301 @ SV901 @ tc_nat ) ) @ SY6690 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1703 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2301 @ SV38 @ tc_nat ) @ SV901 @ tc_nat ) ) @ SY6690 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV38 @ SV2301 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4630]) ).
thf(5413,plain,
! [SV2302: $i,SV1704: $i,SV902: $i,SV39: $i] :
( ( ! [SY6691: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV39 @ SV902 @ tc_nat ) ) @ SV1704 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2302 @ SV902 @ tc_nat ) ) @ SY6691 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SV2302 @ tc_nat ) @ SV902 @ tc_nat ) ) @ SV1704 ) @ SY6691 @ tc_nat ) )
| ~ ( c_lessequals @ SV2302 @ SV39 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4631]) ).
thf(5414,plain,
! [SV1705: $i,SV903: $i,SV40: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV40 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ ( c_HOL_Ominus__class_Ominus @ SV903 @ SV1705 @ SV40 ) ) @ SV1705 )
= SV903 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4632]) ).
thf(5415,plain,
! [SV1706: $i,SV904: $i,SV41: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV41 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV904 ) @ SV1706 ) @ SV904 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV41 @ SV1706 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4633]) ).
thf(5416,plain,
! [SV1707: $i,SV905: $i,SV42: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV42 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV905 ) @ SV1707 ) @ SV905 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV42 @ SV1707 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4634]) ).
thf(5417,plain,
! [SV1708: $i,SV906: $i,SV43: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV43 @ SV906 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1708 @ SV906 @ tc_nat ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV906 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4635]) ).
thf(5418,plain,
! [SV1709: $i,SV907: $i,SV44: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV44 @ SV907 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV44 @ SV1709 @ tc_nat ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV44 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4636]) ).
thf(5419,plain,
! [SV2303: $i,SV1710: $i,SV908: $i,SV45: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV45 )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV908 @ SV1710 @ SV45 ) @ SV2303 @ SV45 )
= ( c_Power_Opower__class_Opower @ SV908 @ ( c_HOL_Otimes__class_Otimes @ SV1710 @ SV2303 @ tc_nat ) @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4637]) ).
thf(5420,plain,
! [SV909: $i,SV46: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV46 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ SV46 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV46 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV46 @ SV909 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4638]) ).
thf(5421,plain,
! [SV1711: $i,SV910: $i,SV47: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV47 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV910 @ ( c_Suc @ SV1711 ) @ SV47 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV910 @ SV1711 @ SV47 ) @ SV910 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4639]) ).
thf(5422,plain,
! [SV1712: $i,SV911: $i,SV48: $i] :
( ( ( ~ ( class_Power_Opower @ SV48 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV911 @ ( c_Suc @ SV1712 ) @ SV48 )
= ( c_HOL_Otimes__class_Otimes @ SV911 @ ( c_Power_Opower__class_Opower @ SV911 @ SV1712 @ SV48 ) @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4640]) ).
thf(5423,plain,
! [SV1713: $i,SV912: $i,SV49: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV912 @ ( c_Suc @ SV1713 ) @ SV49 )
= ( c_HOL_Otimes__class_Otimes @ SV912 @ ( c_Power_Opower__class_Opower @ SV912 @ SV1713 @ SV49 ) @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4641]) ).
thf(5424,plain,
! [SV1714: $i,SV913: $i,SV50: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV913 @ ( c_Suc @ SV1714 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ SV913 @ ( c_Power_Opower__class_Opower @ SV913 @ SV1714 @ SV50 ) @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4642]) ).
thf(5425,plain,
! [SV2304: $i,SV1715: $i,SV914: $i,SV51: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV914 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1715 ) @ SV2304 ) @ tc_nat )
| ~ ( c_lessequals @ SV914 @ SV2304 @ tc_nat )
| ~ ( c_lessequals @ SV51 @ SV1715 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4643]) ).
thf(5426,plain,
! [SV2305: $i,SV1716: $i,SV915: $i,SV52: $i] :
( ( ! [SY6692: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV52 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV915 ) @ SV1716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV2305 ) @ SY6692 ) @ SV52 )
| ~ ( c_lessequals @ SV1716 @ SY6692 @ SV52 )
| ~ ( c_lessequals @ SV915 @ SV2305 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4644]) ).
thf(5427,plain,
! [SV916: $i,SV53: $i] :
( ( ( c_lessequals @ SV53 @ SV916 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV53 @ ( c_Suc @ SV916 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4645]) ).
thf(5428,plain,
! [SV917: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV54 @ ( c_Suc @ SV917 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV54 @ SV917 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4646]) ).
thf(5429,plain,
! [SV918: $i,SV56: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV56 )
= $false )
| ( ( ( c_List_Olistsum @ SV918 @ SV56 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV56 ) @ ( c_HOL_Ozero__class_Ozero @ SV56 ) @ SV918 @ SV56 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4648]) ).
thf(5430,plain,
! [SV1717: $i,SV919: $i,SV57: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV57 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV919 @ SV1717 @ SV57 )
= ( c_HOL_Otimes__class_Otimes @ SV1717 @ SV919 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4649]) ).
thf(5431,plain,
! [SV59: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) )
= ( c_HOL_Ozero__class_Ozero @ SV59 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4650]) ).
thf(5432,plain,
! [SV1718: $i,SV921: $i,SV60: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV60 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV921 @ SV1718 @ SV60 )
= ( c_HOL_Otimes__class_Otimes @ SV1718 @ SV921 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4651]) ).
thf(5433,plain,
! [SV1719: $i,SV923: $i,SV62: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV62 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV923 ) @ SV1719 ) @ SV62 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1719 @ SV62 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV923 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4652]) ).
thf(5434,plain,
! [SV2306: $i,SV1720: $i,SV924: $i,SV63: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV63 )
| ( c_HOL_Oord__class_Oless @ SV924 @ SV1720 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV2306 @ SV1720 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ SV2306 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4653]) ).
thf(5435,plain,
! [SV2307: $i,SV1721: $i,SV925: $i,SV64: $i] :
( ( ~ ( class_Orderings_Oorder @ SV64 )
| ( c_HOL_Oord__class_Oless @ SV925 @ SV1721 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV925 @ SV2307 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV2307 @ SV1721 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4654]) ).
thf(5436,plain,
! [SV2308: $i,SV1722: $i,SV926: $i,SV65: $i] :
( ( ( c_Type_Otyping @ SV65 @ SV926 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV1722 @ SV65 @ SV2308 @ SV926 ) )
| ~ ( c_Type_Otyping @ SV65 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV2308 ) @ SV926 ) @ SV1722 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4655]) ).
thf(5437,plain,
! [SV1723: $i,SV927: $i,SV66: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV66 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV927 @ SV1723 @ SV66 )
= SV1723 )
| ~ ( c_lessequals @ SV927 @ SV1723 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4656]) ).
thf(5438,plain,
! [SV1724: $i,SV928: $i,SV67: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV67 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV928 @ SV1724 @ SV67 )
= SV928 )
| ~ ( c_lessequals @ SV1724 @ SV928 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4657]) ).
thf(5439,plain,
! [SV2309: $i,SV1725: $i,SV929: $i,SV68: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV929 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV1725 ) @ SV2309 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV929 ) @ SV1725 ) ) @ SV2309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4658]) ).
thf(5440,plain,
! [SV2310: $i,SV1726: $i,SV930: $i,SV69: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV69 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV930 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV1726 ) @ SV2310 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV1726 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV930 ) @ SV2310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4659]) ).
thf(5441,plain,
! [SV1729: $i,SV933: $i,SV72: $i] :
( ( ( hBOOL @ ( hAPP @ SV72 @ SV933 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV72 @ SV1729 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1729 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV72 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV72 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4662]) ).
thf(5442,plain,
! [SV1730: $i,SV937: $i,SV76: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV76 ) @ SV937 ) @ SV1730 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV76 @ ( c_HOL_Ominus__class_Ominus @ SV1730 @ SV937 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV937 @ SV1730 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4663]) ).
thf(5443,plain,
! [SV1731: $i,SV938: $i,SV77: $i] :
( ( ( c_lessequals @ SV77 @ ( c_HOL_Ominus__class_Ominus @ SV938 @ SV1731 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV77 ) @ SV1731 ) @ SV938 @ tc_nat )
| ~ ( c_lessequals @ SV1731 @ SV938 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4664]) ).
thf(5444,plain,
! [SV2311: $i,SV1732: $i,SV939: $i,SV78: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV78 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV939 @ SV1732 @ SV78 ) @ SV2311 @ SV78 )
| ~ ( c_lessequals @ SV1732 @ SV2311 @ SV78 )
| ~ ( c_lessequals @ SV939 @ SV2311 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4665]) ).
thf(5445,plain,
! [SV2312: $i,SV1733: $i,SV940: $i,SV79: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV79 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV940 @ SV1733 @ SV79 ) @ SV2312 @ SV79 )
| ~ ( c_lessequals @ SV1733 @ SV2312 @ SV79 )
| ~ ( c_lessequals @ SV940 @ SV2312 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4666]) ).
thf(5446,plain,
! [SV2313: $i,SV1734: $i,SV941: $i,SV80: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV80 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV941 @ SV1734 @ SV80 ) @ SV2313 @ SV80 )
| ~ ( c_lessequals @ SV1734 @ SV2313 @ SV80 )
| ~ ( c_lessequals @ SV941 @ SV2313 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4667]) ).
thf(5447,plain,
! [SV1735: $i,SV942: $i,SV81: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV81 ) )
= $true )
| ( ( c_lessequals @ SV942 @ ( c_Orderings_Oord__class_Omax @ SV942 @ SV1735 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4668]) ).
thf(5448,plain,
! [SV1736: $i,SV943: $i,SV82: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV82 ) )
= $true )
| ( ( c_lessequals @ SV943 @ ( c_Orderings_Oord__class_Omax @ SV1736 @ SV943 @ SV82 ) @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4669]) ).
thf(5449,plain,
! [SV949: $i,SV88: $i] :
( ( ( class_Orderings_Obot @ SV88 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV88 ) @ SV949 @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4670]) ).
thf(5450,plain,
! [SV2314: $i,SV1737: $i,SV950: $i,SV89: $i] :
( ( ( c_Nat_Onat_Onat__rec @ SV89 @ SV950 @ ( c_Suc @ SV1737 ) @ SV2314 )
= ( hAPP @ ( hAPP @ SV950 @ SV1737 ) @ ( c_Nat_Onat_Onat__rec @ SV89 @ SV950 @ SV1737 @ SV2314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4671]) ).
thf(5451,plain,
! [SV2315: $i,SV1738: $i,SV951: $i,SV90: $i] :
( ( ! [SY6693: $i,SY6694: $i,SY6695: $i,SY6696: $i,SY6697: $i] :
( ( ( hAPP @ ( hAPP @ SV90 @ ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ SV1738 ) ) @ SV2315 )
= ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ ( c_HOL_Otimes__class_Otimes @ SV1738 @ SV2315 @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6693 @ SY6694 @ SV90 @ SY6695 @ SY6696 @ SY6697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4672]) ).
thf(5452,plain,
! [SV2316: $i,SV1739: $i,SV952: $i,SV91: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV91 )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV952 @ SV1739 @ SV91 ) @ SV2316 @ SV91 )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV952 @ SV2316 @ SV91 ) @ ( c_Orderings_Oord__class_Omin @ SV1739 @ SV2316 @ SV91 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4673]) ).
thf(5453,plain,
! [SV2317: $i,SV1740: $i,SV953: $i,SV92: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV92 )
| ( ( c_Orderings_Oord__class_Omin @ SV953 @ ( c_Orderings_Oord__class_Omax @ SV1740 @ SV2317 @ SV92 ) @ SV92 )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV953 @ SV1740 @ SV92 ) @ ( c_Orderings_Oord__class_Omin @ SV953 @ SV2317 @ SV92 ) @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4674]) ).
thf(5454,plain,
! [SV2318: $i,SV1741: $i,SV954: $i,SV93: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV93 )
| ( c_lessequals @ SV954 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV1741 ) @ SV2318 ) @ SV93 )
| ~ ( c_lessequals @ SV954 @ SV2318 @ SV93 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV1741 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4675]) ).
thf(5455,plain,
! [SV2319: $i,SV1742: $i,SV955: $i,SV94: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV94 )
| ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV1742 ) @ SV2319 ) @ SV94 )
| ~ ( c_lessequals @ SV955 @ SV1742 @ SV94 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV2319 @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4676]) ).
thf(5456,plain,
! [SV956: $i,SV95: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV95 @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ SV95 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV95 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV95 @ SV956 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4677]) ).
thf(5457,plain,
! [SV957: $i,SV96: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ SV96 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV96 @ SV957 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4678]) ).
thf(5458,plain,
! [SV958: $i,SV97: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV97 @ SV958 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV97 ) @ SV958 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4679]) ).
thf(5459,plain,
! [SV959: $i,SV98: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV98 ) @ SV959 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV98 @ SV959 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4680]) ).
thf(5460,plain,
! [SV960: $i,SV99: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV99 @ SV960 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV99 ) @ SV960 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4681]) ).
thf(5461,plain,
! [SV961: $i,SV100: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV100 ) @ SV961 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV100 @ SV961 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4682]) ).
thf(5462,plain,
! [SV1743: $i,SV962: $i,SV101: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV101 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV962 ) @ SV1743 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV101 @ SV962 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4683]) ).
thf(5463,plain,
! [SV1744: $i,SV963: $i,SV102: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV102 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV963 ) @ SV1744 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV102 @ SV1744 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4684]) ).
thf(5464,plain,
! [SV1745: $i,SV964: $i,SV103: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV103 @ SV964 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV103 ) @ SV1745 ) @ SV964 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4685]) ).
thf(5465,plain,
! [SV1746: $i,SV965: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV104 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV965 ) @ SV1746 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV104 @ SV965 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4686]) ).
thf(5466,plain,
! [SV1747: $i,SV966: $i,SV105: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV105 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV966 ) @ SV1747 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV105 @ SV1747 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4687]) ).
thf(5467,plain,
! [SV2320: $i,SV1748: $i,SV967: $i,SV106: $i] :
( ( ! [SY6698: $i,SY6699: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV106 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV967 @ SV1748 @ SV106 ) ) @ SV2320 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SY6698 @ SV1748 @ SV106 ) ) @ SY6699 ) @ SV106 )
| ~ ( c_lessequals @ SV2320 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6698 @ SV967 @ SV106 ) @ SV1748 @ SV106 ) ) @ SY6699 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4688]) ).
thf(5468,plain,
! [SV2321: $i,SV1749: $i,SV968: $i,SV107: $i] :
( ( ! [SY6700: $i,SY6701: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV107 )
| ( c_lessequals @ SV968 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SV2321 @ SV107 ) @ SY6700 @ SV107 ) ) @ SY6701 ) @ SV107 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV2321 @ SY6700 @ SV107 ) ) @ SV968 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV1749 @ SY6700 @ SV107 ) ) @ SY6701 ) @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4689]) ).
thf(5469,plain,
! [SV2322: $i,SV1750: $i,SV969: $i,SV108: $i] :
( ( ! [SY6702: $i,SY6703: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV108 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV969 @ SV1750 @ SV108 ) ) @ SV2322 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SY6702 @ SV1750 @ SV108 ) ) @ SY6703 ) @ SV108 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV969 @ SY6702 @ SV108 ) @ SV1750 @ SV108 ) ) @ SV2322 ) @ SY6703 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4690]) ).
thf(5470,plain,
! [SV2323: $i,SV1751: $i,SV970: $i,SV109: $i] :
( ( ! [SY6704: $i,SY6705: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV109 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV970 @ SV1751 @ SV109 ) @ SV2323 @ SV109 ) ) @ SY6704 ) @ SY6705 @ SV109 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV970 @ SV2323 @ SV109 ) ) @ SY6704 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV1751 @ SV2323 @ SV109 ) ) @ SY6705 ) @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4691]) ).
thf(5471,plain,
! [SV110: $i,SV971: $i] :
( ( ( c_lessequals @ SV971 @ SV110 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV110 ) @ SV971 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV110 @ SV971 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4692]) ).
thf(5472,plain,
! [SV1752: $i,SV972: $i,SV111: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV111 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ ( c_HOL_Otimes__class_Otimes @ SV972 @ SV972 @ SV111 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1752 @ SV1752 @ SV111 ) ) @ SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4693]) ).
thf(5473,plain,
! [SV1753: $i,SV973: $i,SV112: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV112 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV973 ) @ SV1753 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV1753 ) @ SV973 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4694]) ).
thf(5474,plain,
! [SV1754: $i,SV974: $i,SV113: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV974 ) @ SV1754 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1754 ) @ SV974 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4695]) ).
thf(5475,plain,
! [SV1755: $i,SV976: $i,SV115: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV976 ) @ SV1755 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV1755 ) @ SV976 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4696]) ).
thf(5476,plain,
! [SV2324: $i,SV1756: $i,SV977: $i,SV116: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV116 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV977 ) @ SV1756 ) @ SV2324 @ SV116 @ SV116 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV977 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV1756 @ SV2324 @ SV116 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4697]) ).
thf(5477,plain,
! [SV1757: $i,SV978: $i,SV117: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV978 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV1757 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1757 @ SV117 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1757 @ SV978 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4698]) ).
thf(5478,plain,
! [SV979: $i,SV118: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV118 @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ SV118 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV118 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV118 @ SV979 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4699]) ).
thf(5479,plain,
! [SV2325: $i,SV1758: $i,SV980: $i,SV119: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV980 @ SV1758 @ SV119 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV2325 @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV980 @ SV2325 @ SV119 ) @ ( c_HOL_Otimes__class_Otimes @ SV1758 @ SV2325 @ SV119 ) @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4700]) ).
thf(5480,plain,
! [SV2326: $i,SV1759: $i,SV981: $i,SV120: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV981 @ SV1759 @ SV120 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV2326 @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV981 @ SV120 ) @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV1759 @ SV120 ) @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4701]) ).
thf(5481,plain,
! [SV2327: $i,SV1760: $i,SV982: $i,SV121: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring @ SV121 )
| ( c_HOL_Oord__class_Oless @ SV982 @ SV1760 @ SV121 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV2327 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV982 @ SV2327 @ SV121 ) @ ( c_HOL_Otimes__class_Otimes @ SV1760 @ SV2327 @ SV121 ) @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4702]) ).
thf(5482,plain,
! [SV2328: $i,SV1761: $i,SV983: $i,SV122: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring @ SV122 )
| ( c_HOL_Oord__class_Oless @ SV983 @ SV1761 @ SV122 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV2328 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV983 @ SV122 ) @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV1761 @ SV122 ) @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4703]) ).
thf(5483,plain,
! [SV1762: $i,SV984: $i,SV123: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV123 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV984 @ SV1762 @ SV123 ) @ SV984 @ SV123 )
= ( c_HOL_Otimes__class_Otimes @ SV984 @ ( c_Power_Opower__class_Opower @ SV984 @ SV1762 @ SV123 ) @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4704]) ).
thf(5484,plain,
! [SV2329: $i,SV1763: $i,SV985: $i,SV124: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV124 )
| ( c_lessequals @ SV985 @ SV1763 @ SV124 )
| ( c_lessequals @ SV985 @ SV2329 @ SV124 )
| ~ ( c_lessequals @ SV985 @ ( c_Orderings_Oord__class_Omax @ SV2329 @ SV1763 @ SV124 ) @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4705]) ).
thf(5485,plain,
! [SV2330: $i,SV1764: $i,SV986: $i,SV125: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV986 @ SV1764 @ SV125 ) @ ( c_Power_Opower__class_Opower @ SV986 @ SV2330 @ SV125 ) @ SV125 )
= ( c_Power_Opower__class_Opower @ SV986 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1764 ) @ SV2330 ) @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4706]) ).
thf(5486,plain,
! [SV988: $i,SV127: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV127 @ SV988 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV127 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( c_lessequals @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV127 @ SV988 ) @ SV988 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4707]) ).
thf(5487,plain,
! [SV2331: $i,SV1765: $i,SV989: $i,SV128: $i] :
( ( ! [SY6706: $i,SY6707: $i,SY6708: $i,SY6709: $i,SY6710: $i] :
( ( ( hAPP @ ( hAPP @ SV128 @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2331 ) ) @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SY6706 ) )
= ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2331 ) @ SY6706 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6707 @ SV128 @ SV989 @ SY6708 @ SY6709 @ SY6710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4708]) ).
thf(5488,plain,
! [SV2332: $i,SV1766: $i,SV990: $i,SV129: $i] :
( ( ~ ( c_lessequals @ SV129 @ SV990 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SV1766 @ tc_nat ) ) @ SV2332 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV129 @ SV1766 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV990 @ SV129 @ tc_nat ) @ SV1766 @ tc_nat ) ) @ SV2332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4709]) ).
thf(5489,plain,
! [SV2333: $i,SV1767: $i,SV991: $i,SV131: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV131 )
| ( c_lessequals @ SV991 @ SV1767 @ SV131 )
| ~ ( c_lessequals @ SV991 @ ( c_Orderings_Oord__class_Omin @ SV2333 @ SV1767 @ SV131 ) @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4710]) ).
thf(5490,plain,
! [SV2334: $i,SV1768: $i,SV992: $i,SV132: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV132 )
| ( c_lessequals @ SV992 @ SV1768 @ SV132 )
| ~ ( c_lessequals @ SV992 @ ( c_Orderings_Oord__class_Omin @ SV1768 @ SV2334 @ SV132 ) @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4711]) ).
thf(5491,plain,
! [SV2335: $i,SV1769: $i,SV993: $i,SV133: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV133 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV993 @ SV1769 @ SV133 ) @ SV2335 @ SV133 )
| ~ ( c_lessequals @ SV1769 @ SV2335 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4712]) ).
thf(5492,plain,
! [SV2336: $i,SV1770: $i,SV994: $i,SV134: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV134 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV994 @ SV1770 @ SV134 ) @ SV2336 @ SV134 )
| ~ ( c_lessequals @ SV994 @ SV2336 @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4713]) ).
thf(5493,plain,
! [SV2337: $i,SV1771: $i,SV995: $i,SV135: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV135 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV995 @ SV1771 @ SV135 ) @ SV2337 @ SV135 )
| ~ ( c_lessequals @ SV1771 @ SV2337 @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4714]) ).
thf(5494,plain,
! [SV2338: $i,SV1772: $i,SV996: $i,SV136: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV136 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV996 @ SV1772 @ SV136 ) @ SV2338 @ SV136 )
| ~ ( c_lessequals @ SV996 @ SV2338 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4715]) ).
thf(5495,plain,
! [SV2339: $i,SV1773: $i,SV997: $i,SV137: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV137 )
| ( c_lessequals @ SV997 @ SV1773 @ SV137 )
| ~ ( c_lessequals @ SV997 @ ( c_Orderings_Oord__class_Omin @ SV2339 @ SV1773 @ SV137 ) @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4716]) ).
thf(5496,plain,
! [SV2340: $i,SV1774: $i,SV998: $i,SV138: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV138 )
| ( c_lessequals @ SV998 @ SV1774 @ SV138 )
| ~ ( c_lessequals @ SV998 @ ( c_Orderings_Oord__class_Omin @ SV1774 @ SV2340 @ SV138 ) @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4717]) ).
thf(5497,plain,
! [SV1775: $i,SV999: $i,SV139: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV139 ) )
= $true )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV999 @ SV1775 @ SV139 @ SV139 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1775 @ SV999 @ SV139 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4718]) ).
thf(5498,plain,
! [SV2341: $i,SV1776: $i,SV1000: $i,SV140: $i] :
( ( ! [SY6711: $i,SY6712: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV140 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1776 @ SV140 ) ) @ SV2341 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SY6711 @ SV1776 @ SV140 ) ) @ SY6712 ) @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV2341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6711 @ SV1000 @ SV140 ) @ SV1776 @ SV140 ) ) @ SY6712 ) @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4719]) ).
thf(5499,plain,
! [SV2342: $i,SV1777: $i,SV1001: $i,SV141: $i] :
( ( ! [SY6713: $i,SY6714: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV141 )
| ( c_HOL_Oord__class_Oless @ SV1001 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1777 @ SV2342 @ SV141 ) @ SY6713 @ SV141 ) ) @ SY6714 ) @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV2342 @ SY6713 @ SV141 ) ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV1777 @ SY6713 @ SV141 ) ) @ SY6714 ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4720]) ).
thf(5500,plain,
! [SV2343: $i,SV1778: $i,SV1002: $i,SV142: $i] :
( ( ! [SY6715: $i,SY6716: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV142 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1778 @ SV142 ) ) @ SV2343 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SY6715 @ SV1778 @ SV142 ) ) @ SY6716 ) @ SV142 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1002 @ SY6715 @ SV142 ) @ SV1778 @ SV142 ) ) @ SV2343 ) @ SY6716 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4721]) ).
thf(5501,plain,
! [SV2344: $i,SV1779: $i,SV1003: $i,SV143: $i] :
( ( ! [SY6717: $i,SY6718: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV143 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1003 @ SV1779 @ SV143 ) @ SV2344 @ SV143 ) ) @ SY6717 ) @ SY6718 @ SV143 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1003 @ SV2344 @ SV143 ) ) @ SY6717 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1779 @ SV2344 @ SV143 ) ) @ SY6718 ) @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4722]) ).
thf(5502,plain,
! [SV2345: $i,SV1780: $i,SV1004: $i,SV144: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV144 )
| ( c_lessequals @ SV1004 @ SV1780 @ SV144 )
| ( c_lessequals @ SV2345 @ SV1780 @ SV144 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV2345 @ SV1004 @ SV144 ) @ SV1780 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4723]) ).
thf(5503,plain,
! [SV2346: $i,SV1781: $i,SV1005: $i,SV145: $i] :
( ( ~ ( c_lessequals @ SV145 @ SV1005 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV145 @ SV1781 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1005 @ SV145 @ tc_nat ) @ SV1781 @ tc_nat ) ) @ SV2346 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1005 @ SV1781 @ tc_nat ) ) @ SV2346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4724]) ).
thf(5504,plain,
! [SV1006: $i,SV146: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV146 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV1006 ) @ SV1006 ) @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV146 )
| ~ ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4725]) ).
thf(5505,plain,
! [SV1007: $i,SV147: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV147 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1007 @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1007 ) @ SV1007 ) @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4726]) ).
thf(5506,plain,
! [SV1008: $i,SV148: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV148 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1008 @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV1008 ) @ SV1008 ) @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4727]) ).
thf(5507,plain,
! [SV1009: $i,SV149: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV149 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV1009 ) @ SV1009 ) @ ( c_HOL_Ozero__class_Ozero @ SV149 ) @ SV149 )
| ~ ( c_HOL_Oord__class_Oless @ SV1009 @ ( c_HOL_Ozero__class_Ozero @ SV149 ) @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4728]) ).
thf(5508,plain,
! [SV1782: $i,SV1010: $i,SV150: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV150 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1010 @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1782 @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ ( c_HOL_Otimes__class_Otimes @ SV1010 @ SV1782 @ SV150 ) @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4729]) ).
thf(5509,plain,
! [SV1783: $i,SV1011: $i,SV151: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV151 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1011 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1783 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ ( c_HOL_Otimes__class_Otimes @ SV1783 @ SV1011 @ SV151 ) @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4730]) ).
thf(5510,plain,
! [SV1784: $i,SV1012: $i,SV152: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV152 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SV1784 @ SV152 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1784 @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1012 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4731]) ).
thf(5511,plain,
! [SV1785: $i,SV1013: $i,SV153: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV153 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV1013 @ SV1785 @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1785 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1013 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4732]) ).
thf(5512,plain,
! [SV154: $i,SV1014: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1014 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV154 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV154 @ SV1014 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4733]) ).
thf(5513,plain,
! [SV2347: $i,SV1786: $i,SV1015: $i,SV155: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV155 )
| ( c_HOL_Oord__class_Oless @ SV1015 @ SV1786 @ SV155 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV1786 @ SV155 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1015 @ SV2347 @ SV155 ) @ ( c_Power_Opower__class_Opower @ SV1786 @ SV2347 @ SV155 ) @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4734]) ).
thf(5514,plain,
! [SV2348: $i,SV1787: $i,SV1016: $i,SV156: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV156 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1016 ) @ SV1787 ) ) @ SV2348 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1787 ) @ SV2348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4735]) ).
thf(5515,plain,
! [SV2349: $i,SV1788: $i,SV1017: $i,SV157: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1017 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1788 ) @ SV2349 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1788 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1017 ) @ SV2349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4736]) ).
thf(5516,plain,
! [SV2350: $i,SV1789: $i,SV1018: $i,SV158: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV158 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1018 ) @ SV1789 ) ) @ SV2350 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1018 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1789 ) @ SV2350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4737]) ).
thf(5517,plain,
! [SV2351: $i,SV1790: $i,SV1019: $i,SV159: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV159 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1019 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1790 ) @ SV2351 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1019 ) @ SV1790 ) ) @ SV2351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4738]) ).
thf(5518,plain,
! [SV2352: $i,SV1791: $i,SV1020: $i,SV160: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV160 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV1020 ) @ SV1791 ) ) @ SV2352 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV1020 ) @ SV2352 ) ) @ SV1791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4739]) ).
thf(5519,plain,
! [SV2353: $i,SV1792: $i,SV1021: $i,SV161: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV161 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1021 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1792 ) @ SV2353 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1021 ) @ SV2353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4740]) ).
thf(5520,plain,
! [SV2354: $i,SV1793: $i,SV1022: $i,SV162: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1022 ) @ SV1793 ) ) @ SV2354 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1022 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1793 ) @ SV2354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4741]) ).
thf(5521,plain,
! [SV163: $i,SV1023: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1023 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1023 ) @ SV163 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV163 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4742]) ).
thf(5522,plain,
! [SV2355: $i,SV1794: $i,SV1024: $i,SV164: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV164 )
| ( ( c_Power_Opower__class_Opower @ SV1024 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1794 ) @ SV2355 ) @ SV164 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1024 @ SV1794 @ SV164 ) @ ( c_Power_Opower__class_Opower @ SV1024 @ SV2355 @ SV164 ) @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4743]) ).
thf(5523,plain,
! [SV165: $i,SV1025: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1025 @ SV165 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV165 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4744]) ).
thf(5524,plain,
! [SV1026: $i,SV166: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV166 @ SV1026 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV166 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4745]) ).
thf(5525,plain,
! [SV1797: $i,SV1029: $i,SV169: $i] :
( ( ( c_lessequals @ SV169 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1029 ) @ SV1797 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV169 @ SV1797 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4748]) ).
thf(5526,plain,
! [SV1798: $i,SV1030: $i,SV170: $i] :
( ( ( c_lessequals @ SV170 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1030 ) @ SV1798 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV170 @ SV1030 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4749]) ).
thf(5527,plain,
! [SV1799: $i,SV1031: $i,SV171: $i] :
( ( ( c_lessequals @ SV171 @ SV1031 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1799 ) @ SV171 ) @ SV1031 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4750]) ).
thf(5528,plain,
! [SV1800: $i,SV1032: $i,SV172: $i] :
( ( ( c_lessequals @ SV172 @ SV1032 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV172 ) @ SV1800 ) @ SV1032 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4751]) ).
thf(5529,plain,
! [SV1801: $i,SV1033: $i,SV173: $i] :
( ( ( c_lessequals @ SV173 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1033 ) @ SV1801 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV173 @ SV1801 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4752]) ).
thf(5530,plain,
! [SV1802: $i,SV1034: $i,SV174: $i] :
( ( ( c_lessequals @ SV174 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1034 ) @ SV1802 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV174 @ SV1034 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4753]) ).
thf(5531,plain,
! [SV1803: $i,SV1035: $i,SV175: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV175 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omin @ SV1035 @ SV1803 @ SV175 )
= SV1035 )
| ~ ( c_lessequals @ SV1035 @ SV1803 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4754]) ).
thf(5532,plain,
! [SV1804: $i,SV1036: $i,SV176: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV176 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omin @ SV1036 @ SV1804 @ SV176 )
= SV1804 )
| ~ ( c_lessequals @ SV1804 @ SV1036 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4755]) ).
thf(5533,plain,
! [SV2356: $i,SV1805: $i,SV1037: $i,SV177: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV177 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ SV1037 @ SV1805 @ SV177 ) @ SV2356 @ SV177 )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ SV1037 @ SV2356 @ SV177 ) @ ( c_HOL_Ominus__class_Ominus @ SV1805 @ SV2356 @ SV177 ) @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4756]) ).
thf(5534,plain,
! [SV2357: $i,SV1806: $i,SV1038: $i,SV178: $i] :
( ( ( c_Type_Otypings @ SV178 @ SV1038 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV1806 @ SV178 @ SV2357 @ SV1038 ) )
| ~ ( c_Type_Otyping @ SV178 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV2357 @ SV1038 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4757]) ).
thf(5535,plain,
! [SV1807: $i,SV1039: $i,SV179: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV179 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1039 @ SV1807 @ SV179 )
| ( c_lessequals @ SV1807 @ SV1039 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4758]) ).
thf(5536,plain,
! [SV1040: $i,SV180: $i] :
( ( ( class_Orderings_Olinorder @ SV180 )
= $false )
| ( ( ~ ( c_lessequals @ SV1040 @ SV1040 @ SV180 )
| ~ ( c_HOL_Oord__class_Oless @ SV1040 @ SV1040 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4759]) ).
thf(5537,plain,
! [SV1041: $i,SV181: $i] :
( ( ( class_Orderings_Olinorder @ SV181 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1041 @ SV1041 @ SV181 )
| ( c_lessequals @ SV1041 @ SV1041 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4760]) ).
thf(5538,plain,
! [SV1808: $i,SV1042: $i,SV182: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV182 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SV1808 @ SV182 )
| ~ ( c_lessequals @ SV1808 @ SV1042 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4761]) ).
thf(5539,plain,
! [SV1809: $i,SV1043: $i,SV183: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV183 ) )
= $true )
| ( ( ( c_lessequals @ SV1043 @ SV1809 @ SV183 )
| ( c_HOL_Oord__class_Oless @ SV1809 @ SV1043 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4762]) ).
thf(5540,plain,
! [SV1810: $i,SV1044: $i,SV184: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV184 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1044 @ SV1810 @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ SV1810 @ SV1044 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4763]) ).
thf(5541,plain,
! [SV1811: $i,SV1045: $i,SV185: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV185 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1045 @ SV1811 @ SV185 )
| ( c_lessequals @ SV1811 @ SV1045 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4764]) ).
thf(5542,plain,
! [SV1812: $i,SV1046: $i,SV186: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV186 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1046 @ SV1812 @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SV1812 @ SV1046 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4765]) ).
thf(5543,plain,
! [SV1047: $i,SV187: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV187 ) @ tc_nat )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV187 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV187 @ SV1047 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4766]) ).
thf(5544,plain,
! [SV1049: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ SV189 @ ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV189 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV189 @ SV1049 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4768]) ).
thf(5545,plain,
! [SV2358: $i,SV1813: $i,SV1050: $i,SV190: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV190 )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ SV1050 @ SV1813 @ SV190 ) @ SV2358 @ SV190 )
= ( c_Orderings_Oord__class_Omin @ SV1050 @ ( c_Orderings_Oord__class_Omin @ SV1813 @ SV2358 @ SV190 ) @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4769]) ).
thf(5546,plain,
! [SV2359: $i,SV1814: $i,SV1051: $i,SV191: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV191 )
| ( ( c_Orderings_Oord__class_Omin @ SV1051 @ ( c_Orderings_Oord__class_Omin @ SV1814 @ SV2359 @ SV191 ) @ SV191 )
= ( c_Orderings_Oord__class_Omin @ SV1814 @ ( c_Orderings_Oord__class_Omin @ SV1051 @ SV2359 @ SV191 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4770]) ).
thf(5547,plain,
! [SV2360: $i,SV1815: $i,SV1052: $i,SV192: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV192 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV192 )
| ( c_HOL_Oord__class_Oless @ SV1052 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV1815 ) @ SV2360 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SV2360 @ SV192 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV1815 @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4771]) ).
thf(5548,plain,
! [SV1816: $i,SV1053: $i,SV193: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV193 @ SV1053 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV193 @ SV1816 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1816 @ SV1053 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4772]) ).
thf(5549,plain,
! [SV1817: $i,SV1054: $i,SV194: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV194 @ SV1054 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1817 @ SV1054 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV194 @ SV1817 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4773]) ).
thf(5550,plain,
! [SV1818: $i,SV1055: $i,SV195: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV195 @ SV1055 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1818 @ SV1055 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV195 @ SV1818 @ tc_nat )
| ~ ( c_lessequals @ SV1055 @ SV1818 @ tc_nat )
| ~ ( c_lessequals @ SV1055 @ SV195 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4774]) ).
thf(5551,plain,
! [SV1819: $i,SV1056: $i,SV196: $i] :
( ( ( c_lessequals @ SV196 @ SV1056 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV196 @ SV1819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1056 @ SV1819 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1819 @ SV1056 @ tc_nat )
| ~ ( c_lessequals @ SV1819 @ SV196 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4775]) ).
thf(5552,plain,
! [SV2361: $i,SV1821: $i,SV1059: $i,SV199: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV199 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1821 @ SV199 ) @ ( c_Power_Opower__class_Opower @ SV2361 @ SV1821 @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV1059 @ SV199 )
| ~ ( c_lessequals @ SV1059 @ SV2361 @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4777]) ).
thf(5553,plain,
! [SV1822: $i,SV1060: $i,SV200: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV200 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1060 @ ( c_Orderings_Oord__class_Omax @ SV1060 @ SV1822 @ SV200 ) @ SV200 )
= SV1060 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4778]) ).
thf(5554,plain,
! [SV1823: $i,SV1061: $i,SV201: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV201 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1061 @ SV201 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1823 @ SV201 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4779]) ).
thf(5555,plain,
! [SV1824: $i,SV1062: $i,SV202: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV202 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV1062 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV1824 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4780]) ).
thf(5556,plain,
! [SV2362: $i,SV1825: $i,SV1063: $i,SV203: $i] :
( ( ! [SY6719: $i,SY6720: $i] :
( ( c_List_Ofoldl @ SV203 @ SV1063 @ ( c_List_Olist_OCons @ SV1825 @ SV2362 @ SY6719 ) @ SY6720 @ SY6719 )
= ( c_List_Ofoldl @ SV203 @ ( hAPP @ ( hAPP @ SV203 @ SV1063 ) @ SV1825 ) @ SV2362 @ SY6720 @ SY6719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4781]) ).
thf(5557,plain,
! [SV2363: $i,SV1826: $i,SV1065: $i,SV205: $i] :
( ( ( c_List_Odrop @ ( c_Suc @ SV205 ) @ ( c_List_Olist_OCons @ SV1065 @ SV1826 @ SV2363 ) @ SV2363 )
= ( c_List_Odrop @ SV205 @ SV1826 @ SV2363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4782]) ).
thf(5558,plain,
! [SV1827: $i,SV1066: $i,SV206: $i] :
( ( ( c_lessequals @ SV206 @ SV1066 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1827 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV206 @ SV1827 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1066 @ SV1827 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4783]) ).
thf(5559,plain,
! [SV1828: $i,SV1067: $i,SV207: $i] :
( ( ( c_lessequals @ SV207 @ SV1067 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1828 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1828 @ SV207 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1828 @ SV1067 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4784]) ).
thf(5560,plain,
! [SV1829: $i,SV1068: $i,SV208: $i] :
( ( ( c_lessequals @ SV208 @ SV1068 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1829 @ SV208 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1829 @ SV1068 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1829 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4785]) ).
thf(5561,plain,
! [SV1830: $i,SV1069: $i,SV209: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SV1069 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SV1830 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1069 @ SV1830 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV209 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4786]) ).
thf(5562,plain,
! [SV2364: $i,SV1831: $i,SV1070: $i,SV210: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV210 )
| ( c_lessequals @ SV1070 @ SV1831 @ SV210 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1831 @ SV210 ) @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1070 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SV2364 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4787]) ).
thf(5563,plain,
! [SV2365: $i,SV1832: $i,SV1071: $i,SV211: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV211 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV1832 @ SV211 ) @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV2365 @ SV211 ) @ SV211 )
| ~ ( c_lessequals @ SV2365 @ SV1832 @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4788]) ).
thf(5564,plain,
! [SV2366: $i,SV1833: $i,SV1072: $i,SV212: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV212 )
| ( c_lessequals @ SV1072 @ SV1833 @ SV212 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1072 @ SV212 ) @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1833 @ SV212 ) @ SV212 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SV2366 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4789]) ).
thf(5565,plain,
! [SV2367: $i,SV1834: $i,SV1073: $i,SV213: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV213 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV1834 @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV2367 @ SV213 ) @ SV213 )
| ~ ( c_lessequals @ SV1834 @ SV2367 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV1073 @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4790]) ).
thf(5566,plain,
! [SV2368: $i,SV1835: $i,SV1074: $i,SV214: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV214 )
| ( c_lessequals @ SV1074 @ SV1835 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV2368 @ SV214 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1074 @ SV214 ) @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1835 @ SV214 ) @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4791]) ).
thf(5567,plain,
! [SV2369: $i,SV1836: $i,SV1075: $i,SV215: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV215 )
| ( c_lessequals @ SV1075 @ SV1836 @ SV215 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV2369 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1075 @ SV2369 @ SV215 ) @ ( c_HOL_Otimes__class_Otimes @ SV1836 @ SV2369 @ SV215 ) @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4792]) ).
thf(5568,plain,
! [SV1076: $i,SV216: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV216 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1076 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV216 @ SV1076 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4793]) ).
thf(5569,plain,
! [SV2370: $i,SV1839: $i,SV1079: $i,SV221: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV221 )
| ( c_HOL_Oord__class_Oless @ SV1079 @ ( c_Orderings_Oord__class_Omax @ SV1839 @ SV2370 @ SV221 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SV1079 @ SV1839 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4796]) ).
thf(5570,plain,
! [SV2371: $i,SV1840: $i,SV1080: $i,SV222: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV222 )
| ( c_HOL_Oord__class_Oless @ SV1080 @ ( c_Orderings_Oord__class_Omax @ SV1840 @ SV2371 @ SV222 ) @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ SV1080 @ SV2371 @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4797]) ).
thf(5571,plain,
! [SV2372: $i,SV1841: $i,SV1081: $i,SV223: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV223 )
| ( c_HOL_Oord__class_Oless @ SV1081 @ ( c_Orderings_Oord__class_Omax @ SV1841 @ SV2372 @ SV223 ) @ SV223 )
| ~ ( c_HOL_Oord__class_Oless @ SV1081 @ SV1841 @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4798]) ).
thf(5572,plain,
! [SV2373: $i,SV1842: $i,SV1082: $i,SV224: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV224 )
| ( c_HOL_Oord__class_Oless @ SV1082 @ ( c_Orderings_Oord__class_Omax @ SV1842 @ SV2373 @ SV224 ) @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ SV1082 @ SV2373 @ SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4799]) ).
thf(5573,plain,
! [SV2374: $i,SV1843: $i,SV1083: $i,SV225: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV225 )
| ( c_HOL_Oord__class_Oless @ SV1083 @ SV1843 @ SV225 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SV2374 @ SV225 ) @ SV1843 @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4800]) ).
thf(5574,plain,
! [SV2375: $i,SV1844: $i,SV1084: $i,SV226: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV226 )
| ( c_HOL_Oord__class_Oless @ SV1084 @ SV1844 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV2375 @ SV1084 @ SV226 ) @ SV1844 @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4801]) ).
thf(5575,plain,
! [SV1845: $i,SV1085: $i,SV228: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV228 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1085 @ SV1845 @ SV228 )
= ( c_Orderings_Oord__class_Omin @ SV1845 @ SV1085 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4803]) ).
thf(5576,plain,
! [SV2376: $i,SV1846: $i,SV1086: $i,SV229: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV229 @ SV1086 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1846 @ SV1086 @ tc_nat ) ) @ SV2376 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV229 ) @ SV1846 ) @ SV1086 @ tc_nat ) ) @ SV2376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4804]) ).
thf(5577,plain,
! [SV2377: $i,SV1847: $i,SV1087: $i,SV230: $i] :
( ( ! [SY6721: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV230 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SV1087 @ SV1847 @ SV230 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SV2377 @ SV1847 @ SV230 ) ) @ SY6721 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ SV1087 ) @ SV2377 ) @ SV1847 @ SV230 ) ) @ SY6721 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4805]) ).
thf(5578,plain,
! [SV232: $i,SV1089: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV232 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV232 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4806]) ).
thf(5579,plain,
! [SV1090: $i,SV233: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV233 @ SV1090 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV233 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4807]) ).
thf(5580,plain,
! [SV1848: $i,SV1091: $i,SV234: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV234 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV1091 ) @ SV1848 ) @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV1848 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV1091 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4808]) ).
thf(5581,plain,
! [SV2378: $i,SV1849: $i,SV1092: $i,SV235: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV235 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1092 @ SV1849 @ SV235 ) @ ( c_Power_Opower__class_Opower @ SV2378 @ SV1849 @ SV235 ) @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1849 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV235 ) @ SV1092 @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SV2378 @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4809]) ).
thf(5582,plain,
! [SV1850: $i,SV1093: $i,SV236: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV236 ) )
= $true )
| ( ( ( SV1093
= ( c_HOL_Ozero__class_Ozero @ SV236 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ ( c_HOL_Otimes__class_Otimes @ SV1093 @ SV1093 @ SV236 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1850 @ SV1850 @ SV236 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV236 ) @ SV236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4810]) ).
thf(5583,plain,
! [SV1851: $i,SV1094: $i,SV237: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV237 ) )
= $true )
| ( ( ( SV1094
= ( c_HOL_Ozero__class_Ozero @ SV237 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( c_HOL_Otimes__class_Otimes @ SV1851 @ SV1851 @ SV237 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1094 @ SV1094 @ SV237 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV237 ) @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4811]) ).
thf(5584,plain,
! [SV2379: $i,SV1852: $i,SV1095: $i,SV238: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV238 @ SV1095 @ SV1852 ) @ SV2379 @ SV1852 )
= ( c_List_Olist_OCons @ SV238 @ ( c_List_Oappend @ SV1095 @ SV2379 @ SV1852 ) @ SV1852 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4812]) ).
thf(5585,plain,
! [SV2380: $i,SV1853: $i,SV1096: $i,SV239: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV239 @ SV1096 @ SV1853 ) @ SV2380 @ SV1853 )
= ( c_List_Olist_OCons @ SV239 @ ( c_List_Oappend @ SV1096 @ SV2380 @ SV1853 ) @ SV1853 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4813]) ).
thf(5586,plain,
! [SV2381: $i,SV1854: $i,SV1097: $i,SV240: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV240 @ ( c_Nat_Onat_Onat__case @ SV1097 @ SV1854 @ ( c_Suc @ SV2381 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV240 @ ( hAPP @ SV1854 @ SV2381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4814]) ).
thf(5587,plain,
! [SV2382: $i,SV1855: $i,SV1098: $i,SV241: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_Nat_Onat_Onat__case @ SV1098 @ SV1855 @ ( c_Suc @ SV2382 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV241 @ ( hAPP @ SV1855 @ SV2382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4815]) ).
thf(5588,plain,
! [SV2383: $i,SV1858: $i,SV1101: $i,SV244: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV244 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1101 @ SV1858 @ SV244 ) @ SV2383 @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ SV1101 @ SV2383 @ SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4818]) ).
thf(5589,plain,
! [SV2384: $i,SV1859: $i,SV1102: $i,SV245: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV245 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1102 @ SV1859 @ SV245 ) @ SV2384 @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ SV1859 @ SV2384 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4819]) ).
thf(5590,plain,
! [SV1860: $i,SV1103: $i,SV246: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV246 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ SV1103 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ ( c_HOL_Ozero__class_Ozero @ SV246 ) @ SV1860 @ SV246 @ SV246 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ SV1103 @ SV1860 @ SV246 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4820]) ).
thf(5591,plain,
! [SV2385: $i,SV1861: $i,SV1104: $i,SV247: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV247 )
| ( c_lessequals @ SV1104 @ SV1861 @ SV247 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2385 @ SV1104 @ SV247 ) @ SV1861 @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4821]) ).
thf(5592,plain,
! [SV2386: $i,SV1862: $i,SV1105: $i,SV248: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV248 )
| ( c_lessequals @ SV1105 @ SV1862 @ SV248 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1105 @ SV2386 @ SV248 ) @ SV1862 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4822]) ).
thf(5593,plain,
! [SV2387: $i,SV1863: $i,SV1106: $i,SV249: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV249 )
| ( c_lessequals @ SV1106 @ ( c_Orderings_Oord__class_Omax @ SV1863 @ SV2387 @ SV249 ) @ SV249 )
| ~ ( c_lessequals @ SV1106 @ SV2387 @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4823]) ).
thf(5594,plain,
! [SV2388: $i,SV1864: $i,SV1107: $i,SV250: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV250 )
| ( c_lessequals @ SV1107 @ ( c_Orderings_Oord__class_Omax @ SV1864 @ SV2388 @ SV250 ) @ SV250 )
| ~ ( c_lessequals @ SV1107 @ SV1864 @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4824]) ).
thf(5595,plain,
! [SV2389: $i,SV1865: $i,SV1108: $i,SV251: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV251 )
| ( c_lessequals @ SV1108 @ ( c_Orderings_Oord__class_Omax @ SV1865 @ SV2389 @ SV251 ) @ SV251 )
| ~ ( c_lessequals @ SV1108 @ SV2389 @ SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4825]) ).
thf(5596,plain,
! [SV2390: $i,SV1866: $i,SV1109: $i,SV252: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV252 )
| ( c_lessequals @ SV1109 @ ( c_Orderings_Oord__class_Omax @ SV1866 @ SV2390 @ SV252 ) @ SV252 )
| ~ ( c_lessequals @ SV1109 @ SV1866 @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4826]) ).
thf(5597,plain,
! [SV2391: $i,SV1867: $i,SV1110: $i,SV253: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV253 )
| ( c_lessequals @ SV1110 @ SV1867 @ SV253 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2391 @ SV1110 @ SV253 ) @ SV1867 @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4827]) ).
thf(5598,plain,
! [SV2392: $i,SV1868: $i,SV1111: $i,SV254: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV254 )
| ( c_lessequals @ SV1111 @ SV1868 @ SV254 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1111 @ SV2392 @ SV254 ) @ SV1868 @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4828]) ).
thf(5599,plain,
! [SV1869: $i,SV1112: $i,SV255: $i] :
( ( ( c_lessequals @ SV255 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1112 ) @ SV1869 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1869 @ tc_nat ) @ SV1112 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4829]) ).
thf(5600,plain,
! [SV1870: $i,SV1113: $i,SV256: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV256 @ SV1113 @ tc_nat ) @ SV1870 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV256 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1870 ) @ SV1113 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4830]) ).
thf(5601,plain,
! [SV1871: $i,SV1114: $i,SV257: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV257 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ ( c_Power_Opower__class_Opower @ SV1114 @ SV1871 @ SV257 ) @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV1114 @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4831]) ).
thf(5602,plain,
! [SV2393: $i,SV1872: $i,SV1115: $i,SV258: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV258 )
| ( c_HOL_Oord__class_Oless @ SV1115 @ SV1872 @ SV258 )
| ( c_HOL_Oord__class_Oless @ SV1115 @ SV2393 @ SV258 )
| ~ ( c_HOL_Oord__class_Oless @ SV1115 @ ( c_Orderings_Oord__class_Omax @ SV2393 @ SV1872 @ SV258 ) @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4832]) ).
thf(5603,plain,
! [SV1873: $i,SV1118: $i,SV261: $i] :
( ( ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV261 ) ) @ SV1118 ) @ SV1873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV1118 )
| ~ ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV261 @ SV1118 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4833]) ).
thf(5604,plain,
! [SV2394: $i,SV1874: $i,SV1119: $i,SV262: $i] :
( ( ( c_List_Ofoldl @ SV262 @ SV1119 @ ( c_List_Olist_ONil @ SV1874 ) @ SV2394 @ SV1874 )
= SV1119 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4834]) ).
thf(5605,plain,
! [SV2395: $i,SV1875: $i,SV1120: $i,SV263: $i] :
( ( ( c_Nat_Onat_Onat__case @ SV263 @ SV1120 @ ( c_Suc @ SV1875 ) @ SV2395 )
= ( hAPP @ SV1120 @ SV1875 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4835]) ).
thf(5606,plain,
! [SV1876: $i,SV1121: $i,SV264: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV264 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV264 ) @ ( c_HOL_Otimes__class_Otimes @ SV1121 @ SV1121 @ SV264 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1876 @ SV1876 @ SV264 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4836]) ).
thf(5607,plain,
! [SV2396: $i,SV1877: $i,SV1122: $i,SV265: $i] :
( ( ! [SY6722: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV265 @ SV1122 @ tc_nat ) @ SV1877 @ tc_nat ) ) @ SV2396 ) @ SY6722 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV265 @ SV1877 @ tc_nat ) ) @ SV2396 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV1877 @ tc_nat ) ) @ SY6722 ) @ tc_nat )
| ~ ( c_lessequals @ SV1122 @ SV265 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4837]) ).
thf(5608,plain,
! [SV2397: $i,SV1878: $i,SV1123: $i,SV266: $i] :
( ( ! [SY6723: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV266 @ SV1123 @ tc_nat ) ) @ SV1878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2397 @ SV1123 @ tc_nat ) ) @ SY6723 ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV266 @ SV2397 @ tc_nat ) @ SV1123 @ tc_nat ) ) @ SV1878 ) @ SY6723 @ tc_nat )
| ~ ( c_lessequals @ SV2397 @ SV266 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4838]) ).
thf(5609,plain,
! [SV2398: $i,SV1879: $i,SV1124: $i,SV267: $i] :
( ( ! [SY6724: $i] :
( ( c_lessequals @ SV267 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1124 @ SV1879 @ tc_nat ) @ SV2398 @ tc_nat ) ) @ SY6724 ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1879 @ SV2398 @ tc_nat ) ) @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1124 @ SV2398 @ tc_nat ) ) @ SY6724 ) @ tc_nat )
| ~ ( c_lessequals @ SV1879 @ SV1124 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4839]) ).
thf(5610,plain,
! [SV2399: $i,SV1880: $i,SV1125: $i,SV268: $i] :
( ( ! [SY6725: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SV1125 @ tc_nat ) ) @ SV1880 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2399 @ SV1125 @ tc_nat ) ) @ SY6725 ) @ tc_nat )
| ~ ( c_lessequals @ SV1880 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2399 @ SV268 @ tc_nat ) @ SV1125 @ tc_nat ) ) @ SY6725 ) @ tc_nat )
| ~ ( c_lessequals @ SV268 @ SV2399 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4840]) ).
thf(5611,plain,
! [SV1881: $i,SV1126: $i,SV269: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV269 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SV1126 @ SV1881 @ tc_nat ) @ SV269 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1126 @ SV269 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1881 @ SV269 ) @ SV269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4841]) ).
thf(5612,plain,
! [SV2400: $i,SV1882: $i,SV1127: $i,SV270: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV270 )
| ( c_HOL_Oord__class_Oless @ SV1127 @ SV1882 @ SV270 )
| ( c_HOL_Oord__class_Oless @ SV2400 @ SV1882 @ SV270 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV2400 @ SV1127 @ SV270 ) @ SV1882 @ SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4842]) ).
thf(5613,plain,
! [SV1883: $i,SV1129: $i,SV272: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV272 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1129 ) @ SV1883 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
| ~ ( c_HOL_Oord__class_Oless @ SV1883 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
| ~ ( c_lessequals @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4843]) ).
thf(5614,plain,
! [SV1884: $i,SV1130: $i,SV273: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV273 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV1130 ) @ SV1884 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
| ~ ( c_lessequals @ SV1884 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
| ~ ( c_HOL_Oord__class_Oless @ SV1130 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4844]) ).
thf(5615,plain,
! [SV1131: $i,SV274: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV274 @ SV1131 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV274 @ ( c_Suc @ SV1131 ) @ tc_nat ) )
= $true )
| ( ( SV274 = SV1131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4845]) ).
thf(5616,plain,
! [SV275: $i,SV1132: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1132 @ ( c_Suc @ SV275 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1132 @ SV275 @ tc_nat )
= $true )
| ( ( SV275 = SV1132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4846]) ).
thf(5617,plain,
! [SV1133: $i,SV276: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV276 @ ( c_Suc @ SV1133 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV276 @ SV1133 @ tc_nat )
= $true )
| ( ( SV276 = SV1133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4847]) ).
thf(5618,plain,
! [SV1885: $i,SV1134: $i,SV278: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV278 ) @ SV1134 ) @ SV1885 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV278 ) @ ( c_HOL_Ominus__class_Ominus @ SV1134 @ SV1885 @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1885 @ SV1134 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4849]) ).
thf(5619,plain,
! [SV1886: $i,SV1135: $i,SV279: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV279 ) @ SV1135 ) @ SV1886 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV279 @ SV1886 @ tc_nat ) ) @ SV1135 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1886 @ SV279 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4850]) ).
thf(5620,plain,
! [SV2401: $i,SV1887: $i,SV1136: $i,SV280: $i] :
( ( ! [SY6726: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV280 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1136 @ SV1887 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SV2401 @ SY6726 @ SV280 ) @ SV280 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1136 @ SV2401 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SV1887 @ SY6726 @ SV280 ) @ SV280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4851]) ).
thf(5621,plain,
! [SV2402: $i,SV1888: $i,SV1137: $i,SV281: $i] :
( ( ! [SY6727: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV281 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1137 @ SV1888 @ SV281 ) @ ( c_HOL_Otimes__class_Otimes @ SV2402 @ SY6727 @ SV281 ) @ SV281 )
= ( c_HOL_Otimes__class_Otimes @ SV1137 @ ( c_HOL_Otimes__class_Otimes @ SV1888 @ ( c_HOL_Otimes__class_Otimes @ SV2402 @ SY6727 @ SV281 ) @ SV281 ) @ SV281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4852]) ).
thf(5622,plain,
! [SV2403: $i,SV1889: $i,SV1138: $i,SV282: $i] :
( ( ! [SY6728: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV282 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1138 @ SV1889 @ SV282 ) @ ( c_HOL_Otimes__class_Otimes @ SV2403 @ SY6728 @ SV282 ) @ SV282 )
= ( c_HOL_Otimes__class_Otimes @ SV2403 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1138 @ SV1889 @ SV282 ) @ SY6728 @ SV282 ) @ SV282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4853]) ).
thf(5623,plain,
! [SV1890: $i,SV1139: $i,SV283: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_HOL_Ominus__class_Ominus @ SV1139 @ SV1890 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV283 ) @ SV1890 ) @ SV1139 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1890 @ SV1139 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4854]) ).
thf(5624,plain,
! [SV1891: $i,SV1140: $i,SV284: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV284 @ SV1140 @ tc_nat ) @ SV1891 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV284 @ SV1891 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4855]) ).
thf(5625,plain,
! [SV2404: $i,SV1892: $i,SV1141: $i,SV285: $i] :
( ( ( c_Type_Otype_Otype__rec @ SV285 @ SV1141 @ ( c_Type_Otype_OAtom @ SV1892 ) @ SV2404 )
= ( hAPP @ SV285 @ SV1892 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4856]) ).
thf(5626,plain,
! [SV1893: $i,SV1142: $i,SV286: $i] :
( ( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV286 @ SV1142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1893 @ SV1142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV286 @ SV1893 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4857]) ).
thf(5627,plain,
! [SV1894: $i,SV1144: $i,SV288: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV288 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1144 @ SV1894 @ SV288 )
| ( c_lessequals @ SV1894 @ SV1144 @ SV288 )
| ~ ( c_lessequals @ SV1144 @ SV1894 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4858]) ).
thf(5628,plain,
! [SV1145: $i,SV291: $i] :
( ( ( class_Orderings_Oorder @ SV291 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1145 @ SV1145 @ SV291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4859]) ).
thf(5629,plain,
! [SV1146: $i,SV292: $i] :
( ( ( class_Orderings_Olinorder @ SV292 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1146 @ SV1146 @ SV292 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4860]) ).
thf(5630,plain,
! [SV1147: $i,SV293: $i] :
( ( ( class_Orderings_Opreorder @ SV293 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1147 @ SV1147 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4861]) ).
thf(5631,plain,
! [SV1148: $i,SV294: $i] :
( ( ( c_lessequals @ SV294 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1148 ) @ SV294 ) @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1148 ) @ SV294 ) @ SV294 @ tc_nat )
= SV1148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4862]) ).
thf(5632,plain,
! [SV1149: $i,SV295: $i] :
( ( ( class_Orderings_Olinorder @ SV295 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1149 @ SV1149 @ SV295 )
= SV1149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4863]) ).
thf(5633,plain,
! [SV1895: $i,SV1151: $i,SV297: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV297 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV297 ) @ SV1151 ) @ SV1895 ) @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1895 @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1151 @ SV297 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4864]) ).
thf(5634,plain,
! [SV1896: $i,SV1156: $i,SV302: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV302 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV1156 @ SV1896 @ SV302 ) @ SV302 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV302 ) @ SV1156 ) @ ( c_List_Olistsum @ SV1896 @ SV302 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4865]) ).
thf(5635,plain,
! [SV1897: $i,SV1157: $i,SV303: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV303 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1157 @ SV1897 @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV1897 @ SV1157 @ SV303 )
| ( SV1897 = SV1157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4866]) ).
thf(5636,plain,
! [SV1898: $i,SV1158: $i,SV304: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV304 ) )
= $true )
| ( ( ( SV1158 = SV1898 )
| ( c_HOL_Oord__class_Oless @ SV1898 @ SV1158 @ SV304 )
| ( c_HOL_Oord__class_Oless @ SV1158 @ SV1898 @ SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4867]) ).
thf(5637,plain,
! [SV305: $i,SV1159: $i] :
( ( ( ~ ( c_lessequals @ SV1159 @ SV305 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV305 @ SV1159 @ tc_nat ) )
= $true )
| ( ( SV305 = SV1159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4868]) ).
thf(5638,plain,
! [SV306: $i,SV1160: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1160 @ SV306 @ tc_nat )
= $true )
| ( ( SV1160 = SV306 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV306 @ SV1160 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4869]) ).
thf(5639,plain,
! [SV1899: $i,SV1161: $i,SV307: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV307 @ SV1161 ) @ SV1899 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1161 @ SV1899 @ tc_nat )
| ( SV1899 = SV1161 )
| ( c_HOL_Oord__class_Oless @ SV1899 @ SV1161 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4870]) ).
thf(5640,plain,
! [SV2405: $i,SV1900: $i,SV1162: $i,SV308: $i] :
( ( ! [SY6729: $i] :
( ( SV308 = SV1162 )
| ~ ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2405 ) @ SY6729 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1162 )
| ~ ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2405 ) @ SY6729 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4871]) ).
thf(5641,plain,
! [SV309: $i,SV1163: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1163 @ SV309 @ tc_nat )
= $true )
| ( ( SV1163 = SV309 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV309 @ SV1163 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4872]) ).
thf(5642,plain,
! [SV1901: $i,SV1164: $i,SV310: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV310 ) )
= $true )
| ( ( ( SV1164 = SV1901 )
| ~ ( c_lessequals @ SV1901 @ SV1164 @ SV310 )
| ~ ( c_lessequals @ SV1164 @ SV1901 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4873]) ).
thf(5643,plain,
! [SV1902: $i,SV1165: $i,SV311: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV311 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1165 @ SV1902 @ SV311 )
| ( c_HOL_Oord__class_Oless @ SV1902 @ SV1165 @ SV311 )
| ( SV1902 = SV1165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4874]) ).
thf(5644,plain,
! [SV1903: $i,SV1166: $i,SV312: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV312 ) )
= $true )
| ( ( ( SV1166 = SV1903 )
| ~ ( c_lessequals @ SV1903 @ SV1166 @ SV312 )
| ~ ( c_lessequals @ SV1166 @ SV1903 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4875]) ).
thf(5645,plain,
! [SV1904: $i,SV1167: $i,SV313: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV313 ) )
= $true )
| ( ( ( SV1167 = SV1904 )
| ~ ( c_lessequals @ SV1167 @ SV1904 @ SV313 )
| ~ ( c_lessequals @ SV1904 @ SV1167 @ SV313 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4876]) ).
thf(5646,plain,
! [SV2406: $i,SV1905: $i,SV1168: $i,SV314: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV314 @ SV1168 @ SV1905 ) @ ( c_List_Oreplicate @ SV2406 @ SV1168 @ SV1905 ) @ SV1905 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV2406 @ SV1168 @ SV1905 ) @ ( c_List_Oreplicate @ SV314 @ SV1168 @ SV1905 ) @ SV1905 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4877]) ).
thf(5647,plain,
! [SV1906: $i,SV1169: $i,SV315: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV315 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1169 @ SV1906 @ SV315 )
| ( SV1906 = SV1169 )
| ( c_HOL_Oord__class_Oless @ SV1906 @ SV1169 @ SV315 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4878]) ).
thf(5648,plain,
! [SV1907: $i,SV1170: $i,SV316: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV316 ) )
= $true )
| ( ( ( SV1170 = SV1907 )
| ( c_HOL_Oord__class_Oless @ SV1170 @ SV1907 @ SV316 )
| ( c_HOL_Oord__class_Oless @ SV1907 @ SV1170 @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4879]) ).
thf(5649,plain,
! [SV1908: $i,SV1171: $i,SV317: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV317 ) )
= $true )
| ( ( ( c_lessequals @ SV1171 @ SV1908 @ SV317 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1908 @ SV317 ) @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4880]) ).
thf(5650,plain,
! [SV1909: $i,SV1172: $i,SV318: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV318 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1172 @ SV1909 @ SV318 ) @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV318 )
| ~ ( c_lessequals @ SV1172 @ SV1909 @ SV318 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4881]) ).
thf(5651,plain,
! [SV1173: $i,SV319: $i] :
( ( ( class_Orderings_Olinorder @ SV319 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1173 @ SV1173 @ SV319 )
= SV1173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4882]) ).
thf(5652,plain,
! [SV2407: $i,SV1910: $i,SV1174: $i,SV320: $i] :
( ( ! [SY6730: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV1174 ) @ SV1910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV2407 ) @ SY6730 ) @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SV1910 @ SY6730 @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SV2407 @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4883]) ).
thf(5653,plain,
! [SV2408: $i,SV1911: $i,SV1175: $i,SV321: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV1175 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1911 ) @ SV2408 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1175 @ SV2408 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV321 @ SV1911 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4884]) ).
thf(5654,plain,
! [SV1176: $i,SV322: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV322 @ SV1176 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV322 @ SV1176 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4885]) ).
thf(5655,plain,
! [SV1177: $i,SV323: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV323 @ SV1177 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV323 @ SV1177 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4886]) ).
thf(5656,plain,
! [SV1912: $i,SV1178: $i,SV324: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV324 ) )
= $true )
| ( ( ( c_lessequals @ SV1178 @ SV1912 @ SV324 )
| ~ ( c_HOL_Oord__class_Oless @ SV1178 @ SV1912 @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4887]) ).
thf(5657,plain,
! [SV1913: $i,SV1179: $i,SV325: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV325 ) )
= $true )
| ( ( ( c_lessequals @ SV1179 @ SV1913 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV1179 @ SV1913 @ SV325 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4888]) ).
thf(5658,plain,
! [SV2409: $i,SV1914: $i,SV1180: $i,SV326: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV326 )
| ( c_HOL_Oord__class_Oless @ SV1180 @ SV1914 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ SV1180 @ ( c_Orderings_Oord__class_Omin @ SV1914 @ SV2409 @ SV326 ) @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4889]) ).
thf(5659,plain,
! [SV2410: $i,SV1915: $i,SV1181: $i,SV327: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV327 )
| ( c_HOL_Oord__class_Oless @ SV1181 @ SV1915 @ SV327 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_Orderings_Oord__class_Omin @ SV2410 @ SV1915 @ SV327 ) @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4890]) ).
thf(5660,plain,
! [SV2411: $i,SV1916: $i,SV1182: $i,SV328: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV328 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1182 @ SV1916 @ SV328 ) @ SV2411 @ SV328 )
| ~ ( c_HOL_Oord__class_Oless @ SV1182 @ SV2411 @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4891]) ).
thf(5661,plain,
! [SV2412: $i,SV1917: $i,SV1183: $i,SV329: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV329 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1183 @ SV1917 @ SV329 ) @ SV2412 @ SV329 )
| ~ ( c_HOL_Oord__class_Oless @ SV1917 @ SV2412 @ SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4892]) ).
thf(5662,plain,
! [SV1918: $i,SV1184: $i,SV330: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV330 @ SV1184 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1918 @ SV1184 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV330 @ SV1918 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1184 @ SV1918 @ tc_nat )
| ~ ( c_lessequals @ SV1184 @ SV330 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4893]) ).
thf(5663,plain,
! [SV1920: $i,SV1186: $i,SV332: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV332 ) @ SV1186 ) @ SV1920 ) @ SV332 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1920 @ SV332 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1186 @ SV332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4895]) ).
thf(5664,plain,
! [SV1921: $i,SV1187: $i,SV333: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV333 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV333 ) @ SV1187 ) @ SV1921 ) @ SV333 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1921 @ SV333 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1187 @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4896]) ).
thf(5665,plain,
! [SV1922: $i,SV1188: $i,SV334: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV334 @ SV1188 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1922 @ SV1188 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1188 @ SV334 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV334 @ SV1922 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4897]) ).
thf(5666,plain,
! [SV1923: $i,SV1189: $i,SV335: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV335 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1189 @ SV1923 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
| ~ ( c_lessequals @ SV1923 @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV1189 @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4898]) ).
thf(5667,plain,
! [SV1924: $i,SV1190: $i,SV336: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV336 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1190 @ SV1924 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV1924 @ SV336 )
| ~ ( c_lessequals @ SV1190 @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4899]) ).
thf(5668,plain,
! [SV1925: $i,SV1191: $i,SV337: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV337 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1191 @ SV1925 @ SV337 ) @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
| ~ ( c_lessequals @ SV1925 @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV1191 @ SV337 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4900]) ).
thf(5669,plain,
! [SV1926: $i,SV1192: $i,SV338: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV338 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1192 @ SV1926 @ SV338 ) @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV1926 @ SV338 )
| ~ ( c_lessequals @ SV1192 @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4901]) ).
thf(5670,plain,
! [SV1927: $i,SV1193: $i,SV339: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV339 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1193 @ SV1927 @ SV339 ) @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
| ~ ( c_lessequals @ SV1927 @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV1193 @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4902]) ).
thf(5671,plain,
! [SV1928: $i,SV1194: $i,SV340: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV340 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1928 @ SV340 ) @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV1928 @ SV340 )
| ~ ( c_lessequals @ SV1194 @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4903]) ).
thf(5672,plain,
! [SV1929: $i,SV1195: $i,SV341: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV341 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1195 @ SV1929 @ SV341 ) @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
| ~ ( c_lessequals @ SV1195 @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV1929 @ SV341 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4904]) ).
thf(5673,plain,
! [SV1196: $i,SV342: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV342 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1196 @ SV1196 @ SV342 ) @ ( c_HOL_Ozero__class_Ozero @ SV342 ) @ SV342 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4905]) ).
thf(5674,plain,
! [SV1930: $i,SV1197: $i,SV343: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV343 ) @ SV1197 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV343 ) @ SV1930 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1197 @ SV1930 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4906]) ).
thf(5675,plain,
! [SV1931: $i,SV1198: $i,SV344: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV344 @ SV1198 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1931 ) @ SV344 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1931 ) @ SV1198 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4907]) ).
thf(5676,plain,
! [SV1199: $i,SV345: $i] :
( ( ( ( c_Suc @ SV345 )
= SV1199 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV345 @ SV1199 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV345 ) @ SV1199 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4908]) ).
thf(5677,plain,
! [SV1200: $i,SV346: $i] :
( ( ( c_lessequals @ SV346 @ SV1200 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV1200 ) @ SV346 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4909]) ).
thf(5678,plain,
! [SV2413: $i,SV1932: $i,SV1202: $i,SV348: $i] :
( ( ( c_List_Olist_OCons @ SV348 @ ( c_List_Oappend @ SV1202 @ SV1932 @ SV2413 ) @ SV2413 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV348 @ SV1202 @ SV2413 ) @ SV1932 @ SV2413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4911]) ).
thf(5679,plain,
! [SV2414: $i,SV1933: $i,SV1203: $i,SV349: $i] :
( ( ( c_List_Olist_OCons @ SV349 @ ( c_List_Oappend @ SV1203 @ SV1933 @ SV2414 ) @ SV2414 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV349 @ SV1203 @ SV2414 ) @ SV1933 @ SV2414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4912]) ).
thf(5680,plain,
! [SV2415: $i,SV1934: $i,SV1204: $i,SV350: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV350 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ ( c_Orderings_Oord__class_Omin @ SV1204 @ SV1934 @ SV350 ) ) @ SV2415 )
= ( c_Orderings_Oord__class_Omin @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV1204 ) @ SV2415 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV1934 ) @ SV2415 ) @ SV350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4913]) ).
thf(5681,plain,
! [SV1935: $i,SV1205: $i,SV351: $i] :
( ( ( c_lessequals @ SV351 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1205 ) @ SV351 ) @ SV1935 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1935 @ SV1205 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4914]) ).
thf(5682,plain,
! [SV2416: $i,SV1936: $i,SV1206: $i,SV352: $i] :
( ( ! [SY6731: $i,SY6732: $i,SY6733: $i,SY6734: $i,SY6735: $i] :
( ( ( hAPP @ ( hAPP @ SV352 @ ( hAPP @ ( hAPP @ SV1206 @ SV1936 ) @ SV2416 ) ) @ SY6731 )
= ( hAPP @ ( hAPP @ SV1206 @ ( hAPP @ ( hAPP @ SV352 @ SV1936 ) @ SY6731 ) ) @ ( hAPP @ ( hAPP @ SV352 @ SV2416 ) @ SY6731 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6732 @ SV1206 @ SV352 @ SY6733 @ SY6734 @ SY6735 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4915]) ).
thf(5683,plain,
! [SV2417: $i,SV1937: $i,SV1207: $i,SV353: $i] :
( ( ! [SY6736: $i,SY6737: $i,SY6738: $i,SY6739: $i,SY6740: $i] :
( ( ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ ( hAPP @ ( hAPP @ SV1937 @ SV2417 ) @ SY6736 ) )
= ( hAPP @ ( hAPP @ SV1937 @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2417 ) ) @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SY6736 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1937 @ SV353 @ SY6737 @ SY6738 @ SY6739 @ SY6740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4916]) ).
thf(5684,plain,
! [SV2418: $i,SV1938: $i,SV1208: $i,SV354: $i] :
( ( ! [SY6741: $i,SY6742: $i,SY6743: $i,SY6744: $i] :
( ( ( hAPP @ ( hAPP @ SV354 @ SV1208 ) @ SV1938 )
= ( hAPP @ ( hAPP @ SV354 @ SV1938 ) @ SV1208 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2418 @ SV354 @ SY6741 @ SY6742 @ SY6743 @ SY6744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4917]) ).
thf(5685,plain,
! [SV2419: $i,SV1939: $i,SV1209: $i,SV355: $i] :
( ( ! [SY6745: $i,SY6746: $i,SY6747: $i,SY6748: $i,SY6749: $i] :
( ( ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ ( hAPP @ ( hAPP @ SV355 @ SV1939 ) @ SV2419 ) )
= ( hAPP @ ( hAPP @ SV355 @ ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ SV1939 ) ) @ SV2419 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6745 @ SV355 @ SY6746 @ SY6747 @ SY6748 @ SY6749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4918]) ).
thf(5686,plain,
! [SV2420: $i,SV1940: $i,SV1210: $i,SV356: $i] :
( ( ! [SY6750: $i,SY6751: $i,SY6752: $i] :
( ( ( hAPP @ ( hAPP @ SV356 @ SV1210 ) @ SV1940 )
= SV1940 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2420 @ SV356 @ SY6750 @ SY6751 @ SV1210 @ SY6752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4919]) ).
thf(5687,plain,
! [SV2421: $i,SV1941: $i,SV1211: $i,SV357: $i] :
( ( ! [SY6753: $i,SY6754: $i,SY6755: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV1211 ) @ SV1941 )
= SV1211 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2421 @ SV357 @ SY6753 @ SV1211 @ SY6754 @ SY6755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4920]) ).
thf(5688,plain,
! [SV2422: $i,SV1942: $i,SV1212: $i,SV358: $i] :
( ( ! [SY6756: $i,SY6757: $i,SY6758: $i,SY6759: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV1212 ) @ SV1942 )
= ( hAPP @ ( hAPP @ SV358 @ SV1942 ) @ SV1212 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV358 @ SV2422 @ SY6756 @ SY6757 @ SY6758 @ SY6759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4921]) ).
thf(5689,plain,
! [SV2423: $i,SV1943: $i,SV1213: $i,SV359: $i] :
( ( ! [SY6760: $i,SY6761: $i,SY6762: $i,SY6763: $i,SY6764: $i] :
( ( ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ ( hAPP @ ( hAPP @ SV359 @ SV1943 ) @ SV2423 ) )
= ( hAPP @ ( hAPP @ SV359 @ ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ SV1943 ) ) @ SV2423 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV359 @ SY6760 @ SY6761 @ SY6762 @ SY6763 @ SY6764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4922]) ).
thf(5690,plain,
! [SV2424: $i,SV1944: $i,SV1214: $i,SV360: $i] :
( ( ! [SY6765: $i,SY6766: $i,SY6767: $i] :
( ( ( hAPP @ ( hAPP @ SV360 @ SV1214 ) @ SV1944 )
= SV1944 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV360 @ SV2424 @ SY6765 @ SV1214 @ SY6766 @ SY6767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4923]) ).
thf(5691,plain,
! [SV2425: $i,SV1945: $i,SV1215: $i,SV361: $i] :
( ( ! [SY6768: $i,SY6769: $i,SY6770: $i,SY6771: $i,SY6772: $i] :
( ( ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ ( hAPP @ ( hAPP @ SV361 @ SV1945 ) @ SV2425 ) )
= ( hAPP @ ( hAPP @ SV361 @ ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ SV1945 ) ) @ SV2425 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV361 @ SY6768 @ SY6769 @ SY6770 @ SY6771 @ SY6772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4924]) ).
thf(5692,plain,
! [SV2426: $i,SV1946: $i,SV1216: $i,SV362: $i] :
( ( ! [SY6773: $i,SY6774: $i,SY6775: $i,SY6776: $i] :
( ( ( hAPP @ ( hAPP @ SV362 @ SV1216 ) @ SV1946 )
= ( hAPP @ ( hAPP @ SV362 @ SV1946 ) @ SV1216 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV362 @ SV2426 @ SY6773 @ SY6774 @ SY6775 @ SY6776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4925]) ).
thf(5693,plain,
! [SV2427: $i,SV1947: $i,SV1217: $i,SV363: $i] :
( ( ! [SY6777: $i,SY6778: $i,SY6779: $i,SY6780: $i,SY6781: $i] :
( ( ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV1947 ) ) @ SV2427 )
= ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV2427 ) ) @ SV1947 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV363 @ SY6777 @ SY6778 @ SY6779 @ SY6780 @ SY6781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4926]) ).
thf(5694,plain,
! [SV2428: $i,SV1948: $i,SV1218: $i,SV364: $i] :
( ( ! [SY6782: $i,SY6783: $i,SY6784: $i,SY6785: $i,SY6786: $i] :
( ( ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ SV2428 ) )
= ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ SV2428 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV364 @ SY6782 @ SY6783 @ SY6784 @ SY6785 @ SY6786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4927]) ).
thf(5695,plain,
! [SV2429: $i,SV1949: $i,SV1219: $i,SV365: $i] :
( ( ! [SY6787: $i,SY6788: $i,SY6789: $i,SY6790: $i,SY6791: $i] :
( ( ( hAPP @ ( hAPP @ SV365 @ ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ SV1949 ) ) @ SV2429 )
= ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ ( hAPP @ ( hAPP @ SV365 @ SV1949 ) @ SV2429 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV365 @ SY6787 @ SY6788 @ SY6789 @ SY6790 @ SY6791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4928]) ).
thf(5696,plain,
! [SV2430: $i,SV1950: $i,SV1220: $i,SV366: $i] :
( ( ! [SY6792: $i,SY6793: $i,SY6794: $i,SY6795: $i,SY6796: $i,SY6797: $i] :
( ( ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV1950 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV2430 ) @ SY6792 ) )
= ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV2430 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV1950 ) @ SY6792 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV366 @ SY6793 @ SY6794 @ SY6795 @ SY6796 @ SY6797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4929]) ).
thf(5697,plain,
! [SV2431: $i,SV1951: $i,SV1221: $i,SV367: $i] :
( ( ! [SY6798: $i,SY6799: $i,SY6800: $i,SY6801: $i,SY6802: $i] :
( ( ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ SV2431 ) )
= ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ SV2431 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6798 @ SV367 @ SY6799 @ SY6800 @ SY6801 @ SY6802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4930]) ).
thf(5698,plain,
! [SV2432: $i,SV1952: $i,SV1222: $i,SV368: $i] :
( ( ! [SY6803: $i,SY6804: $i,SY6805: $i,SY6806: $i,SY6807: $i] :
( ( ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ ( hAPP @ ( hAPP @ SV368 @ SV1952 ) @ SV2432 ) )
= ( hAPP @ ( hAPP @ SV368 @ ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ SV1952 ) ) @ SV2432 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6803 @ SV368 @ SY6804 @ SY6805 @ SY6806 @ SY6807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4931]) ).
thf(5699,plain,
! [SV2433: $i,SV1953: $i,SV1223: $i,SV369: $i] :
( ( ! [SY6808: $i,SY6809: $i,SY6810: $i,SY6811: $i,SY6812: $i] :
( ( ( hAPP @ ( hAPP @ SV369 @ ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ SV1953 ) ) @ SV2433 )
= ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ ( hAPP @ ( hAPP @ SV369 @ SV1953 ) @ SV2433 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6808 @ SV369 @ SY6809 @ SY6810 @ SY6811 @ SY6812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4932]) ).
thf(5700,plain,
! [SV2434: $i,SV1954: $i,SV1224: $i,SV370: $i] :
( ( ! [SY6813: $i,SY6814: $i,SY6815: $i,SY6816: $i,SY6817: $i] :
( ( ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV1954 ) ) @ SV2434 )
= ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV2434 ) ) @ SV1954 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6813 @ SV370 @ SY6814 @ SY6815 @ SY6816 @ SY6817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4933]) ).
thf(5701,plain,
! [SV2435: $i,SV1955: $i,SV1225: $i,SV371: $i] :
( ( ! [SY6818: $i,SY6819: $i,SY6820: $i,SY6821: $i,SY6822: $i,SY6823: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ SY6818 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ SY6818 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6819 @ SV371 @ SY6820 @ SY6821 @ SY6822 @ SY6823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4934]) ).
thf(5702,plain,
! [SV2436: $i,SV1956: $i,SV1226: $i,SV372: $i] :
( ( ! [SY6824: $i,SY6825: $i,SY6826: $i,SY6827: $i,SY6828: $i,SY6829: $i] :
( ( ( hAPP @ ( hAPP @ SV372 @ ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ SV1956 ) ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SY6824 ) )
= ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ ( hAPP @ ( hAPP @ SV372 @ SV1956 ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SY6824 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6825 @ SV372 @ SY6826 @ SY6827 @ SY6828 @ SY6829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4935]) ).
thf(5703,plain,
! [SV2437: $i,SV1957: $i,SV1227: $i,SV373: $i] :
( ( ! [SY6830: $i,SY6831: $i,SY6832: $i,SY6833: $i,SY6834: $i,SY6835: $i] :
( ( ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV1957 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV2437 ) @ SY6830 ) )
= ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV2437 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV1957 ) @ SY6830 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6831 @ SV373 @ SY6832 @ SY6833 @ SY6834 @ SY6835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4936]) ).
thf(5704,plain,
! [SV2438: $i,SV1958: $i,SV1228: $i,SV374: $i] :
( ( ! [SY6836: $i,SY6837: $i,SY6838: $i] :
( ( ( hAPP @ ( hAPP @ SV374 @ SV1228 ) @ SV1958 )
= SV1228 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2438 @ SV374 @ SY6836 @ SY6837 @ SV1958 @ SY6838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4937]) ).
thf(5705,plain,
! [SV2439: $i,SV1959: $i,SV1229: $i,SV375: $i] :
( ( ! [SY6839: $i,SY6840: $i,SY6841: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV1229 ) @ SV1959 )
= SV1959 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2439 @ SV375 @ SY6839 @ SY6840 @ SV1229 @ SY6841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4938]) ).
thf(5706,plain,
! [SV2440: $i,SV1960: $i,SV1230: $i,SV376: $i] :
( ( ! [SY6842: $i,SY6843: $i,SY6844: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ SV1230 ) @ SV1960 )
= SV1960 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2440 @ SV376 @ SY6842 @ SV1960 @ SY6843 @ SY6844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4939]) ).
thf(5707,plain,
! [SV2441: $i,SV1961: $i,SV1231: $i,SV377: $i] :
( ( ! [SY6845: $i,SY6846: $i,SY6847: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SV1231 ) @ SV1961 )
= SV1231 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2441 @ SV377 @ SY6845 @ SV1231 @ SY6846 @ SY6847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4940]) ).
thf(5708,plain,
! [SV2442: $i,SV1962: $i,SV1232: $i,SV378: $i] :
( ( ! [SY6848: $i,SY6849: $i,SY6850: $i,SY6851: $i,SY6852: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ ( hAPP @ ( hAPP @ SV1232 @ SV1962 ) @ SV2442 ) ) @ SY6848 )
= ( hAPP @ ( hAPP @ SV1232 @ ( hAPP @ ( hAPP @ SV378 @ SV1962 ) @ SY6848 ) ) @ ( hAPP @ ( hAPP @ SV378 @ SV2442 ) @ SY6848 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1232 @ SV378 @ SY6849 @ SY6850 @ SY6851 @ SY6852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4941]) ).
thf(5709,plain,
! [SV2443: $i,SV1963: $i,SV1233: $i,SV379: $i] :
( ( ! [SY6853: $i,SY6854: $i,SY6855: $i,SY6856: $i] :
( ( ( hAPP @ ( hAPP @ SV379 @ SV1233 ) @ SV1963 )
= ( hAPP @ ( hAPP @ SV379 @ SV1963 ) @ SV1233 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2443 @ SV379 @ SY6853 @ SY6854 @ SY6855 @ SY6856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4942]) ).
thf(5710,plain,
! [SV2444: $i,SV1964: $i,SV1234: $i,SV380: $i] :
( ( ! [SY6857: $i,SY6858: $i,SY6859: $i] :
( ( ( hAPP @ ( hAPP @ SV380 @ SV1234 ) @ SV1964 )
= SV1234 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV380 @ SV2444 @ SY6857 @ SV1964 @ SY6858 @ SY6859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4943]) ).
thf(5711,plain,
! [SV2445: $i,SV1965: $i,SV1235: $i,SV381: $i] :
( ( ! [SY6860: $i,SY6861: $i,SY6862: $i] :
( ( ( hAPP @ ( hAPP @ SV381 @ SV1235 ) @ SV1965 )
= SV1965 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV381 @ SV2445 @ SY6860 @ SV1235 @ SY6861 @ SY6862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4944]) ).
thf(5712,plain,
! [SV2446: $i,SV1966: $i,SV1236: $i,SV382: $i] :
( ( ! [SY6863: $i,SY6864: $i,SY6865: $i] :
( ( ( hAPP @ ( hAPP @ SV382 @ SV1236 ) @ SV1236 )
= ( hAPP @ ( hAPP @ SV1966 @ ( hAPP @ ( hAPP @ SV382 @ SV2446 ) @ SV2446 ) ) @ SV1236 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV382 @ SV1966 @ SY6863 @ SY6864 @ SV2446 @ SY6865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4945]) ).
thf(5713,plain,
! [SV2447: $i,SV1967: $i,SV1237: $i,SV383: $i] :
( ( ! [SY6866: $i,SY6867: $i,SY6868: $i,SY6869: $i] :
( ( ( hAPP @ ( hAPP @ SV383 @ SV1237 ) @ ( hAPP @ ( hAPP @ SV1967 @ SV2447 ) @ SV1237 ) )
= ( hAPP @ ( hAPP @ SV1967 @ ( hAPP @ ( hAPP @ SV383 @ SV2447 ) @ SY6866 ) ) @ SV1237 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV383 @ SV1967 @ SY6867 @ SY6868 @ SY6866 @ SY6869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4946]) ).
thf(5714,plain,
! [SV2448: $i,SV1968: $i,SV1238: $i,SV384: $i] :
( ( ! [SY6870: $i,SY6871: $i,SY6872: $i,SY6873: $i] :
( ( ( hAPP @ ( hAPP @ SV384 @ ( hAPP @ ( hAPP @ SV1238 @ SV1968 ) @ SV2448 ) ) @ SV2448 )
= ( hAPP @ ( hAPP @ SV1238 @ ( hAPP @ ( hAPP @ SV384 @ SV1968 ) @ SY6870 ) ) @ SV2448 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV384 @ SV1238 @ SY6871 @ SY6872 @ SY6870 @ SY6873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4947]) ).
thf(5715,plain,
! [SV2449: $i,SV1969: $i,SV1239: $i,SV385: $i] :
( ( ! [SY6874: $i,SY6875: $i,SY6876: $i,SY6877: $i,SY6878: $i] :
( ( ( hAPP @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ SV1239 @ SV1969 ) @ SV2449 ) ) @ ( hAPP @ ( hAPP @ SV1239 @ SY6874 ) @ SV2449 ) )
= ( hAPP @ ( hAPP @ SV1239 @ ( hAPP @ ( hAPP @ SV385 @ SV1969 ) @ SY6874 ) ) @ SV2449 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV385 @ SV1239 @ SY6875 @ SY6876 @ SY6877 @ SY6878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4948]) ).
thf(5716,plain,
! [SV2450: $i,SV1970: $i,SV1240: $i,SV386: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV386 @ ( c_Type_Otype_Otype__case @ SV1240 @ SV1970 @ ( c_Type_Otype_OAtom @ SV2450 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV386 @ ( hAPP @ SV1240 @ SV2450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4949]) ).
thf(5717,plain,
! [SV2451: $i,SV1971: $i,SV1241: $i,SV387: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV387 @ ( c_Type_Otype_Otype__case @ SV1241 @ SV1971 @ ( c_Type_Otype_OAtom @ SV2451 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV387 @ ( hAPP @ SV1241 @ SV2451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4950]) ).
thf(5718,plain,
! [SV1973: $i,SV1243: $i,SV389: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV389 ) @ SV1243 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV389 ) @ SV1973 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1243 @ SV1973 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4952]) ).
thf(5719,plain,
! [SV1974: $i,SV1244: $i,SV390: $i] :
( ( ( c_lessequals @ SV390 @ SV1244 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1974 ) @ SV390 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1974 ) @ SV1244 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4953]) ).
thf(5720,plain,
! [SV1975: $i,SV1245: $i,SV391: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV391 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV391 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV391 ) @ ( c_HOL_Otimes__class_Otimes @ SV1245 @ SV1245 @ SV391 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1975 @ SV1975 @ SV391 ) ) @ SV391 )
| ( SV1245
= ( c_HOL_Ozero__class_Ozero @ SV391 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4954]) ).
thf(5721,plain,
! [SV1976: $i,SV1246: $i,SV392: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV392 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV392 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV392 ) @ ( c_HOL_Otimes__class_Otimes @ SV1246 @ SV1246 @ SV392 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1976 @ SV1976 @ SV392 ) ) @ SV392 )
| ( SV1976
= ( c_HOL_Ozero__class_Ozero @ SV392 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4955]) ).
thf(5722,plain,
! [SV2452: $i,SV1977: $i,SV1247: $i,SV394: $i] :
( ( ! [SY6879: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV394 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1247 ) @ SV1977 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV2452 ) @ SY6879 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1247 ) @ SV2452 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1977 ) @ SY6879 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4957]) ).
thf(5723,plain,
! [SV1978: $i,SV1248: $i,SV395: $i] :
( ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV395 ) @ SV1248 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV395 ) @ SV1978 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV1248 @ SV1978 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4958]) ).
thf(5724,plain,
! [SV1979: $i,SV1249: $i,SV396: $i] :
( ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV396 ) @ SV1249 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1979 ) @ SV1249 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV396 @ SV1979 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4959]) ).
thf(5725,plain,
! [SV1250: $i,SV397: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV397 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1250 @ SV397 ) @ ( c_HOL_Ozero__class_Ozero @ SV397 ) @ SV397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4960]) ).
thf(5726,plain,
! [SV1980: $i,SV1251: $i,SV398: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV398 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1251 @ SV1980 @ SV398 )
= ( c_Orderings_Oord__class_Omax @ SV1980 @ SV1251 @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4961]) ).
thf(5727,plain,
! [SV2453: $i,SV1981: $i,SV1252: $i,SV400: $i] :
( ( ( c_List_Odrop @ SV400 @ ( c_List_Oreplicate @ SV1252 @ SV1981 @ SV2453 ) @ SV2453 )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ SV1252 @ SV400 @ tc_nat ) @ SV1981 @ SV2453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4962]) ).
thf(5728,plain,
! [SV2454: $i,SV1982: $i,SV1253: $i,SV401: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV401 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV1253 @ SV1982 @ SV401 ) @ ( c_Orderings_Oord__class_Omin @ SV1253 @ SV2454 @ SV401 ) @ SV401 ) @ ( c_Orderings_Oord__class_Omin @ SV1253 @ ( c_Orderings_Oord__class_Omax @ SV1982 @ SV2454 @ SV401 ) @ SV401 ) @ SV401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4963]) ).
thf(5729,plain,
! [SV1983: $i,SV1255: $i,SV404: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV404 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1255 @ ( c_Orderings_Oord__class_Omin @ SV1255 @ SV1983 @ SV404 ) @ SV404 )
= SV1255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4964]) ).
thf(5730,plain,
! [SV2455: $i,SV1984: $i,SV1256: $i,SV406: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV406 )
| ( c_HOL_Oord__class_Oless @ SV1256 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1256 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV1984 @ SV406 ) @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV2455 @ SV406 ) @ SV406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4965]) ).
thf(5731,plain,
! [SV2456: $i,SV1985: $i,SV1257: $i,SV407: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV407 )
| ( c_HOL_Oord__class_Oless @ SV1257 @ SV1985 @ SV407 )
| ( c_HOL_Oord__class_Oless @ SV1985 @ SV1257 @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2456 @ SV1985 @ SV407 ) @ ( c_HOL_Otimes__class_Otimes @ SV2456 @ SV1257 @ SV407 ) @ SV407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4966]) ).
thf(5732,plain,
! [SV2457: $i,SV1986: $i,SV1258: $i,SV408: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV408 )
| ( c_HOL_Oord__class_Oless @ SV1258 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV1258 @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1986 @ SV1258 @ SV408 ) @ ( c_HOL_Otimes__class_Otimes @ SV2457 @ SV1258 @ SV408 ) @ SV408 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4967]) ).
thf(5733,plain,
! [SV2458: $i,SV1987: $i,SV1259: $i,SV409: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV409 )
| ( c_HOL_Oord__class_Oless @ SV1259 @ SV1987 @ SV409 )
| ( c_HOL_Oord__class_Oless @ SV1987 @ SV1259 @ SV409 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1987 @ SV2458 @ SV409 ) @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SV2458 @ SV409 ) @ SV409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4968]) ).
thf(5734,plain,
! [SV410: $i,SV1260: $i] :
( ( ( c_lessequals @ SV1260 @ SV410 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV410 @ ( c_HOL_Ominus__class_Ominus @ SV410 @ SV1260 @ tc_nat ) @ tc_nat )
= SV1260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4969]) ).
thf(5735,plain,
! [SV1261: $i,SV411: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV411 @ SV1261 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV411 ) @ SV1261 )
= ( c_Lambda_OdB_OVar @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4970]) ).
thf(5736,plain,
! [SV1988: $i,SV1263: $i,SV413: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV413 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV1263 @ SV1988 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV413 ) @ SV1988 ) @ ( c_Suc @ SV1263 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1988 @ SV1263 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4972]) ).
thf(5737,plain,
! [SV1989: $i,SV1264: $i,SV414: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV414 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1264 @ SV1989 @ SV414 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1264 @ SV1989 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4973]) ).
thf(5738,plain,
! [SV1990: $i,SV1265: $i,SV415: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV415 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SV1990 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 )
| ~ ( c_HOL_Oord__class_Oless @ SV1265 @ SV1990 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4974]) ).
thf(5739,plain,
! [SV1991: $i,SV1266: $i,SV416: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV416 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1266 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1991 @ SV416 ) @ SV416 )
| ~ ( c_HOL_Oord__class_Oless @ SV1266 @ SV1991 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4975]) ).
thf(5740,plain,
! [SV1992: $i,SV1267: $i,SV417: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV417 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1267 @ SV1992 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1267 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1992 @ SV417 ) @ SV417 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4976]) ).
thf(5741,plain,
! [SV1993: $i,SV1268: $i,SV420: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV420 ) @ SV1268 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1993 @ SV1268 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV420 @ SV1993 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4977]) ).
thf(5742,plain,
! [SV2459: $i,SV1994: $i,SV1269: $i,SV421: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV1269 ) @ SV1994 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV2459 ) @ SV1994 ) @ SV421 )
| ~ ( c_lessequals @ SV1269 @ SV2459 @ SV421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4978]) ).
thf(5743,plain,
! [SV2460: $i,SV1995: $i,SV1270: $i,SV422: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
| ( c_lessequals @ SV1270 @ SV1995 @ SV422 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1270 ) @ SV2460 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1995 ) @ SV2460 ) @ SV422 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4979]) ).
thf(5744,plain,
! [SV2461: $i,SV1996: $i,SV1271: $i,SV423: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV423 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SV1996 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SV2461 ) @ SV423 )
| ~ ( c_lessequals @ SV1996 @ SV2461 @ SV423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4980]) ).
thf(5745,plain,
! [SV2462: $i,SV1997: $i,SV1272: $i,SV424: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
| ( c_lessequals @ SV1272 @ SV1997 @ SV424 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV2462 ) @ SV1272 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV2462 ) @ SV1997 ) @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4981]) ).
thf(5746,plain,
! [SV2463: $i,SV1998: $i,SV1273: $i,SV425: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV425 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV1273 ) @ SV1998 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV2463 ) @ SV1998 ) @ SV425 )
| ~ ( c_lessequals @ SV1273 @ SV2463 @ SV425 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4982]) ).
thf(5747,plain,
! [SV2464: $i,SV1999: $i,SV1274: $i,SV426: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV426 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SV1999 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SV2464 ) @ SV426 )
| ~ ( c_lessequals @ SV1999 @ SV2464 @ SV426 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4983]) ).
thf(5748,plain,
! [SV2000: $i,SV1275: $i,SV427: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV427 ) @ SV1275 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2000 ) @ SV1275 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV427 @ SV2000 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4984]) ).
thf(5749,plain,
! [SV2001: $i,SV1276: $i,SV428: $i] :
( ( ( c_lessequals @ SV428 @ SV1276 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2001 ) @ SV428 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2001 ) @ SV1276 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4985]) ).
thf(5750,plain,
! [SV2002: $i,SV1277: $i,SV429: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV429 ) @ SV1277 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV429 ) @ SV2002 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1277 @ SV2002 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4986]) ).
thf(5751,plain,
! [SV1278: $i,SV430: $i] :
( ( ( c_lessequals @ SV430 @ SV1278 @ tc_nat )
= $false )
| ( ( SV1278
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1278 @ SV430 @ tc_nat ) ) @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4987]) ).
thf(5752,plain,
! [SV1279: $i,SV431: $i] :
( ( ( c_lessequals @ SV431 @ SV1279 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV431 ) @ ( c_HOL_Ominus__class_Ominus @ SV1279 @ SV431 @ tc_nat ) )
= SV1279 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4988]) ).
thf(5753,plain,
! [SV432: $i,SV1280: $i] :
( ( ( c_lessequals @ SV1280 @ SV432 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV432 @ SV1280 @ tc_nat ) ) @ SV1280 )
= SV432 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4989]) ).
thf(5754,plain,
! [SV2465: $i,SV2003: $i,SV1281: $i,SV433: $i] :
( ( ! [SY6880: $i,SY6881: $i,SY6882: $i,SY6883: $i] :
( ( ( hAPP @ ( hAPP @ SV433 @ SV1281 ) @ ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ SV2465 ) )
= ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ ( c_Suc @ SV2465 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6880 @ SV433 @ SV2003 @ SY6881 @ SY6882 @ SY6883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4990]) ).
thf(5755,plain,
! [SV2466: $i,SV2004: $i,SV1282: $i,SV434: $i] :
( ( ! [SY6884: $i,SY6885: $i,SY6886: $i,SY6887: $i] :
( ( ( hAPP @ ( hAPP @ SV434 @ ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ SV2466 ) ) @ SV2004 )
= ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ ( c_Suc @ SV2466 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6884 @ SV434 @ SV1282 @ SY6885 @ SY6886 @ SY6887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4991]) ).
thf(5756,plain,
! [SV2467: $i,SV2005: $i,SV1283: $i,SV435: $i] :
( ( ! [SY6888: $i,SY6889: $i,SY6890: $i,SY6891: $i] :
( ( ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ ( c_Suc @ SV2005 ) )
= ( hAPP @ ( hAPP @ SV2467 @ SV1283 ) @ ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ SV2005 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6888 @ SV2467 @ SV435 @ SY6889 @ SY6890 @ SY6891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4992]) ).
thf(5757,plain,
! [SV2468: $i,SV2006: $i,SV1284: $i,SV436: $i] :
( ( ! [SY6892: $i,SY6893: $i,SY6894: $i,SY6895: $i] :
( ( ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ ( c_Suc @ SV2006 ) )
= ( hAPP @ ( hAPP @ SV2468 @ SV1284 ) @ ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ SV2006 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6892 @ SV2468 @ SV436 @ SY6893 @ SY6894 @ SY6895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4993]) ).
thf(5758,plain,
! [SV2007: $i,SV1285: $i,SV437: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV437 @ SV1285 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2007 @ SV437 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2007 @ SV1285 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4994]) ).
thf(5759,plain,
! [SV2008: $i,SV1286: $i,SV438: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV438 @ SV1286 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV438 @ SV2008 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1286 @ SV2008 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4995]) ).
thf(5760,plain,
! [SV2009: $i,SV1287: $i,SV439: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV439 ) @ ( c_HOL_Ominus__class_Ominus @ SV1287 @ SV2009 @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV439 ) @ SV1287 ) @ SV2009 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2009 @ SV1287 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4996]) ).
thf(5761,plain,
! [SV2010: $i,SV1288: $i,SV440: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV440 @ SV1288 @ tc_nat ) ) @ SV2010 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV440 ) @ SV2010 ) @ SV1288 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1288 @ SV440 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4997]) ).
thf(5762,plain,
! [SV2469: $i,SV2011: $i,SV1289: $i,SV441: $i] :
( ( ( c_List_Odrop @ SV441 @ ( c_List_Odrop @ SV1289 @ SV2011 @ SV2469 ) @ SV2469 )
= ( c_List_Odrop @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV441 ) @ SV1289 ) @ SV2011 @ SV2469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4998]) ).
thf(5763,plain,
! [SV2470: $i,SV2012: $i,SV1290: $i,SV442: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV442 )
| ( c_lessequals @ SV1290 @ SV2012 @ SV442 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV442 ) @ SV2012 @ SV442 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1290 @ ( c_Suc @ SV2470 ) @ SV442 ) @ ( c_Power_Opower__class_Opower @ SV2012 @ ( c_Suc @ SV2470 ) @ SV442 ) @ SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4999]) ).
thf(5764,plain,
! [SV2471: $i,SV2013: $i,SV1291: $i,SV443: $i] :
( ( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV443 ) @ SV1291 ) @ SV2013 @ SV2471 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV443 @ SV2013 @ SV2471 ) @ ( c_List_Oreplicate @ SV1291 @ SV2013 @ SV2471 ) @ SV2471 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5000]) ).
thf(5765,plain,
! [SV2014: $i,SV1292: $i,SV444: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV444 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1292 @ ( c_HOL_Otimes__class_Otimes @ SV1292 @ SV2014 @ SV444 ) @ SV444 )
= ( c_HOL_Otimes__class_Otimes @ SV1292 @ SV2014 @ SV444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5001]) ).
thf(5766,plain,
! [SV1293: $i,SV445: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV445 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV445 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1293 @ SV445 ) @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1293 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5002]) ).
thf(5767,plain,
! [SV1294: $i,SV446: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV446 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1294 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1294 @ SV446 ) @ SV446 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5003]) ).
thf(5768,plain,
! [SV2472: $i,SV2015: $i,SV1295: $i,SV447: $i] :
( ( ! [SY6896: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SV2472 @ SY6896 @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
| ~ ( c_lessequals @ SV2015 @ SY6896 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SV2472 @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5004]) ).
thf(5769,plain,
! [SV2473: $i,SV2016: $i,SV1296: $i,SV448: $i] :
( ( ! [SY6897: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SV2473 @ SY6897 @ SV448 ) @ SV448 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ SV2016 @ SY6897 @ SV448 )
| ~ ( c_lessequals @ SV1296 @ SV2473 @ SV448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5005]) ).
thf(5770,plain,
! [SV2017: $i,SV1297: $i,SV449: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV449 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1297 @ ( c_Power_Opower__class_Opower @ SV1297 @ SV2017 @ SV449 ) @ SV449 )
= ( c_Power_Opower__class_Opower @ SV1297 @ ( c_Suc @ SV2017 ) @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5006]) ).
thf(5771,plain,
! [SV2018: $i,SV1298: $i,SV450: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV450 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1298 @ SV2018 @ SV450 ) @ SV1298 @ SV450 )
= ( c_Power_Opower__class_Opower @ SV1298 @ ( c_Suc @ SV2018 ) @ SV450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5007]) ).
thf(5772,plain,
! [SV2019: $i,SV1299: $i,SV451: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV451 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV1299 @ SV451 )
| ( c_lessequals @ SV1299 @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1299 @ SV451 ) @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5008]) ).
thf(5773,plain,
! [SV2020: $i,SV1300: $i,SV452: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV452 ) )
= $true )
| ( ( ( c_lessequals @ SV1300 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
| ( c_lessequals @ SV2020 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1300 @ SV2020 @ SV452 ) @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5009]) ).
thf(5774,plain,
! [SV2021: $i,SV1301: $i,SV453: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV453 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV1301 @ SV453 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV2021 @ SV453 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1301 @ SV453 ) @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV453 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5010]) ).
thf(5775,plain,
! [SV2022: $i,SV1302: $i,SV454: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV454 ) )
= $true )
| ( ( ( c_lessequals @ SV1302 @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV1302 @ SV454 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1302 @ SV2022 @ SV454 ) @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5011]) ).
thf(5776,plain,
! [SV2023: $i,SV1303: $i,SV455: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV455 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1303 @ SV2023 @ SV455 ) @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SV1303 @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV2023 @ SV455 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5012]) ).
thf(5777,plain,
! [SV2024: $i,SV1304: $i,SV456: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV456 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1304 @ SV2024 @ SV456 ) @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV2024 @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1304 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5013]) ).
thf(5778,plain,
! [SV2025: $i,SV1305: $i,SV457: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV457 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1305 @ SV2025 @ SV457 ) @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV2025 @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SV1305 @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5014]) ).
thf(5779,plain,
! [SV1306: $i,SV458: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV458 ) @ SV1306 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV458 @ SV1306 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5015]) ).
thf(5780,plain,
! [SV1307: $i,SV459: $i] :
( ( ( c_lessequals @ SV459 @ SV1307 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV459 @ ( c_Suc @ SV1307 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5016]) ).
thf(5781,plain,
! [SV2474: $i,SV2026: $i,SV1308: $i,SV460: $i] :
( ( ( c_Type_Otypings @ SV460 @ SV1308 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV2026 @ SV460 @ SV2474 @ SV1308 ) )
| ~ ( c_Type_Otyping @ SV460 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV2474 @ SV1308 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2026 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5017]) ).
thf(5782,plain,
! [SV461: $i,SV1309: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1309 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV461 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV461 @ ( c_HOL_Otimes__class_Otimes @ SV1309 @ SV461 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5018]) ).
thf(5783,plain,
! [SV462: $i,SV1310: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1310 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV462 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV462 @ ( c_HOL_Otimes__class_Otimes @ SV462 @ SV1310 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5019]) ).
thf(5784,plain,
! [SV2027: $i,SV1311: $i,SV464: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV464 @ SV1311 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SV2027 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1311 @ SV2027 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV2027 @ SV1311 @ tc_nat )
| ~ ( c_lessequals @ SV2027 @ SV464 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5020]) ).
thf(5785,plain,
! [SV2028: $i,SV1312: $i,SV465: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV465 @ SV1312 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV2028 @ SV1312 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV465 @ SV2028 @ tc_nat )
| ~ ( c_lessequals @ SV1312 @ SV2028 @ tc_nat )
| ~ ( c_lessequals @ SV1312 @ SV465 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5021]) ).
thf(5786,plain,
! [SV2475: $i,SV2029: $i,SV1313: $i,SV466: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV466 )
| ( c_HOL_Oord__class_Oless @ SV1313 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ SV2029 ) @ SV2475 ) @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ SV1313 @ SV2475 @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV2029 @ SV466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5022]) ).
thf(5787,plain,
! [SV2030: $i,SV1314: $i,SV467: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV467 ) @ SV1314 @ SV2030 )
= ( c_Lambda_OdB_OVar @ SV467 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV467 @ SV2030 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5023]) ).
thf(5788,plain,
! [SV2031: $i,SV1315: $i,SV468: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV468 @ ( c_Lambda_OdB_OVar @ SV1315 ) @ SV2031 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV468 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5024]) ).
thf(5789,plain,
! [SV1316: $i,SV469: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV469 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV469 ) @ SV1316 ) @ SV1316 ) @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1316 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5025]) ).
thf(5790,plain,
! [SV1317: $i,SV470: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV470 )
= $false )
| ( ( ( c_lessequals @ SV1317 @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV470 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV470 ) @ SV1317 ) @ SV1317 ) @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV470 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5026]) ).
thf(5791,plain,
! [SV2032: $i,SV1320: $i,SV473: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV473 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1320 @ SV2032 @ tc_nat ) @ SV473 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1320 @ SV473 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV2032 @ SV473 ) @ SV473 ) )
| ~ ( c_lessequals @ SV2032 @ SV1320 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5029]) ).
thf(5792,plain,
! [SV2476: $i,SV2033: $i,SV1321: $i,SV474: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV474 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1321 @ SV2033 @ SV474 ) @ ( c_HOL_Otimes__class_Otimes @ SV2476 @ SV2033 @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SV2033 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SV2476 @ SV1321 @ SV474 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5030]) ).
thf(5793,plain,
! [SV2477: $i,SV2034: $i,SV1322: $i,SV475: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV475 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2034 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2477 @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SV2477 @ SV2034 @ SV475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5031]) ).
thf(5794,plain,
! [SV2478: $i,SV2035: $i,SV1323: $i,SV476: $i] :
( ( ~ ( class_Ring__and__Field_Omult__mono @ SV476 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1323 @ SV2035 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SV2478 @ SV2035 @ SV476 ) @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV2035 @ SV476 )
| ~ ( c_lessequals @ SV1323 @ SV2478 @ SV476 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5032]) ).
thf(5795,plain,
! [SV2479: $i,SV2036: $i,SV1324: $i,SV477: $i] :
( ( ~ ( class_Ring__and__Field_Omult__mono @ SV477 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2036 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2479 @ SV477 ) @ SV477 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV477 ) @ SV1324 @ SV477 )
| ~ ( c_lessequals @ SV2036 @ SV2479 @ SV477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5033]) ).
thf(5796,plain,
! [SV2480: $i,SV2037: $i,SV1325: $i,SV478: $i] :
( ( ~ ( class_Ring__and__Field_Omult__mono1 @ SV478 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2037 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2480 @ SV478 ) @ SV478 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV478 ) @ SV1325 @ SV478 )
| ~ ( c_lessequals @ SV2037 @ SV2480 @ SV478 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5034]) ).
thf(5797,plain,
! [SV2039: $i,SV1327: $i,SV480: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV480 ) @ SV1327 ) @ SV2039 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV480 @ ( c_HOL_Ominus__class_Ominus @ SV2039 @ SV1327 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5036]) ).
thf(5798,plain,
! [SV2040: $i,SV1328: $i,SV481: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV481 @ ( c_HOL_Ominus__class_Ominus @ SV1328 @ SV2040 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SV2040 ) @ SV1328 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5037]) ).
thf(5799,plain,
! [SV2481: $i,SV2041: $i,SV1329: $i,SV482: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV482 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SV1329 ) @ SV2041 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SV2481 ) @ SV2041 ) @ SV482 )
| ~ ( c_HOL_Oord__class_Oless @ SV1329 @ SV2481 @ SV482 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5038]) ).
thf(5800,plain,
! [SV2482: $i,SV2042: $i,SV1330: $i,SV483: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV483 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SV1330 ) @ SV2042 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SV2482 ) @ SV2042 ) @ SV483 )
| ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SV2482 @ SV483 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5039]) ).
thf(5801,plain,
! [SV2483: $i,SV2043: $i,SV1331: $i,SV484: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV484 )
| ( c_HOL_Oord__class_Oless @ SV1331 @ SV2043 @ SV484 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV1331 ) @ SV2483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV2043 ) @ SV2483 ) @ SV484 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5040]) ).
thf(5802,plain,
! [SV2484: $i,SV2044: $i,SV1332: $i,SV485: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV485 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SV2044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SV2484 ) @ SV485 )
| ~ ( c_HOL_Oord__class_Oless @ SV2044 @ SV2484 @ SV485 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5041]) ).
thf(5803,plain,
! [SV2485: $i,SV2045: $i,SV1333: $i,SV486: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV486 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SV2045 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SV2485 ) @ SV486 )
| ~ ( c_HOL_Oord__class_Oless @ SV2045 @ SV2485 @ SV486 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5042]) ).
thf(5804,plain,
! [SV2486: $i,SV2046: $i,SV1334: $i,SV487: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV487 )
| ( c_HOL_Oord__class_Oless @ SV1334 @ SV2046 @ SV487 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SV2486 ) @ SV1334 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SV2486 ) @ SV2046 ) @ SV487 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5043]) ).
thf(5805,plain,
! [SV2047: $i,SV1335: $i,SV488: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV488 ) @ SV1335 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2047 ) @ SV1335 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV488 @ SV2047 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5044]) ).
thf(5806,plain,
! [SV2048: $i,SV1336: $i,SV489: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV489 @ SV1336 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2048 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2048 ) @ SV1336 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5045]) ).
thf(5807,plain,
! [SV2049: $i,SV1337: $i,SV490: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV490 ) @ SV1337 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV490 ) @ SV2049 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1337 @ SV2049 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5046]) ).
thf(5808,plain,
! [SV491: $i,SV1338: $i] :
( ( ( ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1338 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV491 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV491 @ SV1338 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5047]) ).
thf(5809,plain,
! [SV2487: $i,SV2050: $i,SV1339: $i,SV492: $i] :
( ( ~ ( class_Orderings_Oorder @ SV492 )
| ( c_lessequals @ SV1339 @ SV2050 @ SV492 )
| ~ ( c_lessequals @ SV1339 @ SV2487 @ SV492 )
| ~ ( c_lessequals @ SV2487 @ SV2050 @ SV492 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5048]) ).
thf(5810,plain,
! [SV2488: $i,SV2051: $i,SV1340: $i,SV493: $i] :
( ( ~ ( class_Orderings_Oorder @ SV493 )
| ( c_HOL_Oord__class_Oless @ SV1340 @ SV2051 @ SV493 )
| ~ ( c_lessequals @ SV1340 @ SV2488 @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SV2488 @ SV2051 @ SV493 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5049]) ).
thf(5811,plain,
! [SV2489: $i,SV2052: $i,SV1341: $i,SV494: $i] :
( ( ~ ( class_Orderings_Oorder @ SV494 )
| ( c_HOL_Oord__class_Oless @ SV1341 @ SV2052 @ SV494 )
| ~ ( c_HOL_Oord__class_Oless @ SV1341 @ SV2489 @ SV494 )
| ~ ( c_lessequals @ SV2489 @ SV2052 @ SV494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5050]) ).
thf(5812,plain,
! [SV2053: $i,SV1342: $i,SV495: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV495 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1342 ) @ SV2053 ) @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
| ~ ( c_lessequals @ SV2053 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
| ~ ( c_lessequals @ SV1342 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5051]) ).
thf(5813,plain,
! [SV2490: $i,SV2054: $i,SV1343: $i,SV496: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV496 )
| ( c_lessequals @ SV1343 @ SV2054 @ SV496 )
| ~ ( c_lessequals @ SV2490 @ SV2054 @ SV496 )
| ~ ( c_lessequals @ SV1343 @ SV2490 @ SV496 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5052]) ).
thf(5814,plain,
! [SV2055: $i,SV1344: $i,SV498: $i] :
( ( ( c_lessequals @ SV498 @ SV1344 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV2055 @ SV1344 @ tc_nat )
| ~ ( c_lessequals @ SV498 @ SV2055 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5053]) ).
thf(5815,plain,
! [SV1346: $i,SV501: $i] :
( ( ( c_lessequals @ SV501 @ SV1346 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV501 @ ( c_Suc @ SV1346 ) @ tc_nat ) )
= $true )
| ( ( SV501
= ( c_Suc @ SV1346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5054]) ).
thf(5816,plain,
! [SV1347: $i,SV503: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV503 @ SV1347 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1347 @ ( c_Suc @ SV503 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5055]) ).
thf(5817,plain,
! [SV2056: $i,SV1349: $i,SV505: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV1349 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2056 @ SV1349 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV505 @ SV2056 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1349 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5057]) ).
thf(5818,plain,
! [SV2057: $i,SV1350: $i,SV506: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV1350 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV2057 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1350 @ SV2057 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV506 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5058]) ).
thf(5819,plain,
! [SV2058: $i,SV1351: $i,SV507: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SV1351 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SV2058 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV507 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1351 @ SV2058 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5059]) ).
thf(5820,plain,
! [SV2059: $i,SV1352: $i,SV508: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV508 @ SV1352 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2059 @ SV1352 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1352 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV508 @ SV2059 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5060]) ).
thf(5821,plain,
! [SV2060: $i,SV1353: $i,SV509: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV509 @ SV1353 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2060 @ SV509 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2060 @ SV1353 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2060 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5061]) ).
thf(5822,plain,
! [SV2061: $i,SV1354: $i,SV510: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SV1354 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SV2061 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1354 @ SV2061 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV510 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5062]) ).
thf(5823,plain,
! [SV2491: $i,SV2062: $i,SV1355: $i,SV511: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV511 )
| ( c_HOL_Oord__class_Oless @ SV1355 @ SV2062 @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV2062 @ SV511 ) @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV1355 @ SV511 ) @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ SV2491 @ ( c_HOL_Ozero__class_Ozero @ SV511 ) @ SV511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5063]) ).
thf(5824,plain,
! [SV2492: $i,SV2063: $i,SV1356: $i,SV512: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV512 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2063 @ SV512 ) @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2492 @ SV512 ) @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SV2492 @ SV2063 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SV1356 @ ( c_HOL_Ozero__class_Ozero @ SV512 ) @ SV512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5064]) ).
thf(5825,plain,
! [SV2493: $i,SV2064: $i,SV1357: $i,SV513: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV513 )
| ( c_HOL_Oord__class_Oless @ SV1357 @ SV2064 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV1357 @ SV513 ) @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV2064 @ SV513 ) @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV513 ) @ SV2493 @ SV513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5065]) ).
thf(5826,plain,
! [SV2494: $i,SV2065: $i,SV1358: $i,SV514: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV514 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2065 @ SV514 ) @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2494 @ SV514 ) @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ SV2065 @ SV2494 @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SV1358 @ SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5066]) ).
thf(5827,plain,
! [SV2495: $i,SV2066: $i,SV1359: $i,SV515: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV515 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2066 @ SV515 ) @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2495 @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SV1359 @ ( c_HOL_Ozero__class_Ozero @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SV2495 @ SV2066 @ SV515 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5067]) ).
thf(5828,plain,
! [SV2496: $i,SV2067: $i,SV1360: $i,SV516: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV516 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2067 @ SV516 ) @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2496 @ SV516 ) @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV516 ) @ SV1360 @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ SV2067 @ SV2496 @ SV516 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5068]) ).
thf(5829,plain,
! [SV2497: $i,SV2068: $i,SV1361: $i,SV517: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV517 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2068 @ SV517 ) @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2497 @ SV517 ) @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ SV2068 @ SV2497 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1361 @ SV517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5069]) ).
thf(5830,plain,
! [SV2498: $i,SV2069: $i,SV1362: $i,SV518: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV518 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2069 @ SV518 ) @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2498 @ SV518 ) @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SV2498 @ SV2069 @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SV1362 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5070]) ).
thf(5831,plain,
! [SV2499: $i,SV2070: $i,SV1363: $i,SV519: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV519 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1363 @ SV2070 @ SV519 ) @ ( c_HOL_Otimes__class_Otimes @ SV2499 @ SV2070 @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SV2070 @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SV2499 @ SV1363 @ SV519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5071]) ).
thf(5832,plain,
! [SV2500: $i,SV2071: $i,SV1364: $i,SV520: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV520 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1364 @ SV2071 @ SV520 ) @ ( c_HOL_Otimes__class_Otimes @ SV2500 @ SV2071 @ SV520 ) @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV2071 @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ SV1364 @ SV2500 @ SV520 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5072]) ).
thf(5833,plain,
! [SV2501: $i,SV2072: $i,SV1365: $i,SV521: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV521 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1365 @ SV2072 @ SV521 ) @ ( c_HOL_Otimes__class_Otimes @ SV2501 @ SV2072 @ SV521 ) @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ SV1365 @ SV2501 @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV521 ) @ SV2072 @ SV521 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5073]) ).
thf(5834,plain,
! [SV2502: $i,SV2073: $i,SV1366: $i,SV522: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV522 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1366 @ SV2073 @ SV522 ) @ ( c_HOL_Otimes__class_Otimes @ SV2502 @ SV2073 @ SV522 ) @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SV2502 @ SV1366 @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SV2073 @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV522 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5074]) ).
thf(5835,plain,
! [SV2503: $i,SV2074: $i,SV1367: $i,SV523: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV523 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2074 @ SV523 ) @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2503 @ SV523 ) @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV1367 @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ SV2074 @ SV2503 @ SV523 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5075]) ).
thf(5836,plain,
! [SV2504: $i,SV2076: $i,SV1369: $i,SV525: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV525 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ ( c_Orderings_Oord__class_Omax @ SV1369 @ SV2076 @ SV525 ) ) @ SV2504 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ SV1369 ) @ SV2504 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ SV2076 ) @ SV2504 ) @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5077]) ).
thf(5837,plain,
! [SV1370: $i,SV526: $i] :
( ( ( c_InductTermi_OIT @ SV526 )
= $false )
| ( ( c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV526 ) @ ( c_Lambda_OdB_OVar @ SV1370 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5078]) ).
thf(5838,plain,
! [SV2505: $i,SV2077: $i,SV1371: $i,SV527: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV527 @ SV1371 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2077 @ SV2505 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1371 @ SV2505 @ tc_nat )
| ~ ( c_lessequals @ SV527 @ SV2077 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5079]) ).
thf(5839,plain,
! [SV2506: $i,SV2078: $i,SV1372: $i,SV529: $i] :
( ( ! [SY6898: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV529 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SV2506 @ SY6898 @ SV529 ) @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2506 @ SV529 )
| ~ ( c_lessequals @ SV2078 @ SY6898 @ SV529 )
| ~ ( c_lessequals @ SV1372 @ SV2506 @ SV529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5080]) ).
thf(5840,plain,
! [SV2507: $i,SV2079: $i,SV1373: $i,SV530: $i] :
( ( ! [SY6899: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV530 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SV2507 @ SY6899 @ SV530 ) @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
| ~ ( c_lessequals @ SV2079 @ SY6899 @ SV530 )
| ~ ( c_lessequals @ SV1373 @ SV2507 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5081]) ).
thf(5841,plain,
! [SV2508: $i,SV2080: $i,SV1374: $i,SV531: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV531 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV1374 @ SV2080 @ SV531 ) @ SV2508 @ SV531 )
= ( c_Orderings_Oord__class_Omax @ SV1374 @ ( c_Orderings_Oord__class_Omax @ SV2080 @ SV2508 @ SV531 ) @ SV531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5082]) ).
thf(5842,plain,
! [SV2509: $i,SV2081: $i,SV1375: $i,SV532: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV532 )
| ( ( c_Orderings_Oord__class_Omax @ SV1375 @ ( c_Orderings_Oord__class_Omax @ SV2081 @ SV2509 @ SV532 ) @ SV532 )
= ( c_Orderings_Oord__class_Omax @ SV2081 @ ( c_Orderings_Oord__class_Omax @ SV1375 @ SV2509 @ SV532 ) @ SV532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5083]) ).
thf(5843,plain,
! [SV2510: $i,SV2082: $i,SV1376: $i,SV534: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV534 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV534 ) @ ( c_HOL_Otimes__class_Otimes @ SV1376 @ SV2082 @ SV534 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2510 @ SV2082 @ SV534 ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV534 ) @ SV1376 ) @ SV2510 ) @ SV2082 @ SV534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5084]) ).
thf(5844,plain,
! [SV1377: $i,SV535: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV535 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV535 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1377 @ SV535 ) @ SV535 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5085]) ).
thf(5845,plain,
! [SV1378: $i,SV536: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV536 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1378 @ SV536 ) @ SV536 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5086]) ).
thf(5846,plain,
! [SV537: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV537 ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV537 ) ) @ SV537 )
= $false )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5087]) ).
thf(5847,plain,
! [SV1379: $i,SV538: $i] :
( ( ( c_Lambda_Obeta @ SV538 @ SV1379 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV538 ) @ ( c_Lambda_OdB_OAbs @ SV1379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5088]) ).
thf(5848,plain,
! [SV2083: $i,SV1380: $i,SV539: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV539 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1380 @ ( c_Orderings_Oord__class_Omax @ SV1380 @ SV2083 @ SV539 ) @ SV539 )
= ( c_Orderings_Oord__class_Omax @ SV1380 @ SV2083 @ SV539 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5089]) ).
thf(5849,plain,
! [SV2085: $i,SV1382: $i,SV541: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV541 ) )
= $true )
| ( ( ( c_lessequals @ SV1382 @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV541 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV1382 @ SV541 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV2085 @ SV541 ) @ SV541 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5091]) ).
thf(5850,plain,
! [SV2086: $i,SV1383: $i,SV542: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV542 ) )
= $true )
| ( ( ( c_lessequals @ SV1383 @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV542 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV2086 @ SV542 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ ( c_HOL_Otimes__class_Otimes @ SV2086 @ SV1383 @ SV542 ) @ SV542 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5092]) ).
thf(5851,plain,
! [SV2087: $i,SV1384: $i,SV543: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV543 ) )
= $true )
| ( ( ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV543 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV2087 @ SV543 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ ( c_HOL_Otimes__class_Otimes @ SV1384 @ SV2087 @ SV543 ) @ SV543 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5093]) ).
thf(5852,plain,
! [SV2088: $i,SV1385: $i,SV544: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV544 ) )
= $true )
| ( ( ( c_lessequals @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV544 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV1385 @ SV544 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ ( c_HOL_Otimes__class_Otimes @ SV2088 @ SV1385 @ SV544 ) @ SV544 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5094]) ).
thf(5853,plain,
! [SV2089: $i,SV1388: $i,SV547: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV547 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV547 ) @ SV1388 ) @ SV2089 ) @ SV2089 @ SV547 )
= SV1388 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5095]) ).
thf(5854,plain,
! [SV2511: $i,SV2090: $i,SV1389: $i,SV548: $i] :
( ( ! [SY6900: $i,SY6901: $i] :
( ( c_List_Ofoldl @ SV548 @ SV1389 @ ( c_List_Oappend @ SV2090 @ SV2511 @ SY6900 ) @ SY6901 @ SY6900 )
= ( c_List_Ofoldl @ SV548 @ ( c_List_Ofoldl @ SV548 @ SV1389 @ SV2090 @ SY6901 @ SY6900 ) @ SV2511 @ SY6901 @ SY6900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5096]) ).
thf(5855,plain,
! [SV2512: $i,SV2091: $i,SV1390: $i,SV549: $i] :
( ( ( c_Type_Otype_Otype__case @ SV549 @ SV1390 @ ( c_Type_Otype_OAtom @ SV2091 ) @ SV2512 )
= ( hAPP @ SV549 @ SV2091 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5097]) ).
thf(5856,plain,
! [SV2513: $i,SV2092: $i,SV1391: $i,SV550: $i] :
( ( ! [SY6902: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV550 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV1391 ) @ SV2092 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV2513 ) @ SY6902 ) @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SV2092 @ SY6902 @ SV550 )
| ~ ( c_lessequals @ SV1391 @ SV2513 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5098]) ).
thf(5857,plain,
! [SV2514: $i,SV2093: $i,SV1392: $i,SV551: $i] :
( ( ! [SY6903: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV551 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV1392 ) @ SV2093 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV2514 ) @ SY6903 ) @ SV551 )
| ~ ( c_lessequals @ SV2093 @ SY6903 @ SV551 )
| ~ ( c_HOL_Oord__class_Oless @ SV1392 @ SV2514 @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5099]) ).
thf(5858,plain,
! [SV1393: $i,SV552: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV552 @ SV1393 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV552 ) @ ( c_Suc @ SV1393 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5100]) ).
thf(5859,plain,
! [SV1394: $i,SV553: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV553 ) @ ( c_Suc @ SV1394 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV553 @ SV1394 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5101]) ).
thf(5860,plain,
! [SV1395: $i,SV554: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV554 @ SV1395 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV554 ) @ ( c_Suc @ SV1395 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5102]) ).
thf(5861,plain,
! [SV555: $i,SV1396: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1396 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV555 ) @ SV1396 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5103]) ).
thf(5862,plain,
! [SV1397: $i,SV556: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV556 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV556 ) @ SV1397 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5104]) ).
thf(5863,plain,
! [SV1398: $i,SV557: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV557 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV557 ) @ SV1398 @ SV557 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV557 ) @ SV1398 ) @ SV1398 ) @ SV557 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5105]) ).
thf(5864,plain,
! [SV1399: $i,SV558: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV558 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV558 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV558 ) @ SV1399 ) @ SV1399 ) @ SV558 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV558 ) @ SV1399 @ SV558 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5106]) ).
thf(5865,plain,
! [SV2094: $i,SV1400: $i,SV559: $i] :
( ( ( SV559
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV559 @ SV1400 @ SV2094 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV559 @ SV1400 @ SV2094 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV1400 @ ( c_Lambda_OdB_OAbs @ SV2094 ) @ SV559 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5107]) ).
thf(5866,plain,
! [SV1401: $i,SV560: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV560 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV560 ) @ SV1401 @ SV560 )
= ( c_HOL_Ozero__class_Ozero @ SV560 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5108]) ).
thf(5867,plain,
! [SV1402: $i,SV561: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV561 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV1402 @ SV561 )
= ( c_HOL_Ozero__class_Ozero @ SV561 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5109]) ).
thf(5868,plain,
! [SV1403: $i,SV562: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV562 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1403 @ ( c_HOL_Ozero__class_Ozero @ SV562 ) @ SV562 )
= ( c_HOL_Ozero__class_Ozero @ SV562 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5110]) ).
thf(5869,plain,
! [SV1404: $i,SV563: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV563 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV563 ) @ SV1404 @ SV563 )
= ( c_HOL_Ozero__class_Ozero @ SV563 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5111]) ).
thf(5870,plain,
! [SV1405: $i,SV564: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV564 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1405 @ ( c_HOL_Ozero__class_Ozero @ SV564 ) @ SV564 )
= ( c_HOL_Ozero__class_Ozero @ SV564 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5112]) ).
thf(5871,plain,
! [SV1406: $i,SV565: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV565 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1406 @ ( c_HOL_Ozero__class_Ozero @ SV565 ) @ SV565 )
= ( c_HOL_Ozero__class_Ozero @ SV565 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5113]) ).
thf(5872,plain,
! [SV1407: $i,SV566: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV566 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV566 ) @ SV1407 @ SV566 )
= ( c_HOL_Ozero__class_Ozero @ SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5114]) ).
thf(5873,plain,
! [SV1408: $i,SV567: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV567 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV567 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1408 @ SV1408 @ SV567 )
= ( c_HOL_Ozero__class_Ozero @ SV567 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5115]) ).
thf(5874,plain,
! [SV1409: $i,SV568: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV568 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1409 @ SV1409 @ SV568 )
= ( c_HOL_Ozero__class_Ozero @ SV568 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5116]) ).
thf(5875,plain,
! [SV1410: $i,SV569: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV569 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1410 @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SV569 )
= SV1410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5117]) ).
thf(5876,plain,
! [SV1411: $i,SV570: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV570 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1411 @ SV1411 @ SV570 )
= ( c_HOL_Ozero__class_Ozero @ SV570 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5118]) ).
thf(5877,plain,
! [SV1412: $i,SV571: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV571 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1412 @ SV1412 @ SV571 )
= ( c_HOL_Ozero__class_Ozero @ SV571 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5119]) ).
thf(5878,plain,
! [SV1413: $i,SV573: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV573 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV573 ) @ ( c_HOL_Ozero__class_Ozero @ SV573 ) ) @ SV1413 )
= SV1413 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5121]) ).
thf(5879,plain,
! [SV1414: $i,SV574: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV574 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV574 ) @ ( c_HOL_Ozero__class_Ozero @ SV574 ) ) @ SV1414 )
= SV1414 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5122]) ).
thf(5880,plain,
! [SV1415: $i,SV575: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV575 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV575 )
| ( SV1415
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1415 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5123]) ).
thf(5881,plain,
! [SV1416: $i,SV576: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV576 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV576 ) @ SV1416 ) @ ( c_HOL_Ozero__class_Ozero @ SV576 ) )
= SV1416 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5124]) ).
thf(5882,plain,
! [SV1417: $i,SV577: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV577 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV577 ) @ ( c_HOL_Ozero__class_Ozero @ SV577 ) ) @ SV1417 )
= SV1417 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5125]) ).
thf(5883,plain,
! [SV1418: $i,SV578: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV578 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV578 ) @ SV1418 ) @ ( c_HOL_Ozero__class_Ozero @ SV578 ) )
= SV1418 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5126]) ).
thf(5884,plain,
! [SV1419: $i,SV579: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV579 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV579 ) @ SV1419 ) @ ( c_HOL_Ozero__class_Ozero @ SV579 ) )
= SV1419 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5127]) ).
thf(5885,plain,
! [SV1420: $i,SV580: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV580 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV580 ) @ ( c_HOL_Ozero__class_Ozero @ SV580 ) ) @ SV1420 )
= SV1420 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5128]) ).
thf(5886,plain,
! [SV1423: $i,SV584: $i] :
( ( ( class_Orderings_Oorder @ SV584 )
= $false )
| ( ( c_lessequals @ SV1423 @ SV1423 @ SV584 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5129]) ).
thf(5887,plain,
! [SV1424: $i,SV585: $i] :
( ( ( class_Orderings_Opreorder @ SV585 )
= $false )
| ( ( c_lessequals @ SV1424 @ SV1424 @ SV585 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5130]) ).
thf(5888,plain,
! [SV2515: $i,SV2095: $i,SV1425: $i,SV586: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV586 )
| ( c_HOL_Oord__class_Oless @ SV1425 @ SV2095 @ SV586 )
| ~ ( c_HOL_Oord__class_Oless @ SV2515 @ SV2095 @ SV586 )
| ~ ( c_lessequals @ SV1425 @ SV2515 @ SV586 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5131]) ).
thf(5889,plain,
! [SV2516: $i,SV2096: $i,SV1426: $i,SV587: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV587 )
| ( c_HOL_Oord__class_Oless @ SV1426 @ SV2096 @ SV587 )
| ~ ( c_lessequals @ SV2516 @ SV2096 @ SV587 )
| ~ ( c_HOL_Oord__class_Oless @ SV1426 @ SV2516 @ SV587 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5132]) ).
thf(5890,plain,
! [SV2517: $i,SV2097: $i,SV1427: $i,SV588: $i] :
( ( ! [SY6904: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV588 )
| ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2517 ) @ SV588 )
| ~ ( c_lessequals @ SY6904 @ SV2517 @ SV588 )
| ~ ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SY6904 ) @ SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5133]) ).
thf(5891,plain,
! [SV2099: $i,SV1430: $i,SV591: $i] :
( ( ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1430 @ SV2099 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ominus__class_Ominus @ SV1430 @ SV2099 @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5135]) ).
thf(5892,plain,
! [SV1431: $i,SV592: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV592 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1431 @ SV1431 @ SV592 )
= SV1431 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5136]) ).
thf(5893,plain,
! [SV2100: $i,SV1432: $i,SV593: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV593 @ SV1432 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1432 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV593 @ SV2100 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV593 @ SV2100 ) )
| ( hBOOL @ ( hAPP @ SV593 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5137]) ).
thf(5894,plain,
! [SV2518: $i,SV2101: $i,SV1433: $i,SV594: $i] :
( ( ! [SY6905: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SV2518 @ SY6905 @ SV594 ) @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV2101 @ SY6905 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SV2518 @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5138]) ).
thf(5895,plain,
! [SV1434: $i,SV595: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV595 @ ( c_Suc @ SV1434 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1434 @ SV595 @ tc_nat ) )
= $true )
| ( ( SV595 = SV1434 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5139]) ).
thf(5896,plain,
! [SV2102: $i,SV1435: $i,SV596: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV596 @ SV1435 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2102 @ SV1435 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV596 @ SV2102 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5140]) ).
thf(5897,plain,
! [SV2103: $i,SV1436: $i,SV597: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV597 @ SV1436 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV597 @ SV2103 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1436 @ SV2103 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5141]) ).
thf(5898,plain,
! [SV2104: $i,SV1437: $i,SV598: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV598 @ SV1437 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV598 @ SV2104 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1437 @ SV2104 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5142]) ).
thf(5899,plain,
! [SV2105: $i,SV1438: $i,SV599: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV599 @ SV1438 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2105 @ SV1438 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV599 @ SV2105 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5143]) ).
thf(5900,plain,
! [SV2519: $i,SV2106: $i,SV1439: $i,SV600: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV600 @ SV1439 @ SV2106 ) @ ( c_List_Olist_OCons @ SV1439 @ SV2519 @ SV2106 ) @ SV2106 )
= ( c_List_Olist_OCons @ SV1439 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV600 @ SV1439 @ SV2106 ) @ SV2519 @ SV2106 ) @ SV2106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5144]) ).
thf(5901,plain,
! [SV601: $i,SV1440: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1440 @ SV601 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV601 @ SV1440 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5145]) ).
thf(5902,plain,
! [SV602: $i,SV1441: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1441 @ SV602 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV602 @ SV1441 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5146]) ).
thf(5903,plain,
! [SV1442: $i,SV603: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV603 ) @ SV1442 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV603 @ SV1442 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5147]) ).
thf(5904,plain,
! [SV1443: $i,SV604: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV604 @ SV1443 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV604 @ ( c_Suc @ SV1443 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5148]) ).
thf(5905,plain,
! [SV2520: $i,SV2107: $i,SV1444: $i,SV606: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV606 )
| ( c_HOL_Oord__class_Oless @ SV1444 @ ( c_HOL_Ozero__class_Ozero @ SV606 ) @ SV606 )
| ( c_HOL_Oord__class_Oless @ SV2107 @ SV2520 @ SV606 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2107 @ SV1444 @ SV606 ) @ ( c_HOL_Otimes__class_Otimes @ SV2520 @ SV1444 @ SV606 ) @ SV606 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5150]) ).
thf(5906,plain,
! [SV2521: $i,SV2108: $i,SV1445: $i,SV607: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV607 )
| ( c_HOL_Oord__class_Oless @ SV1445 @ SV2108 @ SV607 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV607 ) @ SV2521 @ SV607 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2108 @ SV2521 @ SV607 ) @ ( c_HOL_Otimes__class_Otimes @ SV1445 @ SV2521 @ SV607 ) @ SV607 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5151]) ).
thf(5907,plain,
! [SV2522: $i,SV2109: $i,SV1446: $i,SV608: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV608 )
| ( c_HOL_Oord__class_Oless @ SV1446 @ ( c_HOL_Ozero__class_Ozero @ SV608 ) @ SV608 )
| ( c_HOL_Oord__class_Oless @ SV2109 @ SV2522 @ SV608 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2109 @ SV608 ) @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2522 @ SV608 ) @ SV608 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5152]) ).
thf(5908,plain,
! [SV2523: $i,SV2110: $i,SV1447: $i,SV609: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV609 )
| ( c_HOL_Oord__class_Oless @ SV1447 @ SV2110 @ SV609 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV609 ) @ SV2523 @ SV609 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2523 @ SV2110 @ SV609 ) @ ( c_HOL_Otimes__class_Otimes @ SV2523 @ SV1447 @ SV609 ) @ SV609 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5153]) ).
thf(5909,plain,
! [SV2524: $i,SV2111: $i,SV1448: $i,SV610: $i] :
( ( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV610 ) @ SV1448 ) @ SV2111 @ SV2524 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV610 @ SV2111 @ SV2524 ) ) @ ( c_Lambda_Osubst @ SV1448 @ SV2111 @ SV2524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5154]) ).
thf(5910,plain,
! [SV2112: $i,SV1449: $i,SV612: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV612 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1449 ) @ SV2112 ) @ SV612 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV612 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1449 @ SV612 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV2112 @ SV612 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5156]) ).
thf(5911,plain,
! [SV1450: $i,SV613: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV613 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1450 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV613 @ SV1450 @ tc_nat ) @ SV613 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5157]) ).
thf(5912,plain,
! [SV2525: $i,SV2113: $i,SV1451: $i,SV614: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV614 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1451 @ ( c_Orderings_Oord__class_Omin @ SV2113 @ SV2525 @ SV614 ) @ SV614 ) @ ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1451 @ SV2113 @ SV614 ) @ ( c_Orderings_Oord__class_Omax @ SV1451 @ SV2525 @ SV614 ) @ SV614 ) @ SV614 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5158]) ).
thf(5913,plain,
! [SV2526: $i,SV2114: $i,SV1452: $i,SV615: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV615 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV1452 @ SV2114 @ SV615 ) @ SV2526 @ SV615 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1452 @ SV2526 @ SV615 ) @ ( c_Power_Opower__class_Opower @ SV2114 @ SV2526 @ SV615 ) @ SV615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5159]) ).
thf(5914,plain,
! [SV2527: $i,SV2115: $i,SV1453: $i,SV616: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV616 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV1453 @ SV2115 @ SV616 ) @ SV2527 @ SV616 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1453 @ SV2527 @ SV616 ) @ ( c_Power_Opower__class_Opower @ SV2115 @ SV2527 @ SV616 ) @ SV616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5160]) ).
thf(5915,plain,
! [SV2116: $i,SV1454: $i,SV617: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV617 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Oappend @ SV1454 @ SV2116 @ SV617 ) @ SV617 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ ( c_List_Olistsum @ SV1454 @ SV617 ) ) @ ( c_List_Olistsum @ SV2116 @ SV617 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5161]) ).
thf(5916,plain,
! [SV1456: $i,SV619: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV619 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV619 @ ( c_Suc @ SV1456 ) @ tc_nat ) @ SV619 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5163]) ).
thf(5917,plain,
! [SV2528: $i,SV2117: $i,SV1457: $i,SV620: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV620 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV1457 @ SV2117 @ SV620 ) @ SV2528 @ SV620 )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1457 @ SV2528 @ SV620 ) @ ( c_Orderings_Oord__class_Omax @ SV2117 @ SV2528 @ SV620 ) @ SV620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5164]) ).
thf(5918,plain,
! [SV2529: $i,SV2118: $i,SV1458: $i,SV621: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV621 )
| ( ( c_Orderings_Oord__class_Omax @ SV1458 @ ( c_Orderings_Oord__class_Omin @ SV2118 @ SV2529 @ SV621 ) @ SV621 )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1458 @ SV2118 @ SV621 ) @ ( c_Orderings_Oord__class_Omax @ SV1458 @ SV2529 @ SV621 ) @ SV621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5165]) ).
thf(5919,plain,
! [SV2530: $i,SV2119: $i,SV1459: $i,SV622: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV622 )
| ( ( c_Power_Opower__class_Opower @ SV1459 @ ( c_HOL_Otimes__class_Otimes @ SV2119 @ SV2530 @ tc_nat ) @ SV622 )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV1459 @ SV2119 @ SV622 ) @ SV2530 @ SV622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5166]) ).
thf(5920,plain,
! [SV2120: $i,SV1460: $i,SV623: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV623 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1460 @ SV2120 @ SV623 )
| ( SV2120 = SV1460 )
| ~ ( c_lessequals @ SV1460 @ SV2120 @ SV623 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5167]) ).
thf(5921,plain,
! [SV2121: $i,SV1461: $i,SV624: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV624 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1461 @ SV2121 @ SV624 )
| ~ ( c_lessequals @ SV1461 @ SV2121 @ SV624 )
| ( SV2121 = SV1461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5168]) ).
thf(5922,plain,
! [SV1462: $i,SV625: $i] :
( ( ( SV625 = SV1462 )
= $true )
| ( ( ~ ( c_lessequals @ SV625 @ SV1462 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV625 @ SV1462 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5169]) ).
thf(5923,plain,
! [SV1463: $i,SV626: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV626 @ SV1463 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV626 @ SV1463 @ tc_nat ) )
= $true )
| ( ( SV626 = SV1463 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5170]) ).
thf(5924,plain,
! [SV1464: $i,SV627: $i] :
( ( ( SV627 = SV1464 )
= $true )
| ( ( ~ ( c_lessequals @ SV627 @ SV1464 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV627 @ SV1464 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5171]) ).
thf(5925,plain,
! [SV2122: $i,SV1465: $i,SV628: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV628 ) )
= $true )
| ( ( ( SV1465 = SV2122 )
| ( c_HOL_Oord__class_Oless @ SV1465 @ SV2122 @ SV628 )
| ~ ( c_lessequals @ SV1465 @ SV2122 @ SV628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5172]) ).
thf(5926,plain,
! [SV2123: $i,SV1466: $i,SV629: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV629 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1466 @ SV2123 @ SV629 )
| ( SV1466 = SV2123 )
| ~ ( c_lessequals @ SV1466 @ SV2123 @ SV629 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5173]) ).
thf(5927,plain,
! [SV2124: $i,SV1467: $i,SV630: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV630 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1467 @ SV2124 @ SV630 )
| ( SV1467 = SV2124 )
| ~ ( c_lessequals @ SV1467 @ SV2124 @ SV630 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5174]) ).
thf(5928,plain,
! [SV2125: $i,SV1468: $i,SV631: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV631 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1468 @ SV2125 @ SV631 )
| ~ ( c_lessequals @ SV1468 @ SV2125 @ SV631 )
| ( SV1468 = SV2125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5175]) ).
thf(5929,plain,
! [SV2126: $i,SV1469: $i,SV632: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV632 ) )
= $true )
| ( ( ( SV1469 = SV2126 )
| ~ ( c_lessequals @ SV1469 @ SV2126 @ SV632 )
| ( c_HOL_Oord__class_Oless @ SV1469 @ SV2126 @ SV632 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5176]) ).
thf(5930,plain,
! [SV2127: $i,SV1470: $i,SV633: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV633 ) )
= $true )
| ( ( ( SV1470 = SV2127 )
| ( c_HOL_Oord__class_Oless @ SV1470 @ SV2127 @ SV633 )
| ~ ( c_lessequals @ SV1470 @ SV2127 @ SV633 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5177]) ).
thf(5931,plain,
! [SV2128: $i,SV1471: $i,SV634: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV634 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ ( c_HOL_Otimes__class_Otimes @ SV1471 @ SV2128 @ SV634 ) @ SV634 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV2128 @ SV634 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV1471 @ SV634 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5178]) ).
thf(5932,plain,
! [SV2129: $i,SV1472: $i,SV635: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV635 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ ( c_HOL_Otimes__class_Otimes @ SV1472 @ SV2129 @ SV635 ) @ SV635 )
| ~ ( c_lessequals @ SV2129 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 )
| ~ ( c_lessequals @ SV1472 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5179]) ).
thf(5933,plain,
! [SV2130: $i,SV1473: $i,SV636: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV636 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ ( c_HOL_Otimes__class_Otimes @ SV1473 @ SV2130 @ SV636 ) @ SV636 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV2130 @ SV636 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV1473 @ SV636 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5180]) ).
thf(5934,plain,
! [SV1474: $i,SV637: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV637 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV637 ) @ ( c_HOL_Otimes__class_Otimes @ SV1474 @ SV1474 @ SV637 ) @ SV637 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5181]) ).
thf(5935,plain,
! [SV2131: $i,SV1475: $i,SV638: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV638 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ ( c_HOL_Otimes__class_Otimes @ SV1475 @ SV2131 @ SV638 ) @ SV638 )
| ~ ( c_lessequals @ SV2131 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 )
| ~ ( c_lessequals @ SV1475 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5182]) ).
thf(5936,plain,
! [SV2132: $i,SV1476: $i,SV639: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV639 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ ( c_HOL_Otimes__class_Otimes @ SV1476 @ SV2132 @ SV639 ) @ SV639 )
| ~ ( c_lessequals @ SV2132 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 )
| ~ ( c_lessequals @ SV1476 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5183]) ).
thf(5937,plain,
! [SV2133: $i,SV1477: $i,SV640: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV640 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ ( c_HOL_Otimes__class_Otimes @ SV1477 @ SV2133 @ SV640 ) @ SV640 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV2133 @ SV640 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV1477 @ SV640 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5184]) ).
thf(5938,plain,
! [SV1478: $i,SV642: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV642 ) @ ( c_Suc @ SV1478 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV642 @ SV1478 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5185]) ).
thf(5939,plain,
! [SV1479: $i,SV643: $i] :
( ( ( c_lessequals @ SV643 @ SV1479 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV643 ) @ ( c_Suc @ SV1479 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5186]) ).
thf(5940,plain,
! [SV2531: $i,SV2134: $i,SV1480: $i,SV644: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV644 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1480 @ SV2134 @ SV644 ) @ SV2531 @ SV644 )
= ( c_HOL_Otimes__class_Otimes @ SV1480 @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV2531 @ SV644 ) @ SV644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5187]) ).
thf(5941,plain,
! [SV2532: $i,SV2135: $i,SV1481: $i,SV645: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV645 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1481 @ SV2135 @ SV645 ) @ SV2532 @ SV645 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1481 @ SV2532 @ SV645 ) @ SV2135 @ SV645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5188]) ).
thf(5942,plain,
! [SV2533: $i,SV2136: $i,SV1482: $i,SV646: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV646 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1482 @ SV2136 @ SV646 ) @ SV2533 @ SV646 )
= ( c_HOL_Otimes__class_Otimes @ SV1482 @ ( c_HOL_Otimes__class_Otimes @ SV2136 @ SV2533 @ SV646 ) @ SV646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5189]) ).
thf(5943,plain,
! [SV2534: $i,SV2137: $i,SV1483: $i,SV647: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV647 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1483 @ ( c_HOL_Otimes__class_Otimes @ SV2137 @ SV2534 @ SV647 ) @ SV647 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1483 @ SV2137 @ SV647 ) @ SV2534 @ SV647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5190]) ).
thf(5944,plain,
! [SV2535: $i,SV2138: $i,SV1484: $i,SV648: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV648 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1484 @ ( c_HOL_Otimes__class_Otimes @ SV2138 @ SV2535 @ SV648 ) @ SV648 )
= ( c_HOL_Otimes__class_Otimes @ SV2138 @ ( c_HOL_Otimes__class_Otimes @ SV1484 @ SV2535 @ SV648 ) @ SV648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5191]) ).
thf(5945,plain,
! [SV2536: $i,SV2139: $i,SV1485: $i,SV649: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV649 @ SV1485 @ SV2139 ) @ SV2536 @ SV2139 )
= ( c_List_Oappend @ SV649 @ ( c_List_Oappend @ SV1485 @ SV2536 @ SV2139 ) @ SV2139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5192]) ).
thf(5946,plain,
! [SV2537: $i,SV2141: $i,SV1487: $i,SV651: $i] :
( ( ( c_List_Oappend @ SV651 @ ( c_List_Oappend @ SV1487 @ SV2141 @ SV2537 ) @ SV2537 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV651 @ SV1487 @ SV2537 ) @ SV2141 @ SV2537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5194]) ).
thf(5947,plain,
! [SV2538: $i,SV2142: $i,SV1488: $i,SV652: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV652 @ SV1488 @ SV2142 ) @ SV2538 @ SV2142 )
= ( c_List_Oappend @ SV652 @ ( c_List_Oappend @ SV1488 @ SV2538 @ SV2142 ) @ SV2142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5195]) ).
thf(5948,plain,
! [SV2539: $i,SV2143: $i,SV1489: $i,SV653: $i] :
( ( ( c_List_Oappend @ SV653 @ ( c_List_Oappend @ SV1489 @ SV2143 @ SV2539 ) @ SV2539 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV653 @ SV1489 @ SV2539 ) @ SV2143 @ SV2539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5196]) ).
thf(5949,plain,
! [SV2540: $i,SV2144: $i,SV1490: $i,SV654: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV654 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1490 @ ( c_HOL_Otimes__class_Otimes @ SV2144 @ SV2540 @ SV654 ) @ SV654 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1490 @ SV2144 @ SV654 ) @ SV2540 @ SV654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5197]) ).
thf(5950,plain,
! [SV2541: $i,SV2145: $i,SV1491: $i,SV655: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV655 )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV655 ) @ SV1491 ) @ SV2145 ) @ SV2541 @ SV655 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV655 ) @ ( c_HOL_Otimes__class_Otimes @ SV1491 @ SV2541 @ SV655 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV2541 @ SV655 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5198]) ).
thf(5951,plain,
! [SV2542: $i,SV2146: $i,SV1492: $i,SV656: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV656 )
| ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV656 ) @ SV1492 ) @ SV2146 ) @ SV2542 @ SV656 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV656 ) @ ( c_HOL_Otimes__class_Otimes @ SV1492 @ SV2542 @ SV656 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2146 @ SV2542 @ SV656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5199]) ).
thf(5952,plain,
! [SV2543: $i,SV2149: $i,SV1495: $i,SV659: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV659 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1495 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV659 ) @ SV2149 ) @ SV2543 ) @ SV659 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV659 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV2149 @ SV659 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV2543 @ SV659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5202]) ).
thf(5953,plain,
! [SV2150: $i,SV1496: $i,SV660: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV660 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1496 @ SV2150 @ SV660 )
| ~ ( c_HOL_Oord__class_Oless @ SV2150 @ SV1496 @ SV660 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5203]) ).
thf(5954,plain,
! [SV2151: $i,SV1497: $i,SV661: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV661 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1497 @ SV2151 @ SV661 )
| ~ ( c_HOL_Oord__class_Oless @ SV2151 @ SV1497 @ SV661 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5204]) ).
thf(5955,plain,
! [SV2152: $i,SV1499: $i,SV663: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV663 ) )
= $true )
| ( ( ( c_lessequals @ SV1499 @ SV2152 @ SV663 )
| ( c_lessequals @ SV2152 @ SV1499 @ SV663 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5206]) ).
thf(5956,plain,
! [SV2153: $i,SV1500: $i,SV664: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV664 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1500 @ SV2153 @ SV664 )
| ~ ( c_HOL_Oord__class_Oless @ SV2153 @ SV1500 @ SV664 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5207]) ).
thf(5957,plain,
! [SV2154: $i,SV1501: $i,SV665: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV665 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1501 @ SV2154 @ SV665 )
| ~ ( c_HOL_Oord__class_Oless @ SV2154 @ SV1501 @ SV665 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5208]) ).
thf(5958,plain,
! [SV1503: $i,SV667: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV667 @ SV1503 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV667 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV667 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV667 @ SV1503 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5210]) ).
thf(5959,plain,
! [SV1504: $i,SV669: $i] :
( ( ( hBOOL @ ( hAPP @ SV669 @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ SV669 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV669 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV669 @ SV1504 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5212]) ).
thf(5960,plain,
! [SV1507: $i,SV678: $i] :
( ( ( hBOOL @ ( hAPP @ SV678 @ ( v_sko__List__Xreplicate__Xinduct__1 @ SV678 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV678 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV678 @ SV1507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5215]) ).
thf(5961,plain,
! [SV2158: $i,SV1508: $i,SV679: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV679 @ ( c_Nat_Onat_Onat__case @ SV1508 @ SV2158 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV679 @ SV1508 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5216]) ).
thf(5962,plain,
! [SV1509: $i,SV680: $i] :
( ( ( hBOOL @ ( hAPP @ SV680 @ ( v_sko__Nat__Xnat__Xinducts__1 @ SV680 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV680 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV680 @ SV1509 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5217]) ).
thf(5963,plain,
! [SV1510: $i,SV683: $i] :
( ( ( hBOOL @ ( hAPP @ SV683 @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV683 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV683 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV683 @ SV1510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5218]) ).
thf(5964,plain,
! [SV1511: $i,SV686: $i] :
( ( ( hBOOL @ ( hAPP @ SV686 @ ( v_sko__List__Xupt__Xinduct__1 @ SV686 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV686 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV686 @ SV1511 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5219]) ).
thf(5965,plain,
! [SV1513: $i,SV689: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV689 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV689 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV689 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV689 @ SV1513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5220]) ).
thf(5966,plain,
! [SV2544: $i,SV2160: $i,SV1515: $i,SV698: $i] :
( ( ! [SY6906: $i,SY6907: $i,SY6908: $i] :
( ( ( hAPP @ ( hAPP @ SV698 @ SV1515 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV2160 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2544 @ SY6906 @ SV698 @ SY6907 @ SV2160 @ SY6908 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5222]) ).
thf(5967,plain,
! [SV1516: $i,SV699: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV699 )
= $false )
| ( ( ( c_List_Olistsum @ SV1516 @ SV699 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV699 ) @ SV1516 @ ( c_HOL_Ozero__class_Ozero @ SV699 ) @ SV699 @ SV699 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5223]) ).
thf(5968,plain,
! [SV1517: $i,SV700: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV700 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV700 ) @ ( c_HOL_Ozero__class_Ozero @ SV700 ) @ SV1517 @ SV700 @ SV700 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV700 ) @ SV1517 @ ( c_HOL_Ozero__class_Ozero @ SV700 ) @ SV700 @ SV700 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5224]) ).
thf(5969,plain,
! [SV2161: $i,SV1518: $i,SV701: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV701 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SV1518 @ SV2161 @ SV701 @ SV701 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SV1518 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SV2161 @ ( c_HOL_Ozero__class_Ozero @ SV701 ) @ SV701 @ SV701 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5225]) ).
thf(5970,plain,
! [SV2545: $i,SV2162: $i,SV1519: $i,SV702: $i] :
( ( ( c_Type_Otyping @ SV702 @ SV1519 @ SV2162 )
| ~ ( c_Lambda_Obeta @ SV2545 @ SV1519 )
| ~ ( c_Type_Otyping @ SV702 @ SV2545 @ SV2162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5226]) ).
thf(5971,plain,
! [SV2163: $i,SV1520: $i,SV703: $i] :
( ( ( ( hAPP @ SV703 @ SV1520 )
= SV2163 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV703 @ ( c_Lambda_OdB_OVar @ SV1520 ) @ SV2163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5227]) ).
thf(5972,plain,
! [SV2164: $i,SV1522: $i,SV705: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV705 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV705 @ SV1522 ) @ tc_Type_Otype ) @ SV1522 @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV705 @ SV1522 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV705 @ ( c_Lambda_OdB_OAbs @ SV1522 ) @ SV2164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5228]) ).
thf(5973,plain,
! [SV2165: $i,SV1523: $i,SV706: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV706 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV1523 @ SV706 @ SV2165 ) @ tc_Type_Otype ) @ SV2165 @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV1523 @ SV706 @ SV2165 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV706 @ ( c_Lambda_OdB_OAbs @ SV2165 ) @ SV1523 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5229]) ).
thf(5974,plain,
! [SV2546: $i,SV2166: $i,SV1524: $i,SV707: $i] :
( ( ( c_Type_Otyping @ SV707 @ SV1524 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV2166 @ SV707 @ SV1524 @ SV2546 ) ) @ SV2166 ) )
| ~ ( c_Type_Otyping @ SV707 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1524 ) @ SV2546 ) @ SV2166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5230]) ).
thf(5975,plain,
! [SV2547: $i,SV2167: $i,SV1525: $i,SV708: $i] :
( ( ! [SY6909: $i] :
( ( c_Type_Otype_Otype__rec @ SV708 @ SV1525 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2167 ) @ SV2547 ) @ SY6909 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV1525 @ SV2167 ) @ SV2547 ) @ ( c_Type_Otype_Otype__rec @ SV708 @ SV1525 @ SV2167 @ SY6909 ) ) @ ( c_Type_Otype_Otype__rec @ SV708 @ SV1525 @ SV2547 @ SY6909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5231]) ).
thf(5976,plain,
! [SV2548: $i,SV2168: $i,SV1526: $i,SV709: $i] :
( ( ! [SY6910: $i] :
( ( c_Type_Otype_Otype__case @ SV709 @ SV1526 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2168 ) @ SV2548 ) @ SY6910 )
= ( hAPP @ ( hAPP @ SV1526 @ SV2168 ) @ SV2548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5232]) ).
thf(5977,plain,
! [SV2549: $i,SV2169: $i,SV1527: $i,SV710: $i] :
( ( ! [SY6911: $i] :
( ~ ( hBOOL @ ( hAPP @ SV710 @ ( c_Type_Otype_Otype__case @ SV1527 @ SV2169 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2549 ) @ SY6911 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV710 @ ( hAPP @ ( hAPP @ SV2169 @ SV2549 ) @ SY6911 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5233]) ).
thf(5978,plain,
! [SV2550: $i,SV2170: $i,SV1528: $i,SV711: $i] :
( ( ! [SY6912: $i] :
( ~ ( hBOOL @ ( hAPP @ SV711 @ ( c_Type_Otype_Otype__case @ SV1528 @ SV2170 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2550 ) @ SY6912 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV711 @ ( hAPP @ ( hAPP @ SV2170 @ SV2550 ) @ SY6912 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5234]) ).
thf(5979,plain,
! [SV2551: $i,SV2171: $i,SV1529: $i,SV712: $i] :
( ( ! [SY6913: $i,SY6914: $i] :
( ( c_List_Ofoldr @ SV712 @ ( c_List_Olist_OCons @ SV1529 @ SV2171 @ SV2551 ) @ SY6913 @ SV2551 @ SY6914 )
= ( hAPP @ ( hAPP @ SV712 @ SV1529 ) @ ( c_List_Ofoldr @ SV712 @ SV2171 @ SY6913 @ SV2551 @ SY6914 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5235]) ).
thf(5980,plain,
! [SV2552: $i,SV2172: $i,SV1530: $i,SV713: $i] :
( ( ! [SY6915: $i,SY6916: $i] :
( ( c_List_Ofoldr @ SV713 @ ( c_List_Oappend @ SV1530 @ SV2172 @ SV2552 ) @ SY6915 @ SV2552 @ SY6916 )
= ( c_List_Ofoldr @ SV713 @ SV1530 @ ( c_List_Ofoldr @ SV713 @ SV2172 @ SY6915 @ SV2552 @ SY6916 ) @ SV2552 @ SY6916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5236]) ).
thf(5981,plain,
! [SV2553: $i,SV2173: $i,SV1531: $i,SV714: $i] :
( ( ( c_List_Ofoldr @ SV714 @ ( c_List_Olist_ONil @ SV1531 ) @ SV2173 @ SV1531 @ SV2553 )
= SV2173 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5237]) ).
thf(5982,plain,
! [SV1532: $i,SV715: $i] :
( ( ( c_InductTermi_OIT @ SV715 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ SV715 @ SV1532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5238]) ).
thf(5983,plain,
! [SV2176: $i,SV1535: $i,SV718: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV718 @ SV1535 ) @ ( c_Lambda_Olift @ SV2176 @ SV1535 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV718 @ SV2176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5241]) ).
thf(5984,plain,
! [SV2554: $i,SV2177: $i,SV1536: $i,SV719: $i] :
( ( ! [SY6917: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV719 @ SV1536 @ SV2177 @ SV2554 ) @ SY6917 )
= ( hAPP @ SV719 @ SY6917 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY6917 @ SV1536 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5242]) ).
thf(5985,plain,
! [SV2555: $i,SV2178: $i,SV1537: $i,SV720: $i] :
( ( ( c_Type_Otyping @ SV720 @ SV1537 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV2178 @ SV720 @ SV1537 @ SV2555 ) @ SV2178 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV720 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1537 @ SV2555 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5243]) ).
thf(5986,plain,
! [SV2556: $i,SV2179: $i,SV1538: $i,SV721: $i] :
( ( ! [SY6918: $i] :
( ( c_Type_Otyping @ SV721 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1538 @ SV2179 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2556 )
| ~ ( c_Type_Otypings @ SV721 @ SV2179 @ SY6918 )
| ~ ( c_Type_Otyping @ SV721 @ SV1538 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SY6918 @ SV2556 @ tc_Type_Otype @ tc_Type_Otype ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5244]) ).
thf(5987,plain,
! [SV2557: $i,SV2180: $i,SV1539: $i,SV722: $i] :
( ( ( c_Type_Otyping @ SV722 @ SV1539 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV2180 @ SV722 @ SV1539 @ SV2557 ) @ SV2180 @ tc_Type_Otype @ tc_Type_Otype ) )
| ~ ( c_Type_Otyping @ SV722 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1539 @ SV2557 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5245]) ).
thf(5988,plain,
! [SV1540: $i,SV723: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV723 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV723 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV723 )
| ~ ( class_Power_Opower @ SV723 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV723 ) @ SV1540 @ SV723 )
= ( c_HOL_Ozero__class_Ozero @ SV723 ) )
| ( SV1540
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5246]) ).
thf(5989,plain,
! [SV1541: $i,SV724: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV724 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV724 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV724 ) @ SV1541 @ SV724 )
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1541
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5247]) ).
thf(5990,plain,
! [SV2558: $i,SV2181: $i,SV1542: $i,SV726: $i] :
( ( ! [SY6919: $i] :
( ( c_Type_Oshift @ ( c_Type_Oshift @ SV726 @ SV1542 @ SV2181 @ SV2558 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY6919 @ SV2558 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV726 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY6919 @ SV2558 ) @ ( c_Suc @ SV1542 ) @ SV2181 @ SV2558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5249]) ).
thf(5991,plain,
! [SV2559: $i,SV2182: $i,SV1543: $i,SV727: $i] :
( ( ! [SY6920: $i] :
( ( c_Type_Otyping @ SV727 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1543 ) @ SV2182 ) @ SV2559 )
| ~ ( c_Type_Otyping @ SV727 @ SV2182 @ SY6920 )
| ~ ( c_Type_Otyping @ SV727 @ SV1543 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SY6920 ) @ SV2559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5250]) ).
thf(5992,plain,
! [SV2560: $i,SV2183: $i,SV1544: $i,SV728: $i] :
( ( ! [SY6921: $i,SY6922: $i] :
( ~ ( c_Type_Otyping @ SV728 @ SV1544 @ SV2183 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV728 @ SV2560 @ SV2183 @ tc_Type_Otype ) @ SY6921 @ SY6922 )
| ( c_Type_Otyping @ SV728 @ ( c_Lambda_Osubst @ SY6921 @ SV1544 @ SV2560 ) @ SY6922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5251]) ).
thf(5993,plain,
! [SV2561: $i,SV2184: $i,SV1545: $i,SV729: $i] :
( ( ( c_Type_Otyping @ SV729 @ ( c_Lambda_OdB_OAbs @ SV1545 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2184 ) @ SV2561 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV729 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2184 @ tc_Type_Otype ) @ SV1545 @ SV2561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5252]) ).
thf(5994,plain,
! [SV2562: $i,SV2185: $i,SV1546: $i,SV730: $i] :
( ( ! [SY6923: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV730 @ SV1546 @ SV2185 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV2562 @ SV1546 ) @ SY6923 )
| ~ ( c_Type_Otyping @ SV730 @ SV2562 @ SY6923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5253]) ).
thf(5995,plain,
! [SV2563: $i,SV2186: $i,SV1547: $i,SV731: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV731 @ SV1547 @ SV2186 @ SV2563 ) @ SV1547 )
= SV2186 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5254]) ).
thf(5996,plain,
! [SV732: $i,SV1548: $i] :
( ( ( class_Orderings_Opreorder @ SV1548 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV732 @ SV1548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5255]) ).
thf(5997,plain,
! [SV733: $i,SV1549: $i] :
( ( ( class_Orderings_Oorder @ SV1549 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV733 @ SV1549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5256]) ).
thf(5998,plain,
! [SV734: $i,SV1550: $i] :
( ( ( class_Orderings_Obot @ SV1550 )
= $false )
| ( ( class_Orderings_Obot @ ( tc_fun @ SV734 @ SV1550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5257]) ).
thf(5999,plain,
! [SV2187: $i,SV1552: $i,SV736: $i] :
( ( ( SV736 = SV1552 )
= $true )
| ( ( ~ ( c_fequal @ SV736 @ SV1552 @ SV2187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5258]) ).
thf(6000,plain,
! [SV2564: $i,SV2188: $i,SV1553: $i,SV737: $i] :
( ( ! [SY6924: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV737 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1553 @ SV2188 @ SV737 )
!= ( c_HOL_Ominus__class_Ominus @ SV2564 @ SY6924 @ SV737 ) )
| ( c_lessequals @ SV2188 @ SV1553 @ SV737 )
| ~ ( c_lessequals @ SY6924 @ SV2564 @ SV737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5259]) ).
thf(6001,plain,
! [SV2565: $i,SV2189: $i,SV1554: $i,SV738: $i] :
( ( ! [SY6925: $i] :
( ( ( c_List_Olist_OCons @ SV738 @ SV1554 @ SV2189 )
!= ( c_List_Olist_OCons @ SV2565 @ SY6925 @ SV2189 ) )
| ( SV738 = SV2565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5260]) ).
thf(6002,plain,
! [SV2190: $i,SV1555: $i,SV739: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV739 @ SV1555 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV739 @ SV2190 @ tc_nat ) )
= $true )
| ( ( ( SV1555 = SV2190 )
| ( SV739
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5261]) ).
thf(6003,plain,
! [SV2191: $i,SV1556: $i,SV740: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV740 ) @ SV1556 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV740 ) @ SV2191 ) )
= $true )
| ( ( SV1556 = SV2191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5262]) ).
thf(6004,plain,
! [SV2192: $i,SV1557: $i,SV741: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV741 ) @ SV1557 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV741 ) @ SV2192 ) )
= $true )
| ( ( SV1557 = SV2192 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5263]) ).
thf(6005,plain,
! [SV2566: $i,SV2193: $i,SV1558: $i,SV742: $i] :
( ( ! [SY6926: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV1558 @ tc_nat ) ) @ SV2193 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2566 @ SV1558 @ tc_nat ) ) @ SY6926 ) )
| ~ ( c_lessequals @ SV2566 @ SV742 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV742 @ SV2566 @ tc_nat ) @ SV1558 @ tc_nat ) ) @ SV2193 )
= SY6926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5264]) ).
thf(6006,plain,
! [SV2194: $i,SV1559: $i,SV743: $i] :
( ( ( ( c_List_Oappend @ SV743 @ SV1559 @ SV2194 )
!= SV743 )
= $true )
| ( ( SV1559
= ( c_List_Olist_ONil @ SV2194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5265]) ).
thf(6007,plain,
! [SV2567: $i,SV2195: $i,SV1560: $i,SV744: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV744 ) @ SV1560 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV2195 ) @ SV2567 ) )
| ( SV744 = SV2195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5266]) ).
thf(6008,plain,
! [SV2196: $i,SV1561: $i,SV745: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1561 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV2196 @ SV1561 @ tc_nat ) )
= $true )
| ( ( ( SV1561
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV745 = SV2196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5267]) ).
thf(6009,plain,
! [SV1562: $i,SV746: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV746 )
= ( c_Lambda_OdB_OAbs @ SV1562 ) )
= $false )
| ( ( SV746 = SV1562 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5268]) ).
thf(6010,plain,
! [SV2568: $i,SV2197: $i,SV1563: $i,SV747: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV747 ) @ SV1563 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV2197 ) @ SV2568 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1563 = SV2568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5269]) ).
thf(6011,plain,
! [SV2198: $i,SV1564: $i,SV748: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV748 ) @ SV1564 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV748 ) @ SV2198 @ tc_nat ) )
= $true )
| ( ( SV1564 = SV2198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5270]) ).
thf(6012,plain,
! [SV1565: $i,SV749: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV749 ) @ SV1565 ) )
= $false )
| ( ( ( SV1565
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1565
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5271]) ).
thf(6013,plain,
! [SV2569: $i,SV2199: $i,SV1566: $i,SV750: $i] :
( ( ! [SY6927: $i,SY6928: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV750 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV1566 @ SV2199 @ SV750 ) ) @ SV2569 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SY6927 @ SV2199 @ SV750 ) ) @ SY6928 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ SY6927 @ SV750 ) @ SV2199 @ SV750 ) ) @ SV2569 )
= SY6928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5272]) ).
thf(6014,plain,
! [SV2570: $i,SV2200: $i,SV1567: $i,SV751: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV751 ) ) @ SV1567 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2200 ) @ SV2570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5273]) ).
thf(6015,plain,
! [SV1568: $i,SV752: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV752 ) @ SV1568 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV1568
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5274]) ).
thf(6016,plain,
! [SV1569: $i,SV753: $i] :
( ( ( SV753
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV753 ) @ SV1569 ) )
= $false )
| ( ( SV1569
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5275]) ).
thf(6017,plain,
! [SV2571: $i,SV2201: $i,SV1570: $i,SV754: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV754 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SV1570 ) @ SV2201 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SV2571 ) @ SV2201 ) )
| ( SV1570 = SV2571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5276]) ).
thf(6018,plain,
! [SV2202: $i,SV1571: $i,SV755: $i] :
( ( ( ( c_List_Olist_ONil @ SV755 )
!= ( c_List_Oappend @ SV1571 @ SV2202 @ SV755 ) )
= $true )
| ( ( SV2202
= ( c_List_Olist_ONil @ SV755 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5277]) ).
thf(6019,plain,
! [SV1572: $i,SV756: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV756 ) @ SV1572 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV1572
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1572
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5278]) ).
thf(6020,plain,
! [SV1573: $i,SV757: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV757 ) @ SV1573 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV757
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1573
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5279]) ).
thf(6021,plain,
! [SV2572: $i,SV2203: $i,SV1574: $i,SV758: $i] :
( ( ( ( c_List_Oappend @ SV758 @ SV1574 @ SV2203 )
!= ( c_List_Oappend @ SV2572 @ SV1574 @ SV2203 ) )
| ( SV758 = SV2572 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5280]) ).
thf(6022,plain,
! [SV2573: $i,SV2204: $i,SV1575: $i,SV759: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1575 ) @ SV2204 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SV2573 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SV2204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5281]) ).
thf(6023,plain,
! [SV2574: $i,SV2205: $i,SV1576: $i,SV760: $i] :
( ( ! [SY6929: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV760 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV2205 @ SV760 )
!= ( c_HOL_Ominus__class_Ominus @ SV2574 @ SY6929 @ SV760 ) )
| ( c_HOL_Oord__class_Oless @ SV2574 @ SY6929 @ SV760 )
| ~ ( c_HOL_Oord__class_Oless @ SV1576 @ SV2205 @ SV760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5282]) ).
thf(6024,plain,
! [SV2206: $i,SV1577: $i,SV761: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV761 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV1577 @ SV2206 @ SV761 )
!= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
| ( SV1577
= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
| ( SV2206
= ( c_HOL_Ozero__class_Ozero @ SV761 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5283]) ).
thf(6025,plain,
! [SV2207: $i,SV1578: $i,SV762: $i] :
( ( SV762
= ( c_List_Olist_OCons @ SV1578 @ SV762 @ SV2207 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5284]) ).
thf(6026,plain,
! [SV2575: $i,SV2208: $i,SV1579: $i,SV763: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV763 )
| ( ( c_Power_Opower__class_Opower @ SV1579 @ SV2208 @ SV763 )
!= ( c_Power_Opower__class_Opower @ SV2575 @ SV2208 @ SV763 ) )
| ( SV1579 = SV2575 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2208 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV2575 @ SV763 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5285]) ).
thf(6027,plain,
! [SV2576: $i,SV2209: $i,SV1580: $i,SV764: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV764 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SV2209 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SV2576 ) )
| ( SV2209 = SV2576 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5286]) ).
thf(6028,plain,
! [SV1581: $i,SV765: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV765 ) @ SV1581 ) )
= $false )
| ( ( ( SV765
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV765
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5287]) ).
thf(6029,plain,
! [SV2577: $i,SV2210: $i,SV1582: $i,SV766: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV766 ) @ SV1582 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2210 ) @ SV2577 ) )
| ( SV1582 = SV2577 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5288]) ).
thf(6030,plain,
! [SV2211: $i,SV1584: $i,SV769: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV769 ) @ SV1584 )
= ( c_Lambda_OdB_OAbs @ SV2211 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5290]) ).
thf(6031,plain,
! [SV1585: $i,SV770: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV770 @ SV1585 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( SV770
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5291]) ).
thf(6032,plain,
! [SV2212: $i,SV1586: $i,SV771: $i] :
( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV771 ) @ SV1586 )
= ( c_Type_Otype_OAtom @ SV2212 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5292]) ).
thf(6033,plain,
! [SV2213: $i,SV1587: $i,SV772: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV772 @ SV1587 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV2213 @ SV1587 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV772 = SV2213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5293]) ).
thf(6034,plain,
! [SV2214: $i,SV1588: $i,SV773: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV773 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV773 )
| ( SV1588
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV773 ) @ SV1588 ) @ SV2214 ) )
| ( SV2214
= ( c_HOL_Ozero__class_Ozero @ SV773 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5294]) ).
thf(6035,plain,
! [SV2578: $i,SV2215: $i,SV1589: $i,SV774: $i] :
( ( ! [SY6930: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV774 )
| ~ ( class_Int_Onumber__ring @ SV774 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2578 @ SV774 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SY6930 @ SV774 ) ) )
| ( SV2578 = SY6930 )
| ( SV2215
= ( c_HOL_Ozero__class_Ozero @ SV774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5295]) ).
thf(6036,plain,
! [SV2579: $i,SV2216: $i,SV1590: $i,SV775: $i] :
( ( ! [SY6931: $i] :
( ( ( c_List_Oreplicate @ SV775 @ SV1590 @ SV2216 )
!= ( c_List_Oreplicate @ SV2579 @ SY6931 @ SV2216 ) )
| ( SV775 = SV2579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5296]) ).
thf(6037,plain,
! [SV1591: $i,SV776: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV776 ) @ SV1591 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV1591
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV776
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5297]) ).
thf(6038,plain,
! [SV2580: $i,SV2217: $i,SV1592: $i,SV778: $i] :
( ( ! [SY6932: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV778 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1592 @ SV2217 @ SV778 )
!= ( c_HOL_Ominus__class_Ominus @ SV2580 @ SY6932 @ SV778 ) )
| ( c_HOL_Oord__class_Oless @ SV1592 @ SV2217 @ SV778 )
| ~ ( c_HOL_Oord__class_Oless @ SV2580 @ SY6932 @ SV778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5298]) ).
thf(6039,plain,
! [SV2218: $i,SV1593: $i,SV779: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV779 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV1593 @ SV2218 @ SV779 )
!= SV2218 )
| ( c_lessequals @ SV1593 @ SV2218 @ SV779 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5299]) ).
thf(6040,plain,
! [SV2581: $i,SV2219: $i,SV1594: $i,SV780: $i] :
( ( ! [SY6933: $i] :
( ( ( c_List_Oappend @ SV780 @ ( c_List_Olist_OCons @ SV1594 @ ( c_List_Olist_ONil @ SV2219 ) @ SV2219 ) @ SV2219 )
!= ( c_List_Oappend @ SV2581 @ ( c_List_Olist_OCons @ SY6933 @ ( c_List_Olist_ONil @ SV2219 ) @ SV2219 ) @ SV2219 ) )
| ( SV1594 = SY6933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5300]) ).
thf(6041,plain,
! [SV1595: $i,SV781: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV781 ) @ SV1595 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV781
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5301]) ).
thf(6042,plain,
! [SV2582: $i,SV2220: $i,SV1596: $i,SV782: $i] :
( ( ( ( c_List_Oappend @ SV782 @ SV1596 @ SV2220 )
!= ( c_List_Oappend @ SV782 @ SV2582 @ SV2220 ) )
| ( SV1596 = SV2582 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5302]) ).
thf(6043,plain,
! [SV2221: $i,SV1597: $i,SV783: $i] :
( ( ( c_Type_Otype_OAtom @ SV783 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1597 ) @ SV2221 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5303]) ).
thf(6044,plain,
! [SV2583: $i,SV2222: $i,SV1598: $i,SV784: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SV1598 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2222 @ SV2583 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SV2583 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2222 @ SV1598 @ tc_nat ) ) )
| ( SV1598 = SV2583 )
| ( SV784 = SV2222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5304]) ).
thf(6045,plain,
! [SV2223: $i,SV1599: $i,SV786: $i] :
( ( ( ( c_List_Olist_ONil @ SV786 )
!= ( c_List_Oreplicate @ SV1599 @ SV2223 @ SV786 ) )
= $true )
| ( ( SV1599
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5305]) ).
thf(6046,plain,
! [SV2584: $i,SV2224: $i,SV1600: $i,SV787: $i] :
( ( ! [SY6934: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV787 )
| ~ ( class_Int_Onumber__ring @ SV787 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2224 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SY6934 @ SV787 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SY6934 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2224 @ SV787 ) ) )
| ( SV2224 = SY6934 )
| ( SV1600 = SV2584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5306]) ).
thf(6047,plain,
! [SV1601: $i,SV788: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV788 @ SV1601 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( SV1601
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5307]) ).
thf(6048,plain,
! [SV2585: $i,SV2225: $i,SV1602: $i,SV789: $i] :
( ( ! [SY6935: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV789 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1602 @ SV2225 @ SV789 )
!= ( c_HOL_Ominus__class_Ominus @ SV2585 @ SY6935 @ SV789 ) )
| ( c_lessequals @ SY6935 @ SV2585 @ SV789 )
| ~ ( c_lessequals @ SV2225 @ SV1602 @ SV789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5308]) ).
thf(6049,plain,
! [SV2226: $i,SV1603: $i,SV790: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV790 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV1603 @ SV2226 @ SV790 )
!= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
| ( SV2226
= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
| ( SV1603
= ( c_HOL_Ozero__class_Ozero @ SV790 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5309]) ).
thf(6050,plain,
! [SV1604: $i,SV791: $i] :
( ( ( ( c_Suc @ SV791 )
= ( c_Suc @ SV1604 ) )
= $false )
| ( ( SV791 = SV1604 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5310]) ).
thf(6051,plain,
! [SV1605: $i,SV792: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV792 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV792 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV792 )
| ~ ( class_Power_Opower @ SV792 )
| ( ( c_Power_Opower__class_Opower @ SV1605 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV792 )
!= ( c_HOL_Ozero__class_Ozero @ SV792 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5311]) ).
thf(6052,plain,
! [SV2227: $i,SV1606: $i,SV793: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV793 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV793 ) @ SV1606 ) @ SV2227 )
!= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV2227 @ SV793 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV1606 @ SV793 )
| ( SV1606
= ( c_HOL_Ozero__class_Ozero @ SV793 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5312]) ).
thf(6053,plain,
! [SV2586: $i,SV2228: $i,SV1607: $i,SV794: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV794 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1607 ) @ SV2228 ) )
| ( hBOOL @ ( hAPP @ SV794 @ SV2586 ) )
| ( hBOOL @ ( hAPP @ SV794 @ SV1607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5313]) ).
thf(6054,plain,
! [SV2229: $i,SV1608: $i,SV795: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV795 @ SV1608 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SV2229 @ SV1608 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1608 @ SV2229 @ tc_nat )
| ~ ( c_lessequals @ SV1608 @ SV795 @ tc_nat )
| ( SV795 = SV2229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5314]) ).
thf(6055,plain,
! [SV2587: $i,SV2230: $i,SV1609: $i,SV796: $i] :
( ( ! [SY6936: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV796 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SV2587 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SY6936 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ SV2587 )
= SY6936 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5315]) ).
thf(6056,plain,
! [SV2231: $i,SV1610: $i,SV797: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV797 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV797 ) @ ( c_HOL_Otimes__class_Otimes @ SV1610 @ SV1610 @ SV797 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2231 @ SV2231 @ SV797 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV797 ) )
| ( SV2231
= ( c_HOL_Ozero__class_Ozero @ SV797 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5316]) ).
thf(6057,plain,
! [SV2588: $i,SV2232: $i,SV1611: $i,SV798: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV798 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1611 @ SV1611 @ SV798 )
!= ( c_HOL_Ominus__class_Ominus @ SV2232 @ SV2588 @ SV798 ) )
| ( SV2232 = SV2588 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5317]) ).
thf(6058,plain,
! [SV2589: $i,SV2233: $i,SV1612: $i,SV799: $i] :
( ( ! [SY6937: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV799 @ SV1612 @ tc_nat ) ) @ SV2233 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2589 @ SV1612 @ tc_nat ) ) @ SY6937 ) )
| ~ ( c_lessequals @ SV799 @ SV2589 @ tc_nat )
| ( SV2233
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2589 @ SV799 @ tc_nat ) @ SV1612 @ tc_nat ) ) @ SY6937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5318]) ).
thf(6059,plain,
! [SV2590: $i,SV2234: $i,SV1613: $i,SV800: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV800 ) @ SV1613 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2234 ) @ SV2590 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV2234 @ SV1613 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV800 @ SV2590 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5319]) ).
thf(6060,plain,
! [SV2591: $i,SV2235: $i,SV1614: $i,SV801: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV801 ) @ SV1614 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV2235 ) @ SV2591 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV801 = SV2235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5320]) ).
thf(6061,plain,
! [SV2236: $i,SV1615: $i,SV802: $i] :
( ( ( ( c_List_Oappend @ SV802 @ SV1615 @ SV2236 )
!= ( c_List_Olist_ONil @ SV2236 ) )
= $true )
| ( ( SV1615
= ( c_List_Olist_ONil @ SV2236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5321]) ).
thf(6062,plain,
! [SV2237: $i,SV1616: $i,SV803: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1616 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV803 @ SV2237 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV803 @ tc_nat )
| ( SV1616 = SV2237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5322]) ).
thf(6063,plain,
! [SV2238: $i,SV1617: $i,SV804: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV804 ) @ SV1617 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2238 ) @ SV1617 ) )
= $true )
| ( ( SV804 = SV2238 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5323]) ).
thf(6064,plain,
! [SV1618: $i,SV805: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV805 )
= ( c_Lambda_OdB_OVar @ SV1618 ) )
= $false )
| ( ( SV805 = SV1618 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5324]) ).
thf(6065,plain,
! [SV2592: $i,SV2239: $i,SV1619: $i,SV806: $i] :
( ( ! [SY6938: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV806 )
| ~ ( class_Int_Onumber__ring @ SV806 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2239 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SY6938 @ SV806 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SY6938 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2239 @ SV806 ) ) )
| ( SV2239 = SY6938 )
| ( SV1619 = SV2592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5325]) ).
thf(6066,plain,
! [SV2593: $i,SV2240: $i,SV1620: $i,SV807: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV807 ) @ SV1620 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2240 ) @ SV2593 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1620 = SV2593 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5326]) ).
thf(6067,plain,
! [SV2594: $i,SV2241: $i,SV1621: $i,SV808: $i] :
( ( ! [SY6939: $i,SY6940: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV808 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV1621 @ SV2241 @ SV808 ) ) @ SV2594 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SY6939 @ SV2241 @ SV808 ) ) @ SY6940 ) )
| ( SV2594
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY6939 @ SV1621 @ SV808 ) @ SV2241 @ SV808 ) ) @ SY6940 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5327]) ).
thf(6068,plain,
! [SV2242: $i,SV1622: $i,SV809: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV809 @ SV1622 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV809 @ SV2242 @ tc_nat ) )
= $true )
| ( ( ( SV809
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1622 = SV2242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5328]) ).
thf(6069,plain,
! [SV2243: $i,SV1623: $i,SV810: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV810 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV810 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1623 @ SV2243 @ SV810 )
!= ( c_HOL_Ozero__class_Ozero @ SV810 ) )
| ( SV1623 = SV2243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5329]) ).
thf(6070,plain,
! [SV1624: $i,SV811: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV811 @ SV1624 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( c_lessequals @ SV811 @ SV1624 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5330]) ).
thf(6071,plain,
! [SV2595: $i,SV2244: $i,SV1625: $i,SV812: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1625 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2244 @ SV2595 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV2595 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2244 @ SV1625 @ tc_nat ) ) )
| ( SV1625 = SV2595 )
| ( SV812 = SV2244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5331]) ).
thf(6072,plain,
! [SV1627: $i,SV814: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV814 @ SV1627 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1627 @ SV814 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1627 = SV814 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5333]) ).
thf(6073,plain,
! [SV2245: $i,SV1628: $i,SV815: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV815 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1628 @ SV2245 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV815 )
= SV1628 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5334]) ).
thf(6074,plain,
! [SV2246: $i,SV1629: $i,SV816: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV816 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV1629 @ SV2246 @ SV816 )
!= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
| ( SV2246
= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
| ( SV1629
= ( c_HOL_Ozero__class_Ozero @ SV816 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5335]) ).
thf(6075,plain,
! [SV1630: $i,SV817: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV817 ) @ SV1630 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV817
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV817
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5336]) ).
thf(6076,plain,
! [SV2596: $i,SV2247: $i,SV1631: $i,SV818: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV818 ) @ SV1631 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV2247 ) @ SV2596 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5337]) ).
thf(6077,plain,
! [SV2597: $i,SV2248: $i,SV1632: $i,SV819: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV819 ) @ SV1632 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2248 ) @ SV2597 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV819 = SV2248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5338]) ).
thf(6078,plain,
! [SV2598: $i,SV2249: $i,SV1633: $i,SV820: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV820 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SV2249 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SV2598 ) )
| ( SV2249 = SV2598 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5339]) ).
thf(6079,plain,
! [SV2250: $i,SV1634: $i,SV821: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV821 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1634 @ SV821 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV2250 @ SV821 ) )
| ( SV1634 = SV2250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5340]) ).
thf(6080,plain,
! [SV2251: $i,SV1635: $i,SV822: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV822 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV822 ) @ ( c_HOL_Otimes__class_Otimes @ SV1635 @ SV1635 @ SV822 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2251 @ SV2251 @ SV822 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV822 ) )
| ( SV1635
= ( c_HOL_Ozero__class_Ozero @ SV822 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5341]) ).
thf(6081,plain,
! [SV2599: $i,SV2252: $i,SV1636: $i,SV823: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV823 )
| ( ( c_Power_Opower__class_Opower @ SV1636 @ ( c_Suc @ SV2252 ) @ SV823 )
!= ( c_Power_Opower__class_Opower @ SV2599 @ ( c_Suc @ SV2252 ) @ SV823 ) )
| ( SV1636 = SV2599 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV2599 @ SV823 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV1636 @ SV823 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5342]) ).
thf(6082,plain,
! [SV2253: $i,SV1637: $i,SV824: $i] :
( ( ( ( c_List_Oappend @ SV824 @ SV1637 @ SV2253 )
!= SV1637 )
= $true )
| ( ( SV824
= ( c_List_Olist_ONil @ SV2253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5343]) ).
thf(6083,plain,
! [SV2254: $i,SV1638: $i,SV825: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV825 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1638 ) @ SV2254 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5344]) ).
thf(6084,plain,
! [SV2255: $i,SV1639: $i,SV826: $i] :
( ( ( SV826
!= ( c_List_Oappend @ SV1639 @ SV826 @ SV2255 ) )
= $true )
| ( ( SV1639
= ( c_List_Olist_ONil @ SV2255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5345]) ).
thf(6085,plain,
! [SV1640: $i,SV827: $i] :
( ( ( ( c_Suc @ SV827 )
= ( c_Suc @ SV1640 ) )
= $false )
| ( ( SV827 = SV1640 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5346]) ).
thf(6086,plain,
! [SV2256: $i,SV1641: $i,SV828: $i] :
( ( ( c_List_Olist_OCons @ SV828 @ SV1641 @ SV2256 )
= ( c_List_Olist_ONil @ SV2256 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5347]) ).
thf(6087,plain,
! [SV2257: $i,SV1642: $i,SV829: $i] :
( ( ( c_List_Olist_OCons @ SV829 @ SV1642 @ SV2257 )
= ( c_List_Olist_ONil @ SV2257 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5348]) ).
thf(6088,plain,
! [SV2600: $i,SV2258: $i,SV1643: $i,SV830: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV830 ) @ SV1643 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV2258 ) @ SV2600 ) )
| ( SV1643 = SV2600 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5349]) ).
thf(6089,plain,
! [SV2601: $i,SV2259: $i,SV1644: $i,SV832: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV832 )
| ~ ( class_Int_Onumber__ring @ SV832 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2259 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2601 ) )
| ( SV2259 = SV2601 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5350]) ).
thf(6090,plain,
! [SV2260: $i,SV1645: $i,SV833: $i] :
( ( ( ( c_List_Oreplicate @ SV833 @ SV1645 @ SV2260 )
!= ( c_List_Olist_ONil @ SV2260 ) )
= $true )
| ( ( SV833
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5351]) ).
thf(6091,plain,
! [SV2261: $i,SV1646: $i,SV834: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV834 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omin @ SV1646 @ SV2261 @ SV834 )
!= SV1646 )
| ( c_lessequals @ SV1646 @ SV2261 @ SV834 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5352]) ).
thf(6092,plain,
! [SV1647: $i,SV835: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV835 @ SV1647 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( SV1647
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV835
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5353]) ).
thf(6093,plain,
! [SV2262: $i,SV1648: $i,SV836: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV836 @ SV1648 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV2262 ) )
= $true )
| ( ( SV836
= ( c_Lambda_OdB_OAbs @ SV2262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5354]) ).
thf(6094,plain,
! [SV2602: $i,SV2263: $i,SV1649: $i,SV837: $i] :
( ( ! [SY6941: $i] :
( ( ( c_List_Oreplicate @ SV837 @ SV1649 @ SV2263 )
!= ( c_List_Oreplicate @ SV2602 @ SY6941 @ SV2263 ) )
| ( SV1649 = SY6941 )
| ( SV837
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5355]) ).
thf(6095,plain,
! [SV2603: $i,SV2264: $i,SV1650: $i,SV838: $i] :
( ( ! [SY6942: $i,SY6943: $i,SY6944: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SY6942 ) )
| ~ ( c_Type_Otyping @ SY6943 @ SV2603 @ SV1650 )
| ~ ( c_InductTermi_OIT @ SV2603 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY6943 @ SY6942 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SY6944 )
| ~ ( c_InductTermi_OIT @ SV2264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5356]) ).
thf(6096,plain,
! [SV2265: $i,SV1651: $i,SV839: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV839 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV839 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV839 )
| ~ ( class_Power_Opower @ SV839 )
| ( ( c_Power_Opower__class_Opower @ SV1651 @ SV2265 @ SV839 )
!= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
| ( SV1651
= ( c_HOL_Ozero__class_Ozero @ SV839 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5357]) ).
thf(6097,plain,
! [SV2266: $i,SV1652: $i,SV840: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV840 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1652 @ SV2266 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV840 )
= SV1652 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5358]) ).
thf(6098,plain,
! [SV2604: $i,SV2267: $i,SV1653: $i,SV841: $i] :
( ( ! [SY6945: $i] :
( ( ( c_List_Oappend @ SV841 @ ( c_List_Olist_OCons @ SV1653 @ ( c_List_Olist_ONil @ SV2267 ) @ SV2267 ) @ SV2267 )
!= ( c_List_Oappend @ SV2604 @ ( c_List_Olist_OCons @ SY6945 @ ( c_List_Olist_ONil @ SV2267 ) @ SV2267 ) @ SV2267 ) )
| ( SV841 = SV2604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5359]) ).
thf(6099,plain,
! [SV2268: $i,SV1654: $i,SV842: $i] :
( ( ( SV842
!= ( c_List_Oappend @ SV842 @ SV1654 @ SV2268 ) )
= $true )
| ( ( SV1654
= ( c_List_Olist_ONil @ SV2268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5360]) ).
thf(6100,plain,
! [SV2269: $i,SV1655: $i,SV843: $i] :
( ( ( c_Lambda_OdB_OVar @ SV843 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1655 ) @ SV2269 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5361]) ).
thf(6101,plain,
! [SV1656: $i,SV845: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV845 ) @ SV1656 ) )
= $false )
| ( ( ( SV1656
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV845
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5362]) ).
thf(6102,plain,
! [SV2270: $i,SV1657: $i,SV846: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV846 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1657 @ SV2270 @ SV846 )
!= ( c_HOL_Ozero__class_Ozero @ SV846 ) )
| ( SV1657
= ( c_HOL_Ozero__class_Ozero @ SV846 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5363]) ).
thf(6103,plain,
! [SV2271: $i,SV1658: $i,SV847: $i] :
( ( ( c_List_Olist_ONil @ SV847 )
= ( c_List_Olist_OCons @ SV1658 @ SV2271 @ SV847 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5364]) ).
thf(6104,plain,
! [SV2605: $i,SV2272: $i,SV1659: $i,SV848: $i] :
( ( ! [SY6946: $i] :
( ( ( c_List_Olist_OCons @ SV848 @ SV1659 @ SV2272 )
!= ( c_List_Olist_OCons @ SV2605 @ SY6946 @ SV2272 ) )
| ( SV1659 = SY6946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5365]) ).
thf(6105,plain,
! [SV2273: $i,SV1660: $i,SV849: $i] :
( ( ( ( c_List_Olist_ONil @ SV849 )
!= ( c_List_Oappend @ SV1660 @ SV2273 @ SV849 ) )
= $true )
| ( ( SV1660
= ( c_List_Olist_ONil @ SV849 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5366]) ).
thf(6106,plain,
! [SV1661: $i,SV850: $i] :
( ( ( ( c_Type_Otype_OAtom @ SV850 )
= ( c_Type_Otype_OAtom @ SV1661 ) )
= $false )
| ( ( SV850 = SV1661 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5367]) ).
thf(6107,plain,
! [SV1662: $i,SV851: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV851 ) @ SV1662 ) )
= $false )
| ( ( ( SV851
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1662
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5368]) ).
thf(6108,plain,
! [SV1663: $i,SV852: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV852 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV852 ) @ SV1663 ) @ SV1663 )
!= ( c_HOL_Ozero__class_Ozero @ SV852 ) )
| ( SV1663
= ( c_HOL_Ozero__class_Ozero @ SV852 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5369]) ).
thf(6109,plain,
! [SV2606: $i,SV2274: $i,SV1664: $i,SV853: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV853 ) @ SV1664 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2274 ) @ SV2606 ) )
| ( SV853 = SV2274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5370]) ).
thf(6110,plain,
! [SV2275: $i,SV1665: $i,SV854: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV854 ) @ SV1665 )
= ( c_Lambda_OdB_OVar @ SV2275 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5371]) ).
thf(6111,plain,
! [SV2276: $i,SV1666: $i,SV855: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV855 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV855 ) @ SV1666 ) @ SV2276 )
!= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV2276 @ SV855 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV1666 @ SV855 )
| ( SV2276
= ( c_HOL_Ozero__class_Ozero @ SV855 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5372]) ).
thf(6112,plain,
! [SV2277: $i,SV1667: $i,SV856: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV856 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1667 @ SV2277 @ SV856 )
!= ( c_HOL_Ozero__class_Ozero @ SV856 ) )
| ( SV1667 = SV2277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5373]) ).
thf(6113,plain,
! [SV2278: $i,SV1668: $i,SV857: $i] :
( ( ( ( c_List_Oappend @ SV857 @ SV1668 @ SV2278 )
!= ( c_List_Olist_ONil @ SV2278 ) )
= $true )
| ( ( SV857
= ( c_List_Olist_ONil @ SV2278 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5374]) ).
thf(6114,plain,
! [SV2607: $i,SV2279: $i,SV1669: $i,SV858: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV858 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1669 @ SV2279 @ SV858 )
!= ( c_HOL_Ominus__class_Ominus @ SV2607 @ SV2607 @ SV858 ) )
| ( SV1669 = SV2279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5375]) ).
thf(6115,plain,
! [SV2280: $i,SV1670: $i,SV859: $i] :
( ( ( c_List_Olist_OCons @ SV859 @ SV1670 @ SV2280 )
= SV1670 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5376]) ).
thf(6116,plain,
! [SV1671: $i,SV860: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV860 ) @ SV1671 )
= SV860 )
= $false )
| ( ( SV1671
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5377]) ).
thf(6117,plain,
! [SV2608: $i,SV2281: $i,SV1672: $i,SV861: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SV2281 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SV2608 @ tc_nat ) ) )
| ( SV2281 = SV2608 )
| ( SV1672
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5378]) ).
thf(6118,plain,
! [SV2609: $i,SV2282: $i,SV1673: $i,SV863: $i] :
( ( ! [SY6947: $i,SY6948: $i,SY6949: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SY6947 ) )
| ~ ( c_Type_Otyping @ SY6948 @ SV2609 @ SV863 )
| ~ ( c_InductTermi_OIT @ SV2609 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY6948 @ SY6947 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SY6949 )
| ~ ( c_InductTermi_OIT @ SV2282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5379]) ).
thf(6119,plain,
! [SV2283: $i,SV1674: $i,SV864: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV864 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1674 @ SV2283 @ SV864 )
!= ( c_HOL_Ozero__class_Ozero @ SV864 ) )
| ( SV1674 = SV2283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5380]) ).
thf(6120,plain,
! [SV2610: $i,SV2284: $i,SV1675: $i,SV865: $i,SV1: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1 @ SV865 @ tc_nat ) ) @ SV1675 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2284 @ SV865 @ tc_nat ) ) @ SV2610 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1675 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2284 @ SV1 @ tc_nat ) @ SV865 @ tc_nat ) ) @ SV2610 ) @ tc_nat )
| ~ ( c_lessequals @ SV1 @ SV2284 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5381]) ).
thf(6121,plain,
! [SV2611: $i,SV2285: $i,SV1676: $i,SV866: $i,SV2: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV866 @ SV1676 @ tc_nat ) @ SV2285 @ tc_nat ) ) @ SV2611 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV2285 @ tc_nat ) ) @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV866 @ SV2285 @ tc_nat ) ) @ SV2611 ) @ tc_nat )
| ~ ( c_lessequals @ SV1676 @ SV866 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5382]) ).
thf(6122,plain,
! [SV2612: $i,SV2286: $i,SV1677: $i,SV867: $i,SV3: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV3 @ SV867 @ tc_nat ) ) @ SV1677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2286 @ SV867 @ tc_nat ) ) @ SV2612 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV3 @ SV2286 @ tc_nat ) @ SV867 @ tc_nat ) ) @ SV1677 ) @ SV2612 @ tc_nat )
| ~ ( c_lessequals @ SV2286 @ SV3 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5383]) ).
thf(6123,plain,
! [SV2613: $i,SV2287: $i,SV1678: $i,SV868: $i,SV4: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV868 @ tc_nat ) @ SV1678 @ tc_nat ) ) @ SV2287 ) @ SV2613 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV4 @ SV1678 @ tc_nat ) ) @ SV2287 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV868 @ SV1678 @ tc_nat ) ) @ SV2613 ) @ tc_nat )
| ~ ( c_lessequals @ SV868 @ SV4 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5384]) ).
thf(6124,plain,
! [SV2614: $i,SV2288: $i,SV1679: $i,SV869: $i,SV5: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV5 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV869 @ SV1679 @ SV5 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2288 @ SV869 @ SV5 ) @ SV1679 @ SV5 ) ) @ SV2614 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV2288 @ SV1679 @ SV5 ) ) @ SV2614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5385]) ).
thf(6125,plain,
! [SV872: $i,SV8: $i] :
( ( ( ~ ( class_Power_Opower @ SV8 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ ( c_Suc @ SV872 ) @ SV8 )
= ( c_HOL_Ozero__class_Ozero @ SV8 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5386]) ).
thf(6126,plain,
! [SV2615: $i,SV2289: $i,SV1680: $i,SV873: $i,SV9: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV2289 @ SV2615 @ SV9 ) @ SV9 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV2289 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1680 @ SV2615 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV873 @ SV2289 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5387]) ).
thf(6127,plain,
! [SV874: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ SV10 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV10 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV10 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV10 @ SV874 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5388]) ).
thf(6128,plain,
! [SV1681: $i,SV875: $i,SV11: $i] :
( ( ( class_Orderings_Olinorder @ SV11 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV875 @ SV1681 @ SV11 ) @ SV875 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5389]) ).
thf(6129,plain,
! [SV1682: $i,SV876: $i,SV12: $i] :
( ( ( class_Orderings_Olinorder @ SV12 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV876 @ SV1682 @ SV12 ) @ SV1682 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5390]) ).
thf(6130,plain,
! [SV2290: $i,SV1683: $i,SV877: $i,SV13: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV13 ) )
= $true )
| ( ( ( c_lessequals @ SV877 @ ( c_Orderings_Oord__class_Omin @ SV1683 @ SV2290 @ SV13 ) @ SV13 )
| ~ ( c_lessequals @ SV877 @ SV2290 @ SV13 )
| ~ ( c_lessequals @ SV877 @ SV1683 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5391]) ).
thf(6131,plain,
! [SV2291: $i,SV1684: $i,SV878: $i,SV14: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV14 ) )
= $true )
| ( ( ( c_lessequals @ SV878 @ ( c_Orderings_Oord__class_Omin @ SV1684 @ SV2291 @ SV14 ) @ SV14 )
| ~ ( c_lessequals @ SV878 @ SV2291 @ SV14 )
| ~ ( c_lessequals @ SV878 @ SV1684 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5392]) ).
thf(6132,plain,
! [SV2292: $i,SV1685: $i,SV879: $i,SV15: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV15 ) )
= $true )
| ( ( ( c_lessequals @ SV879 @ ( c_Orderings_Oord__class_Omin @ SV1685 @ SV2292 @ SV15 ) @ SV15 )
| ~ ( c_lessequals @ SV879 @ SV2292 @ SV15 )
| ~ ( c_lessequals @ SV879 @ SV1685 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5393]) ).
thf(6133,plain,
! [SV2616: $i,SV2293: $i,SV1686: $i,SV880: $i,SV16: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV16 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SV880 @ SV1686 @ SV16 ) ) @ SV2293 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SV2616 @ SV1686 @ SV16 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV880 @ SV2616 @ SV16 ) @ SV1686 @ SV16 ) ) @ SV2293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5394]) ).
thf(6134,plain,
! [SV1687: $i,SV881: $i,SV17: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV17 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SV881 @ SV1687 @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV881 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5395]) ).
thf(6135,plain,
! [SV2294: $i,SV1688: $i,SV883: $i,SV19: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV19 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV883 @ SV1688 @ SV19 ) @ SV2294 @ SV19 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV883 @ SV2294 @ SV19 ) @ ( c_HOL_Ominus__class_Ominus @ SV1688 @ SV2294 @ SV19 ) @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5397]) ).
thf(6136,plain,
! [SV2295: $i,SV1689: $i,SV884: $i,SV20: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV20 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV884 @ SV1689 @ SV20 ) @ SV2295 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SV1689 @ SV2295 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SV884 @ SV2295 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5398]) ).
thf(6137,plain,
! [SV1690: $i,SV21: $i,SV885: $i] :
( ( ( c_lessequals @ SV885 @ SV21 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV21 @ SV885 @ tc_nat ) ) @ SV1690 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV21 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV885 ) @ SV1690 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5399]) ).
thf(6138,plain,
! [SV2296: $i,SV1691: $i,SV886: $i,SV22: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV22 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV22 )
| ( c_HOL_Oord__class_Oless @ SV886 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1691 ) @ SV2296 ) @ SV22 )
| ~ ( c_lessequals @ SV886 @ SV2296 @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV1691 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5400]) ).
thf(6139,plain,
! [SV1692: $i,SV887: $i,SV23: $i] :
( ( ( ~ ( c_lessequals @ SV23 @ SV887 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1692 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV23 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV887 ) @ SV1692 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5401]) ).
thf(6140,plain,
! [SV1693: $i,SV888: $i,SV24: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV24 )
= $false )
| ( ( ( c_lessequals @ SV888 @ SV1693 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV888 @ SV24 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1693 @ SV24 ) @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5402]) ).
thf(6141,plain,
! [SV1694: $i,SV889: $i,SV25: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV25 )
= $false )
| ( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV889 @ SV25 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1694 @ SV25 ) @ SV25 )
| ~ ( c_lessequals @ SV889 @ SV1694 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5403]) ).
thf(6142,plain,
! [SV2297: $i,SV1695: $i,SV890: $i,SV26: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV26 @ SV890 @ SV1695 ) @ ( c_Lambda_Osubst @ SV2297 @ SV890 @ SV1695 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV26 @ SV2297 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5404]) ).
thf(6143,plain,
! [SV2298: $i,SV1696: $i,SV891: $i,SV27: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV27 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV891 @ ( c_Orderings_Oord__class_Omin @ SV1696 @ SV2298 @ SV27 ) @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV2298 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV1696 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5405]) ).
thf(6144,plain,
! [SV2299: $i,SV1699: $i,SV894: $i,SV30: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV30 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV30 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV1699 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV2299 @ SV30 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV2299 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV1699 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5406]) ).
thf(6145,plain,
! [SV2300: $i,SV1700: $i,SV895: $i,SV31: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV31 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV31 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1700 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV2300 @ SV31 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV2300 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1700 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5407]) ).
thf(6146,plain,
! [SV897: $i,SV34: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV897 @ SV34 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV897 ) @ SV897 ) @ SV34 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5408]) ).
thf(6147,plain,
! [SV898: $i,SV35: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV35 ) @ SV898 ) @ SV898 ) @ SV35 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV898 @ SV35 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5409]) ).
thf(6148,plain,
! [SV1701: $i,SV899: $i,SV36: $i] :
( ( ( class_Orderings_Olinorder @ SV36 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV899 @ ( c_Orderings_Oord__class_Omin @ SV899 @ SV1701 @ SV36 ) @ SV36 )
= ( c_Orderings_Oord__class_Omin @ SV899 @ SV1701 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5410]) ).
thf(6149,plain,
! [SV900: $i,SV1702: $i,SV37: $i] :
( ( ( SV37 = SV1702 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1702 @ SV37 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV37 ) @ SV900 @ SV1702 )
= ( c_Lambda_OdB_OVar @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5411]) ).
thf(6150,plain,
! [SV2617: $i,SV2301: $i,SV1703: $i,SV901: $i,SV38: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV38 @ SV901 @ tc_nat ) ) @ SV1703 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2301 @ SV901 @ tc_nat ) ) @ SV2617 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1703 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2301 @ SV38 @ tc_nat ) @ SV901 @ tc_nat ) ) @ SV2617 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV38 @ SV2301 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5412]) ).
thf(6151,plain,
! [SV2618: $i,SV2302: $i,SV1704: $i,SV902: $i,SV39: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV39 @ SV902 @ tc_nat ) ) @ SV1704 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2302 @ SV902 @ tc_nat ) ) @ SV2618 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SV2302 @ tc_nat ) @ SV902 @ tc_nat ) ) @ SV1704 ) @ SV2618 @ tc_nat ) )
| ~ ( c_lessequals @ SV2302 @ SV39 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5413]) ).
thf(6152,plain,
! [SV1705: $i,SV903: $i,SV40: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV40 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV40 ) @ ( c_HOL_Ominus__class_Ominus @ SV903 @ SV1705 @ SV40 ) ) @ SV1705 )
= SV903 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5414]) ).
thf(6153,plain,
! [SV1706: $i,SV904: $i,SV41: $i] :
( ( ( hBOOL @ ( hAPP @ SV41 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV904 ) @ SV1706 ) @ SV904 @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV41 @ SV1706 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5415]) ).
thf(6154,plain,
! [SV1707: $i,SV905: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ SV42 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV905 ) @ SV1707 ) @ SV905 @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV42 @ SV1707 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5416]) ).
thf(6155,plain,
! [SV2303: $i,SV1710: $i,SV908: $i,SV45: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV45 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV908 @ SV1710 @ SV45 ) @ SV2303 @ SV45 )
= ( c_Power_Opower__class_Opower @ SV908 @ ( c_HOL_Otimes__class_Otimes @ SV1710 @ SV2303 @ tc_nat ) @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5419]) ).
thf(6156,plain,
! [SV909: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ SV46 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ SV46 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV46 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV46 @ SV909 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5420]) ).
thf(6157,plain,
! [SV1711: $i,SV910: $i,SV47: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV47 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV910 @ ( c_Suc @ SV1711 ) @ SV47 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV910 @ SV1711 @ SV47 ) @ SV910 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5421]) ).
thf(6158,plain,
! [SV1712: $i,SV911: $i,SV48: $i] :
( ( ( class_Power_Opower @ SV48 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV911 @ ( c_Suc @ SV1712 ) @ SV48 )
= ( c_HOL_Otimes__class_Otimes @ SV911 @ ( c_Power_Opower__class_Opower @ SV911 @ SV1712 @ SV48 ) @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5422]) ).
thf(6159,plain,
! [SV1713: $i,SV912: $i,SV49: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV912 @ ( c_Suc @ SV1713 ) @ SV49 )
= ( c_HOL_Otimes__class_Otimes @ SV912 @ ( c_Power_Opower__class_Opower @ SV912 @ SV1713 @ SV49 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5423]) ).
thf(6160,plain,
! [SV1714: $i,SV913: $i,SV50: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV913 @ ( c_Suc @ SV1714 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ SV913 @ ( c_Power_Opower__class_Opower @ SV913 @ SV1714 @ SV50 ) @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5424]) ).
thf(6161,plain,
! [SV2304: $i,SV1715: $i,SV914: $i,SV51: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV914 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1715 ) @ SV2304 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV914 @ SV2304 @ tc_nat )
| ~ ( c_lessequals @ SV51 @ SV1715 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5425]) ).
thf(6162,plain,
! [SV2619: $i,SV2305: $i,SV1716: $i,SV915: $i,SV52: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV52 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV915 ) @ SV1716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV2305 ) @ SV2619 ) @ SV52 )
| ~ ( c_lessequals @ SV1716 @ SV2619 @ SV52 )
| ~ ( c_lessequals @ SV915 @ SV2305 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5426]) ).
thf(6163,plain,
! [SV1717: $i,SV919: $i,SV57: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV57 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV919 @ SV1717 @ SV57 )
= ( c_HOL_Otimes__class_Otimes @ SV1717 @ SV919 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5430]) ).
thf(6164,plain,
! [SV59: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) )
= ( c_HOL_Ozero__class_Ozero @ SV59 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5431]) ).
thf(6165,plain,
! [SV1718: $i,SV921: $i,SV60: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV60 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV921 @ SV1718 @ SV60 )
= ( c_HOL_Otimes__class_Otimes @ SV1718 @ SV921 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5432]) ).
thf(6166,plain,
! [SV1719: $i,SV923: $i,SV62: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV62 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV923 ) @ SV1719 ) @ SV62 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1719 @ SV62 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV923 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5433]) ).
thf(6167,plain,
! [SV2306: $i,SV1720: $i,SV924: $i,SV63: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV63 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV924 @ SV1720 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV2306 @ SV1720 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ SV2306 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5434]) ).
thf(6168,plain,
! [SV2307: $i,SV1721: $i,SV925: $i,SV64: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV64 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV925 @ SV1721 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV925 @ SV2307 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV2307 @ SV1721 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5435]) ).
thf(6169,plain,
! [SV2308: $i,SV1722: $i,SV926: $i,SV65: $i] :
( ( ( c_Type_Otyping @ SV65 @ SV926 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV1722 @ SV65 @ SV2308 @ SV926 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV65 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV2308 ) @ SV926 ) @ SV1722 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5436]) ).
thf(6170,plain,
! [SV1723: $i,SV927: $i,SV66: $i] :
( ( ( class_Orderings_Olinorder @ SV66 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV927 @ SV1723 @ SV66 )
= SV1723 )
| ~ ( c_lessequals @ SV927 @ SV1723 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5437]) ).
thf(6171,plain,
! [SV1724: $i,SV928: $i,SV67: $i] :
( ( ( class_Orderings_Olinorder @ SV67 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV928 @ SV1724 @ SV67 )
= SV928 )
| ~ ( c_lessequals @ SV1724 @ SV928 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5438]) ).
thf(6172,plain,
! [SV2309: $i,SV1725: $i,SV929: $i,SV68: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV929 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV1725 ) @ SV2309 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV929 ) @ SV1725 ) ) @ SV2309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5439]) ).
thf(6173,plain,
! [SV2310: $i,SV1726: $i,SV930: $i,SV69: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV69 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV930 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV1726 ) @ SV2310 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV1726 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV930 ) @ SV2310 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5440]) ).
thf(6174,plain,
! [SV933: $i,SV1729: $i,SV72: $i] :
( ( ( hBOOL @ ( hAPP @ SV72 @ SV1729 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1729 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV72 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV72 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV72 @ SV933 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5441]) ).
thf(6175,plain,
! [SV937: $i,SV1730: $i,SV76: $i] :
( ( ( ~ ( c_lessequals @ SV76 @ ( c_HOL_Ominus__class_Ominus @ SV1730 @ SV937 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV937 @ SV1730 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV76 ) @ SV937 ) @ SV1730 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5442]) ).
thf(6176,plain,
! [SV938: $i,SV1731: $i,SV77: $i] :
( ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV77 ) @ SV1731 ) @ SV938 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1731 @ SV938 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV77 @ ( c_HOL_Ominus__class_Ominus @ SV938 @ SV1731 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5443]) ).
thf(6177,plain,
! [SV2311: $i,SV1732: $i,SV939: $i,SV78: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV78 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV939 @ SV1732 @ SV78 ) @ SV2311 @ SV78 )
| ~ ( c_lessequals @ SV1732 @ SV2311 @ SV78 )
| ~ ( c_lessequals @ SV939 @ SV2311 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5444]) ).
thf(6178,plain,
! [SV2312: $i,SV1733: $i,SV940: $i,SV79: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV79 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV940 @ SV1733 @ SV79 ) @ SV2312 @ SV79 )
| ~ ( c_lessequals @ SV1733 @ SV2312 @ SV79 )
| ~ ( c_lessequals @ SV940 @ SV2312 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5445]) ).
thf(6179,plain,
! [SV2313: $i,SV1734: $i,SV941: $i,SV80: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV80 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV941 @ SV1734 @ SV80 ) @ SV2313 @ SV80 )
| ~ ( c_lessequals @ SV1734 @ SV2313 @ SV80 )
| ~ ( c_lessequals @ SV941 @ SV2313 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5446]) ).
thf(6180,plain,
! [SV1735: $i,SV942: $i,SV81: $i] :
( ( ( class_Orderings_Olinorder @ SV81 )
= $false )
| ( ( c_lessequals @ SV942 @ ( c_Orderings_Oord__class_Omax @ SV942 @ SV1735 @ SV81 ) @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5447]) ).
thf(6181,plain,
! [SV1736: $i,SV943: $i,SV82: $i] :
( ( ( class_Orderings_Olinorder @ SV82 )
= $false )
| ( ( c_lessequals @ SV943 @ ( c_Orderings_Oord__class_Omax @ SV1736 @ SV943 @ SV82 ) @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5448]) ).
thf(6182,plain,
! [SV2620: $i,SV2315: $i,SV1738: $i,SV951: $i,SV90: $i] :
( ( ! [SY6950: $i,SY6951: $i,SY6952: $i,SY6953: $i] :
( ( ( hAPP @ ( hAPP @ SV90 @ ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ SV1738 ) ) @ SV2315 )
= ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ ( c_HOL_Otimes__class_Otimes @ SV1738 @ SV2315 @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2620 @ SY6950 @ SV90 @ SY6951 @ SY6952 @ SY6953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5451]) ).
thf(6183,plain,
! [SV2316: $i,SV1739: $i,SV952: $i,SV91: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV91 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV952 @ SV1739 @ SV91 ) @ SV2316 @ SV91 )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV952 @ SV2316 @ SV91 ) @ ( c_Orderings_Oord__class_Omin @ SV1739 @ SV2316 @ SV91 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5452]) ).
thf(6184,plain,
! [SV2317: $i,SV1740: $i,SV953: $i,SV92: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV92 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ SV953 @ ( c_Orderings_Oord__class_Omax @ SV1740 @ SV2317 @ SV92 ) @ SV92 )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV953 @ SV1740 @ SV92 ) @ ( c_Orderings_Oord__class_Omin @ SV953 @ SV2317 @ SV92 ) @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5453]) ).
thf(6185,plain,
! [SV2318: $i,SV1741: $i,SV954: $i,SV93: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV93 )
| ( c_lessequals @ SV954 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV1741 ) @ SV2318 ) @ SV93 )
| ~ ( c_lessequals @ SV954 @ SV2318 @ SV93 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV1741 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5454]) ).
thf(6186,plain,
! [SV2319: $i,SV1742: $i,SV955: $i,SV94: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV94 )
| ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV1742 ) @ SV2319 ) @ SV94 )
| ~ ( c_lessequals @ SV955 @ SV1742 @ SV94 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV2319 @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5455]) ).
thf(6187,plain,
! [SV956: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ SV95 @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ SV95 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV95 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV95 @ SV956 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5456]) ).
thf(6188,plain,
! [SV957: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ SV96 @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ SV96 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV96 @ SV957 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5457]) ).
thf(6189,plain,
! [SV1743: $i,SV962: $i,SV101: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV101 @ SV962 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV101 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV962 ) @ SV1743 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5462]) ).
thf(6190,plain,
! [SV963: $i,SV1744: $i,SV102: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV102 @ SV1744 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV102 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV963 ) @ SV1744 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5463]) ).
thf(6191,plain,
! [SV964: $i,SV1745: $i,SV103: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV103 ) @ SV1745 ) @ SV964 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV103 @ SV964 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5464]) ).
thf(6192,plain,
! [SV1746: $i,SV965: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV104 @ SV965 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV104 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV965 ) @ SV1746 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5465]) ).
thf(6193,plain,
! [SV966: $i,SV1747: $i,SV105: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV105 @ SV1747 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV105 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV966 ) @ SV1747 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5466]) ).
thf(6194,plain,
! [SV2621: $i,SV2320: $i,SV1748: $i,SV967: $i,SV106: $i] :
( ( ! [SY6954: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV106 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV967 @ SV1748 @ SV106 ) ) @ SV2320 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV2621 @ SV1748 @ SV106 ) ) @ SY6954 ) @ SV106 )
| ~ ( c_lessequals @ SV2320 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2621 @ SV967 @ SV106 ) @ SV1748 @ SV106 ) ) @ SY6954 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5467]) ).
thf(6195,plain,
! [SV2622: $i,SV2321: $i,SV1749: $i,SV968: $i,SV107: $i] :
( ( ! [SY6955: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV107 )
| ( c_lessequals @ SV968 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SV2321 @ SV107 ) @ SV2622 @ SV107 ) ) @ SY6955 ) @ SV107 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV2321 @ SV2622 @ SV107 ) ) @ SV968 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV1749 @ SV2622 @ SV107 ) ) @ SY6955 ) @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5468]) ).
thf(6196,plain,
! [SV2623: $i,SV2322: $i,SV1750: $i,SV969: $i,SV108: $i] :
( ( ! [SY6956: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV108 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV969 @ SV1750 @ SV108 ) ) @ SV2322 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV2623 @ SV1750 @ SV108 ) ) @ SY6956 ) @ SV108 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV969 @ SV2623 @ SV108 ) @ SV1750 @ SV108 ) ) @ SV2322 ) @ SY6956 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5469]) ).
thf(6197,plain,
! [SV2624: $i,SV2323: $i,SV1751: $i,SV970: $i,SV109: $i] :
( ( ! [SY6957: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV109 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV970 @ SV1751 @ SV109 ) @ SV2323 @ SV109 ) ) @ SV2624 ) @ SY6957 @ SV109 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV970 @ SV2323 @ SV109 ) ) @ SV2624 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV1751 @ SV2323 @ SV109 ) ) @ SY6957 ) @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5470]) ).
thf(6198,plain,
! [SV1752: $i,SV972: $i,SV111: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV111 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ ( c_HOL_Otimes__class_Otimes @ SV972 @ SV972 @ SV111 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1752 @ SV1752 @ SV111 ) ) @ SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5472]) ).
thf(6199,plain,
! [SV1753: $i,SV973: $i,SV112: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV112 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV973 ) @ SV1753 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV1753 ) @ SV973 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5473]) ).
thf(6200,plain,
! [SV1754: $i,SV974: $i,SV113: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV974 ) @ SV1754 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1754 ) @ SV974 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5474]) ).
thf(6201,plain,
! [SV1755: $i,SV976: $i,SV115: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV115 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV976 ) @ SV1755 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV1755 ) @ SV976 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5475]) ).
thf(6202,plain,
! [SV2324: $i,SV1756: $i,SV977: $i,SV116: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV116 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV977 ) @ SV1756 ) @ SV2324 @ SV116 @ SV116 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV977 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV1756 @ SV2324 @ SV116 @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5476]) ).
thf(6203,plain,
! [SV978: $i,SV117: $i,SV1757: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1757 @ SV117 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1757 @ SV978 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV978 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV1757 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5477]) ).
thf(6204,plain,
! [SV979: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ SV118 @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ SV118 ) ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV118 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV118 @ SV979 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5478]) ).
thf(6205,plain,
! [SV2325: $i,SV1758: $i,SV980: $i,SV119: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV119 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV980 @ SV1758 @ SV119 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV2325 @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV980 @ SV2325 @ SV119 ) @ ( c_HOL_Otimes__class_Otimes @ SV1758 @ SV2325 @ SV119 ) @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5479]) ).
thf(6206,plain,
! [SV2326: $i,SV1759: $i,SV981: $i,SV120: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV120 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV981 @ SV1759 @ SV120 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV2326 @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV981 @ SV120 ) @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV1759 @ SV120 ) @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5480]) ).
thf(6207,plain,
! [SV2327: $i,SV1760: $i,SV982: $i,SV121: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring @ SV121 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV982 @ SV1760 @ SV121 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV2327 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV982 @ SV2327 @ SV121 ) @ ( c_HOL_Otimes__class_Otimes @ SV1760 @ SV2327 @ SV121 ) @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5481]) ).
thf(6208,plain,
! [SV2328: $i,SV1761: $i,SV983: $i,SV122: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring @ SV122 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV983 @ SV1761 @ SV122 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV2328 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV983 @ SV122 ) @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV1761 @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5482]) ).
thf(6209,plain,
! [SV1762: $i,SV984: $i,SV123: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV123 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV984 @ SV1762 @ SV123 ) @ SV984 @ SV123 )
= ( c_HOL_Otimes__class_Otimes @ SV984 @ ( c_Power_Opower__class_Opower @ SV984 @ SV1762 @ SV123 ) @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5483]) ).
thf(6210,plain,
! [SV2329: $i,SV1763: $i,SV985: $i,SV124: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV124 ) )
= $true )
| ( ( ( c_lessequals @ SV985 @ SV1763 @ SV124 )
| ( c_lessequals @ SV985 @ SV2329 @ SV124 )
| ~ ( c_lessequals @ SV985 @ ( c_Orderings_Oord__class_Omax @ SV2329 @ SV1763 @ SV124 ) @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5484]) ).
thf(6211,plain,
! [SV2330: $i,SV1764: $i,SV986: $i,SV125: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV986 @ SV1764 @ SV125 ) @ ( c_Power_Opower__class_Opower @ SV986 @ SV2330 @ SV125 ) @ SV125 )
= ( c_Power_Opower__class_Opower @ SV986 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1764 ) @ SV2330 ) @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5485]) ).
thf(6212,plain,
! [SV988: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP @ SV127 @ SV988 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV127 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( c_lessequals @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV127 @ SV988 ) @ SV988 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5486]) ).
thf(6213,plain,
! [SV2625: $i,SV2331: $i,SV1765: $i,SV989: $i,SV128: $i] :
( ( ! [SY6958: $i,SY6959: $i,SY6960: $i,SY6961: $i] :
( ( ( hAPP @ ( hAPP @ SV128 @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2331 ) ) @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2625 ) )
= ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2331 ) @ SV2625 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6958 @ SV128 @ SV989 @ SY6959 @ SY6960 @ SY6961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5487]) ).
thf(6214,plain,
! [SV2332: $i,SV1766: $i,SV990: $i,SV129: $i] :
( ( ( ~ ( c_lessequals @ SV129 @ SV990 @ tc_nat ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SV1766 @ tc_nat ) ) @ SV2332 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV129 @ SV1766 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV990 @ SV129 @ tc_nat ) @ SV1766 @ tc_nat ) ) @ SV2332 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5488]) ).
thf(6215,plain,
! [SV2333: $i,SV1767: $i,SV991: $i,SV131: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV131 ) )
= $true )
| ( ( ( c_lessequals @ SV991 @ SV1767 @ SV131 )
| ~ ( c_lessequals @ SV991 @ ( c_Orderings_Oord__class_Omin @ SV2333 @ SV1767 @ SV131 ) @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5489]) ).
thf(6216,plain,
! [SV2334: $i,SV1768: $i,SV992: $i,SV132: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV132 ) )
= $true )
| ( ( ( c_lessequals @ SV992 @ SV1768 @ SV132 )
| ~ ( c_lessequals @ SV992 @ ( c_Orderings_Oord__class_Omin @ SV1768 @ SV2334 @ SV132 ) @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5490]) ).
thf(6217,plain,
! [SV2335: $i,SV1769: $i,SV993: $i,SV133: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV133 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV993 @ SV1769 @ SV133 ) @ SV2335 @ SV133 )
| ~ ( c_lessequals @ SV1769 @ SV2335 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5491]) ).
thf(6218,plain,
! [SV2336: $i,SV1770: $i,SV994: $i,SV134: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV134 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV994 @ SV1770 @ SV134 ) @ SV2336 @ SV134 )
| ~ ( c_lessequals @ SV994 @ SV2336 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5492]) ).
thf(6219,plain,
! [SV2337: $i,SV1771: $i,SV995: $i,SV135: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV135 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV995 @ SV1771 @ SV135 ) @ SV2337 @ SV135 )
| ~ ( c_lessequals @ SV1771 @ SV2337 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5493]) ).
thf(6220,plain,
! [SV2338: $i,SV1772: $i,SV996: $i,SV136: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV136 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV996 @ SV1772 @ SV136 ) @ SV2338 @ SV136 )
| ~ ( c_lessequals @ SV996 @ SV2338 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5494]) ).
thf(6221,plain,
! [SV2339: $i,SV1773: $i,SV997: $i,SV137: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV137 ) )
= $true )
| ( ( ( c_lessequals @ SV997 @ SV1773 @ SV137 )
| ~ ( c_lessequals @ SV997 @ ( c_Orderings_Oord__class_Omin @ SV2339 @ SV1773 @ SV137 ) @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5495]) ).
thf(6222,plain,
! [SV2340: $i,SV1774: $i,SV998: $i,SV138: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV138 ) )
= $true )
| ( ( ( c_lessequals @ SV998 @ SV1774 @ SV138 )
| ~ ( c_lessequals @ SV998 @ ( c_Orderings_Oord__class_Omin @ SV1774 @ SV2340 @ SV138 ) @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5496]) ).
thf(6223,plain,
! [SV1775: $i,SV999: $i,SV139: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV139 )
= $false )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV999 @ SV1775 @ SV139 @ SV139 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV139 ) @ SV1775 @ SV999 @ SV139 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5497]) ).
thf(6224,plain,
! [SV2626: $i,SV2341: $i,SV1776: $i,SV1000: $i,SV140: $i] :
( ( ! [SY6962: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV140 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1776 @ SV140 ) ) @ SV2341 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV2626 @ SV1776 @ SV140 ) ) @ SY6962 ) @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV2341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2626 @ SV1000 @ SV140 ) @ SV1776 @ SV140 ) ) @ SY6962 ) @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5498]) ).
thf(6225,plain,
! [SV2627: $i,SV2342: $i,SV1777: $i,SV1001: $i,SV141: $i] :
( ( ! [SY6963: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV141 )
| ( c_HOL_Oord__class_Oless @ SV1001 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1777 @ SV2342 @ SV141 ) @ SV2627 @ SV141 ) ) @ SY6963 ) @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV2342 @ SV2627 @ SV141 ) ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV1777 @ SV2627 @ SV141 ) ) @ SY6963 ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5499]) ).
thf(6226,plain,
! [SV2628: $i,SV2343: $i,SV1778: $i,SV1002: $i,SV142: $i] :
( ( ! [SY6964: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV142 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1778 @ SV142 ) ) @ SV2343 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV2628 @ SV1778 @ SV142 ) ) @ SY6964 ) @ SV142 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1002 @ SV2628 @ SV142 ) @ SV1778 @ SV142 ) ) @ SV2343 ) @ SY6964 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5500]) ).
thf(6227,plain,
! [SV2629: $i,SV2344: $i,SV1779: $i,SV1003: $i,SV143: $i] :
( ( ! [SY6965: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV143 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1003 @ SV1779 @ SV143 ) @ SV2344 @ SV143 ) ) @ SV2629 ) @ SY6965 @ SV143 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1003 @ SV2344 @ SV143 ) ) @ SV2629 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1779 @ SV2344 @ SV143 ) ) @ SY6965 ) @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5501]) ).
thf(6228,plain,
! [SV2345: $i,SV1780: $i,SV1004: $i,SV144: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV144 ) )
= $true )
| ( ( ( c_lessequals @ SV1004 @ SV1780 @ SV144 )
| ( c_lessequals @ SV2345 @ SV1780 @ SV144 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV2345 @ SV1004 @ SV144 ) @ SV1780 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5502]) ).
thf(6229,plain,
! [SV2346: $i,SV1781: $i,SV1005: $i,SV145: $i] :
( ( ( ~ ( c_lessequals @ SV145 @ SV1005 @ tc_nat ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV145 @ SV1781 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1005 @ SV145 @ tc_nat ) @ SV1781 @ tc_nat ) ) @ SV2346 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1005 @ SV1781 @ tc_nat ) ) @ SV2346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5503]) ).
thf(6230,plain,
! [SV1006: $i,SV146: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV1006 ) @ SV1006 ) @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV146 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV146 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5504]) ).
thf(6231,plain,
! [SV147: $i,SV1007: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1007 @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1007 ) @ SV1007 ) @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5505]) ).
thf(6232,plain,
! [SV148: $i,SV1008: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1008 @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV148 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV1008 ) @ SV1008 ) @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV148 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5506]) ).
thf(6233,plain,
! [SV1009: $i,SV149: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV1009 ) @ SV1009 ) @ ( c_HOL_Ozero__class_Ozero @ SV149 ) @ SV149 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1009 @ ( c_HOL_Ozero__class_Ozero @ SV149 ) @ SV149 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5507]) ).
thf(6234,plain,
! [SV1782: $i,SV1010: $i,SV150: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV150 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1010 @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1782 @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ ( c_HOL_Otimes__class_Otimes @ SV1010 @ SV1782 @ SV150 ) @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5508]) ).
thf(6235,plain,
! [SV1783: $i,SV1011: $i,SV151: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV151 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1011 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1783 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ ( c_HOL_Otimes__class_Otimes @ SV1783 @ SV1011 @ SV151 ) @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5509]) ).
thf(6236,plain,
! [SV1784: $i,SV1012: $i,SV152: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV152 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SV1784 @ SV152 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1784 @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1012 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5510]) ).
thf(6237,plain,
! [SV1785: $i,SV1013: $i,SV153: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV153 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV1013 @ SV1785 @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1785 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1013 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5511]) ).
thf(6238,plain,
! [SV154: $i,SV1014: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1014 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV154 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV154 @ SV1014 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5512]) ).
thf(6239,plain,
! [SV2347: $i,SV1786: $i,SV1015: $i,SV155: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV155 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1786 @ SV155 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV1786 @ SV155 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1015 @ SV2347 @ SV155 ) @ ( c_Power_Opower__class_Opower @ SV1786 @ SV2347 @ SV155 ) @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5513]) ).
thf(6240,plain,
! [SV2348: $i,SV1787: $i,SV1016: $i,SV156: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV156 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1016 ) @ SV1787 ) ) @ SV2348 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1787 ) @ SV2348 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5514]) ).
thf(6241,plain,
! [SV2349: $i,SV1788: $i,SV1017: $i,SV157: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV157 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1017 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1788 ) @ SV2349 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1788 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1017 ) @ SV2349 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5515]) ).
thf(6242,plain,
! [SV2350: $i,SV1789: $i,SV1018: $i,SV158: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV158 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1018 ) @ SV1789 ) ) @ SV2350 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1018 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1789 ) @ SV2350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5516]) ).
thf(6243,plain,
! [SV2351: $i,SV1790: $i,SV1019: $i,SV159: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV159 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1019 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1790 ) @ SV2351 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1019 ) @ SV1790 ) ) @ SV2351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5517]) ).
thf(6244,plain,
! [SV2352: $i,SV1791: $i,SV1020: $i,SV160: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV160 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV1020 ) @ SV1791 ) ) @ SV2352 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV1020 ) @ SV2352 ) ) @ SV1791 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5518]) ).
thf(6245,plain,
! [SV2353: $i,SV1792: $i,SV1021: $i,SV161: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV161 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1021 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1792 ) @ SV2353 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1021 ) @ SV2353 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5519]) ).
thf(6246,plain,
! [SV2354: $i,SV1793: $i,SV1022: $i,SV162: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1022 ) @ SV1793 ) ) @ SV2354 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1022 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1793 ) @ SV2354 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5520]) ).
thf(6247,plain,
! [SV163: $i,SV1023: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1023 ) @ SV163 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1023 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV163 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5521]) ).
thf(6248,plain,
! [SV2355: $i,SV1794: $i,SV1024: $i,SV164: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV164 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1024 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1794 ) @ SV2355 ) @ SV164 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1024 @ SV1794 @ SV164 ) @ ( c_Power_Opower__class_Opower @ SV1024 @ SV2355 @ SV164 ) @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5522]) ).
thf(6249,plain,
! [SV1029: $i,SV1797: $i,SV169: $i] :
( ( ( c_lessequals @ SV169 @ SV1797 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV169 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1029 ) @ SV1797 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5525]) ).
thf(6250,plain,
! [SV1798: $i,SV1030: $i,SV170: $i] :
( ( ( c_lessequals @ SV170 @ SV1030 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV170 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1030 ) @ SV1798 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5526]) ).
thf(6251,plain,
! [SV1031: $i,SV171: $i,SV1799: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1799 ) @ SV171 ) @ SV1031 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV171 @ SV1031 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5527]) ).
thf(6252,plain,
! [SV1032: $i,SV1800: $i,SV172: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV172 ) @ SV1800 ) @ SV1032 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV172 @ SV1032 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5528]) ).
thf(6253,plain,
! [SV1033: $i,SV1801: $i,SV173: $i] :
( ( ( c_lessequals @ SV173 @ SV1801 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV173 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1033 ) @ SV1801 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5529]) ).
thf(6254,plain,
! [SV1802: $i,SV1034: $i,SV174: $i] :
( ( ( c_lessequals @ SV174 @ SV1034 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV174 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1034 ) @ SV1802 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5530]) ).
thf(6255,plain,
! [SV1803: $i,SV1035: $i,SV175: $i] :
( ( ( class_Orderings_Olinorder @ SV175 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omin @ SV1035 @ SV1803 @ SV175 )
= SV1035 )
| ~ ( c_lessequals @ SV1035 @ SV1803 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5531]) ).
thf(6256,plain,
! [SV1804: $i,SV1036: $i,SV176: $i] :
( ( ( class_Orderings_Olinorder @ SV176 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omin @ SV1036 @ SV1804 @ SV176 )
= SV1804 )
| ~ ( c_lessequals @ SV1804 @ SV1036 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5532]) ).
thf(6257,plain,
! [SV2356: $i,SV1805: $i,SV1037: $i,SV177: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV177 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ SV1037 @ SV1805 @ SV177 ) @ SV2356 @ SV177 )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ SV1037 @ SV2356 @ SV177 ) @ ( c_HOL_Ominus__class_Ominus @ SV1805 @ SV2356 @ SV177 ) @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5533]) ).
thf(6258,plain,
! [SV2357: $i,SV1806: $i,SV1038: $i,SV178: $i] :
( ( ( c_Type_Otypings @ SV178 @ SV1038 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV1806 @ SV178 @ SV2357 @ SV1038 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV178 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV2357 @ SV1038 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1806 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5534]) ).
thf(6259,plain,
! [SV1807: $i,SV1039: $i,SV179: $i] :
( ( ( class_Orderings_Olinorder @ SV179 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1039 @ SV1807 @ SV179 )
| ( c_lessequals @ SV1807 @ SV1039 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5535]) ).
thf(6260,plain,
! [SV180: $i,SV1040: $i] :
( ( ( ~ ( c_lessequals @ SV1040 @ SV1040 @ SV180 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1040 @ SV1040 @ SV180 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5536]) ).
thf(6261,plain,
! [SV181: $i,SV1041: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1041 @ SV1041 @ SV181 )
= $true )
| ( ( c_lessequals @ SV1041 @ SV1041 @ SV181 )
= $true )
| ( ( class_Orderings_Olinorder @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5537]) ).
thf(6262,plain,
! [SV1808: $i,SV1042: $i,SV182: $i] :
( ( ( class_Orderings_Olinorder @ SV182 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SV1808 @ SV182 )
| ~ ( c_lessequals @ SV1808 @ SV1042 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5538]) ).
thf(6263,plain,
! [SV1809: $i,SV1043: $i,SV183: $i] :
( ( ( class_Orderings_Olinorder @ SV183 )
= $false )
| ( ( ( c_lessequals @ SV1043 @ SV1809 @ SV183 )
| ( c_HOL_Oord__class_Oless @ SV1809 @ SV1043 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5539]) ).
thf(6264,plain,
! [SV1810: $i,SV1044: $i,SV184: $i] :
( ( ( class_Orderings_Olinorder @ SV184 )
= $false )
| ( ( ~ ( c_lessequals @ SV1044 @ SV1810 @ SV184 )
| ~ ( c_HOL_Oord__class_Oless @ SV1810 @ SV1044 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5540]) ).
thf(6265,plain,
! [SV1811: $i,SV1045: $i,SV185: $i] :
( ( ( class_Orderings_Olinorder @ SV185 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1045 @ SV1811 @ SV185 )
| ( c_lessequals @ SV1811 @ SV1045 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5541]) ).
thf(6266,plain,
! [SV1812: $i,SV1046: $i,SV186: $i] :
( ( ( class_Orderings_Opreorder @ SV186 )
= $false )
| ( ( ~ ( c_lessequals @ SV1046 @ SV1812 @ SV186 )
| ~ ( c_HOL_Oord__class_Oless @ SV1812 @ SV1046 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5542]) ).
thf(6267,plain,
! [SV1047: $i,SV187: $i] :
( ( ( hBOOL @ ( hAPP @ SV187 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV187 ) @ tc_nat )
= $true )
| ( ( hBOOL @ ( hAPP @ SV187 @ SV1047 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5543]) ).
thf(6268,plain,
! [SV2358: $i,SV1813: $i,SV1050: $i,SV190: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV190 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ SV1050 @ SV1813 @ SV190 ) @ SV2358 @ SV190 )
= ( c_Orderings_Oord__class_Omin @ SV1050 @ ( c_Orderings_Oord__class_Omin @ SV1813 @ SV2358 @ SV190 ) @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5545]) ).
thf(6269,plain,
! [SV2359: $i,SV1814: $i,SV1051: $i,SV191: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV191 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1051 @ ( c_Orderings_Oord__class_Omin @ SV1814 @ SV2359 @ SV191 ) @ SV191 )
= ( c_Orderings_Oord__class_Omin @ SV1814 @ ( c_Orderings_Oord__class_Omin @ SV1051 @ SV2359 @ SV191 ) @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5546]) ).
thf(6270,plain,
! [SV2360: $i,SV1815: $i,SV1052: $i,SV192: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV192 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV192 )
| ( c_HOL_Oord__class_Oless @ SV1052 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV1815 ) @ SV2360 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SV2360 @ SV192 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV1815 @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5547]) ).
thf(6271,plain,
! [SV193: $i,SV1053: $i,SV1816: $i] :
( ( ( c_lessequals @ SV1816 @ SV1053 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV193 @ SV1053 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV193 @ SV1816 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5548]) ).
thf(6272,plain,
! [SV1054: $i,SV1817: $i,SV194: $i] :
( ( ( c_lessequals @ SV194 @ SV1817 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV194 @ SV1054 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1817 @ SV1054 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5549]) ).
thf(6273,plain,
! [SV1055: $i,SV1818: $i,SV195: $i] :
( ( ( ~ ( c_lessequals @ SV195 @ SV1818 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1055 @ SV1818 @ tc_nat )
| ~ ( c_lessequals @ SV1055 @ SV195 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV195 @ SV1055 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1818 @ SV1055 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5550]) ).
thf(6274,plain,
! [SV1056: $i,SV1819: $i,SV196: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV196 @ SV1819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1056 @ SV1819 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1819 @ SV1056 @ tc_nat )
| ~ ( c_lessequals @ SV1819 @ SV196 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV196 @ SV1056 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5551]) ).
thf(6275,plain,
! [SV2361: $i,SV1821: $i,SV1059: $i,SV199: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV199 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1821 @ SV199 ) @ ( c_Power_Opower__class_Opower @ SV2361 @ SV1821 @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV1059 @ SV199 )
| ~ ( c_lessequals @ SV1059 @ SV2361 @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5552]) ).
thf(6276,plain,
! [SV1822: $i,SV1060: $i,SV200: $i] :
( ( ( class_Orderings_Olinorder @ SV200 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1060 @ ( c_Orderings_Oord__class_Omax @ SV1060 @ SV1822 @ SV200 ) @ SV200 )
= SV1060 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5553]) ).
thf(6277,plain,
! [SV1823: $i,SV201: $i,SV1061: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1061 @ SV201 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1823 @ SV201 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV201 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5554]) ).
thf(6278,plain,
! [SV1824: $i,SV1062: $i,SV202: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV1062 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV1824 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV202 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5555]) ).
thf(6279,plain,
! [SV2630: $i,SV2362: $i,SV1825: $i,SV1063: $i,SV203: $i] :
( ( ! [SY6966: $i] :
( ( c_List_Ofoldl @ SV203 @ SV1063 @ ( c_List_Olist_OCons @ SV1825 @ SV2362 @ SV2630 ) @ SY6966 @ SV2630 )
= ( c_List_Ofoldl @ SV203 @ ( hAPP @ ( hAPP @ SV203 @ SV1063 ) @ SV1825 ) @ SV2362 @ SY6966 @ SV2630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5556]) ).
thf(6280,plain,
! [SV1066: $i,SV206: $i,SV1827: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1827 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV206 @ SV1827 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1066 @ SV1827 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV206 @ SV1066 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5558]) ).
thf(6281,plain,
! [SV1067: $i,SV207: $i,SV1828: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1828 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1828 @ SV207 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1828 @ SV1067 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV207 @ SV1067 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5559]) ).
thf(6282,plain,
! [SV1068: $i,SV208: $i,SV1829: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1829 @ SV208 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1829 @ SV1068 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1829 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV208 @ SV1068 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5560]) ).
thf(6283,plain,
! [SV209: $i,SV1830: $i,SV1069: $i] :
( ( ( ~ ( c_lessequals @ SV1069 @ SV1830 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV209 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SV1069 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SV1830 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5561]) ).
thf(6284,plain,
! [SV2364: $i,SV1831: $i,SV1070: $i,SV210: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV210 ) )
= $true )
| ( ( ( c_lessequals @ SV1070 @ SV1831 @ SV210 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1831 @ SV210 ) @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1070 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SV2364 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5562]) ).
thf(6285,plain,
! [SV2365: $i,SV1832: $i,SV1071: $i,SV211: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV211 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV1832 @ SV211 ) @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV2365 @ SV211 ) @ SV211 )
| ~ ( c_lessequals @ SV2365 @ SV1832 @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5563]) ).
thf(6286,plain,
! [SV2366: $i,SV1833: $i,SV1072: $i,SV212: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV212 ) )
= $true )
| ( ( ( c_lessequals @ SV1072 @ SV1833 @ SV212 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1072 @ SV212 ) @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1833 @ SV212 ) @ SV212 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SV2366 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5564]) ).
thf(6287,plain,
! [SV2367: $i,SV1834: $i,SV1073: $i,SV213: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV213 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV1834 @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV2367 @ SV213 ) @ SV213 )
| ~ ( c_lessequals @ SV1834 @ SV2367 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV1073 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5565]) ).
thf(6288,plain,
! [SV2368: $i,SV1835: $i,SV1074: $i,SV214: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV214 ) )
= $true )
| ( ( ( c_lessequals @ SV1074 @ SV1835 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV2368 @ SV214 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1074 @ SV214 ) @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1835 @ SV214 ) @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5566]) ).
thf(6289,plain,
! [SV2369: $i,SV1836: $i,SV1075: $i,SV215: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV215 ) )
= $true )
| ( ( ( c_lessequals @ SV1075 @ SV1836 @ SV215 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV2369 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1075 @ SV2369 @ SV215 ) @ ( c_HOL_Otimes__class_Otimes @ SV1836 @ SV2369 @ SV215 ) @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5567]) ).
thf(6290,plain,
! [SV1076: $i,SV216: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV216 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1076 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV216 @ SV1076 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5568]) ).
thf(6291,plain,
! [SV2370: $i,SV1839: $i,SV1079: $i,SV221: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV221 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1079 @ ( c_Orderings_Oord__class_Omax @ SV1839 @ SV2370 @ SV221 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SV1079 @ SV1839 @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5569]) ).
thf(6292,plain,
! [SV2371: $i,SV1840: $i,SV1080: $i,SV222: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV222 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1080 @ ( c_Orderings_Oord__class_Omax @ SV1840 @ SV2371 @ SV222 ) @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ SV1080 @ SV2371 @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5570]) ).
thf(6293,plain,
! [SV2372: $i,SV1841: $i,SV1081: $i,SV223: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV223 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1081 @ ( c_Orderings_Oord__class_Omax @ SV1841 @ SV2372 @ SV223 ) @ SV223 )
| ~ ( c_HOL_Oord__class_Oless @ SV1081 @ SV1841 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5571]) ).
thf(6294,plain,
! [SV2373: $i,SV1842: $i,SV1082: $i,SV224: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV224 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1082 @ ( c_Orderings_Oord__class_Omax @ SV1842 @ SV2373 @ SV224 ) @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ SV1082 @ SV2373 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5572]) ).
thf(6295,plain,
! [SV2374: $i,SV1843: $i,SV1083: $i,SV225: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV225 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1083 @ SV1843 @ SV225 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SV2374 @ SV225 ) @ SV1843 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5573]) ).
thf(6296,plain,
! [SV2375: $i,SV1844: $i,SV1084: $i,SV226: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV226 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1084 @ SV1844 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV2375 @ SV1084 @ SV226 ) @ SV1844 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5574]) ).
thf(6297,plain,
! [SV1845: $i,SV1085: $i,SV228: $i] :
( ( ( class_Orderings_Olinorder @ SV228 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1085 @ SV1845 @ SV228 )
= ( c_Orderings_Oord__class_Omin @ SV1845 @ SV1085 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5575]) ).
thf(6298,plain,
! [SV2631: $i,SV2377: $i,SV1847: $i,SV1087: $i,SV230: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring @ SV230 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SV1087 @ SV1847 @ SV230 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SV2377 @ SV1847 @ SV230 ) ) @ SV2631 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ SV1087 ) @ SV2377 ) @ SV1847 @ SV230 ) ) @ SV2631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5577]) ).
thf(6299,plain,
! [SV1848: $i,SV1091: $i,SV234: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV234 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV1091 ) @ SV1848 ) @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV1848 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV1091 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5580]) ).
thf(6300,plain,
! [SV2378: $i,SV1849: $i,SV1092: $i,SV235: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV235 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1092 @ SV1849 @ SV235 ) @ ( c_Power_Opower__class_Opower @ SV2378 @ SV1849 @ SV235 ) @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1849 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV235 ) @ SV1092 @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SV2378 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5581]) ).
thf(6301,plain,
! [SV1850: $i,SV1093: $i,SV236: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV236 )
= $false )
| ( ( ( SV1093
= ( c_HOL_Ozero__class_Ozero @ SV236 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ ( c_HOL_Otimes__class_Otimes @ SV1093 @ SV1093 @ SV236 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1850 @ SV1850 @ SV236 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV236 ) @ SV236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5582]) ).
thf(6302,plain,
! [SV1851: $i,SV1094: $i,SV237: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV237 )
= $false )
| ( ( ( SV1094
= ( c_HOL_Ozero__class_Ozero @ SV237 ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( c_HOL_Otimes__class_Otimes @ SV1851 @ SV1851 @ SV237 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1094 @ SV1094 @ SV237 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV237 ) @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5583]) ).
thf(6303,plain,
! [SV2381: $i,SV1854: $i,SV1097: $i,SV240: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV240 @ ( c_Nat_Onat_Onat__case @ SV1097 @ SV1854 @ ( c_Suc @ SV2381 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV240 @ ( hAPP @ SV1854 @ SV2381 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5586]) ).
thf(6304,plain,
! [SV2382: $i,SV1855: $i,SV1098: $i,SV241: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV241 @ ( c_Nat_Onat_Onat__case @ SV1098 @ SV1855 @ ( c_Suc @ SV2382 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV241 @ ( hAPP @ SV1855 @ SV2382 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5587]) ).
thf(6305,plain,
! [SV2383: $i,SV1858: $i,SV1101: $i,SV244: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV244 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1101 @ SV1858 @ SV244 ) @ SV2383 @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ SV1101 @ SV2383 @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5588]) ).
thf(6306,plain,
! [SV2384: $i,SV1859: $i,SV1102: $i,SV245: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV245 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1102 @ SV1859 @ SV245 ) @ SV2384 @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ SV1859 @ SV2384 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5589]) ).
thf(6307,plain,
! [SV1860: $i,SV1103: $i,SV246: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV246 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ SV1103 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ ( c_HOL_Ozero__class_Ozero @ SV246 ) @ SV1860 @ SV246 @ SV246 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV246 ) @ SV1103 @ SV1860 @ SV246 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5590]) ).
thf(6308,plain,
! [SV2385: $i,SV1861: $i,SV1104: $i,SV247: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV247 ) )
= $true )
| ( ( ( c_lessequals @ SV1104 @ SV1861 @ SV247 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2385 @ SV1104 @ SV247 ) @ SV1861 @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5591]) ).
thf(6309,plain,
! [SV2386: $i,SV1862: $i,SV1105: $i,SV248: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV248 ) )
= $true )
| ( ( ( c_lessequals @ SV1105 @ SV1862 @ SV248 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1105 @ SV2386 @ SV248 ) @ SV1862 @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5592]) ).
thf(6310,plain,
! [SV2387: $i,SV1863: $i,SV1106: $i,SV249: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV249 ) )
= $true )
| ( ( ( c_lessequals @ SV1106 @ ( c_Orderings_Oord__class_Omax @ SV1863 @ SV2387 @ SV249 ) @ SV249 )
| ~ ( c_lessequals @ SV1106 @ SV2387 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5593]) ).
thf(6311,plain,
! [SV2388: $i,SV1864: $i,SV1107: $i,SV250: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV250 ) )
= $true )
| ( ( ( c_lessequals @ SV1107 @ ( c_Orderings_Oord__class_Omax @ SV1864 @ SV2388 @ SV250 ) @ SV250 )
| ~ ( c_lessequals @ SV1107 @ SV1864 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5594]) ).
thf(6312,plain,
! [SV2389: $i,SV1865: $i,SV1108: $i,SV251: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV251 ) )
= $true )
| ( ( ( c_lessequals @ SV1108 @ ( c_Orderings_Oord__class_Omax @ SV1865 @ SV2389 @ SV251 ) @ SV251 )
| ~ ( c_lessequals @ SV1108 @ SV2389 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5595]) ).
thf(6313,plain,
! [SV2390: $i,SV1866: $i,SV1109: $i,SV252: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV252 ) )
= $true )
| ( ( ( c_lessequals @ SV1109 @ ( c_Orderings_Oord__class_Omax @ SV1866 @ SV2390 @ SV252 ) @ SV252 )
| ~ ( c_lessequals @ SV1109 @ SV1866 @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5596]) ).
thf(6314,plain,
! [SV2391: $i,SV1867: $i,SV1110: $i,SV253: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV253 ) )
= $true )
| ( ( ( c_lessequals @ SV1110 @ SV1867 @ SV253 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2391 @ SV1110 @ SV253 ) @ SV1867 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5597]) ).
thf(6315,plain,
! [SV2392: $i,SV1868: $i,SV1111: $i,SV254: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV254 ) )
= $true )
| ( ( ( c_lessequals @ SV1111 @ SV1868 @ SV254 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1111 @ SV2392 @ SV254 ) @ SV1868 @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5598]) ).
thf(6316,plain,
! [SV1112: $i,SV1869: $i,SV255: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV255 @ SV1869 @ tc_nat ) @ SV1112 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV255 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1112 ) @ SV1869 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5599]) ).
thf(6317,plain,
! [SV1113: $i,SV1870: $i,SV256: $i] :
( ( ( c_lessequals @ SV256 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1870 ) @ SV1113 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV256 @ SV1113 @ tc_nat ) @ SV1870 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5600]) ).
thf(6318,plain,
! [SV1871: $i,SV1114: $i,SV257: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV257 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ ( c_Power_Opower__class_Opower @ SV1114 @ SV1871 @ SV257 ) @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV1114 @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5601]) ).
thf(6319,plain,
! [SV2393: $i,SV1872: $i,SV1115: $i,SV258: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV258 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1115 @ SV1872 @ SV258 )
| ( c_HOL_Oord__class_Oless @ SV1115 @ SV2393 @ SV258 )
| ~ ( c_HOL_Oord__class_Oless @ SV1115 @ ( c_Orderings_Oord__class_Omax @ SV2393 @ SV1872 @ SV258 ) @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5602]) ).
thf(6320,plain,
! [SV1873: $i,SV261: $i,SV1118: $i] :
( ( ( ~ ( c_InductTermi_OIT @ SV1118 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV261 @ SV1118 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV261 ) ) @ SV1118 ) @ SV1873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5603]) ).
thf(6321,plain,
! [SV1876: $i,SV1121: $i,SV264: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV264 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV264 ) @ ( c_HOL_Otimes__class_Otimes @ SV1121 @ SV1121 @ SV264 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1876 @ SV1876 @ SV264 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5606]) ).
thf(6322,plain,
! [SV2632: $i,SV2396: $i,SV1877: $i,SV1122: $i,SV265: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV265 @ SV1122 @ tc_nat ) @ SV1877 @ tc_nat ) ) @ SV2396 ) @ SV2632 @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV265 @ SV1877 @ tc_nat ) ) @ SV2396 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV1877 @ tc_nat ) ) @ SV2632 ) @ tc_nat )
| ~ ( c_lessequals @ SV1122 @ SV265 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5607]) ).
thf(6323,plain,
! [SV2633: $i,SV2397: $i,SV1878: $i,SV1123: $i,SV266: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV266 @ SV1123 @ tc_nat ) ) @ SV1878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2397 @ SV1123 @ tc_nat ) ) @ SV2633 ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV266 @ SV2397 @ tc_nat ) @ SV1123 @ tc_nat ) ) @ SV1878 ) @ SV2633 @ tc_nat )
| ~ ( c_lessequals @ SV2397 @ SV266 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5608]) ).
thf(6324,plain,
! [SV2634: $i,SV2398: $i,SV1879: $i,SV1124: $i,SV267: $i] :
( ( ( c_lessequals @ SV267 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1124 @ SV1879 @ tc_nat ) @ SV2398 @ tc_nat ) ) @ SV2634 ) @ tc_nat )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1879 @ SV2398 @ tc_nat ) ) @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1124 @ SV2398 @ tc_nat ) ) @ SV2634 ) @ tc_nat )
| ~ ( c_lessequals @ SV1879 @ SV1124 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5609]) ).
thf(6325,plain,
! [SV2635: $i,SV2399: $i,SV1880: $i,SV1125: $i,SV268: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SV1125 @ tc_nat ) ) @ SV1880 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2399 @ SV1125 @ tc_nat ) ) @ SV2635 ) @ tc_nat )
| ~ ( c_lessequals @ SV1880 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2399 @ SV268 @ tc_nat ) @ SV1125 @ tc_nat ) ) @ SV2635 ) @ tc_nat )
| ~ ( c_lessequals @ SV268 @ SV2399 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5610]) ).
thf(6326,plain,
! [SV1881: $i,SV1126: $i,SV269: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV269 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SV1126 @ SV1881 @ tc_nat ) @ SV269 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1126 @ SV269 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1881 @ SV269 ) @ SV269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5611]) ).
thf(6327,plain,
! [SV2400: $i,SV1882: $i,SV1127: $i,SV270: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV270 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1127 @ SV1882 @ SV270 )
| ( c_HOL_Oord__class_Oless @ SV2400 @ SV1882 @ SV270 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV2400 @ SV1127 @ SV270 ) @ SV1882 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5612]) ).
thf(6328,plain,
! [SV1883: $i,SV1129: $i,SV272: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV272 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1129 ) @ SV1883 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
| ~ ( c_HOL_Oord__class_Oless @ SV1883 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
| ~ ( c_lessequals @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5613]) ).
thf(6329,plain,
! [SV1884: $i,SV1130: $i,SV273: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV273 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV1130 ) @ SV1884 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
| ~ ( c_lessequals @ SV1884 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
| ~ ( c_HOL_Oord__class_Oless @ SV1130 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5614]) ).
thf(6330,plain,
! [SV1131: $i,SV274: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV274 @ ( c_Suc @ SV1131 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV274 @ SV1131 @ tc_nat )
= $true )
| ( ( SV274 = SV1131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5615]) ).
thf(6331,plain,
! [SV275: $i,SV1132: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1132 @ ( c_Suc @ SV275 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1132 @ SV275 @ tc_nat )
= $true )
| ( ( SV275 = SV1132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5616]) ).
thf(6332,plain,
! [SV1133: $i,SV276: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV276 @ ( c_Suc @ SV1133 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV276 @ SV1133 @ tc_nat )
= $true )
| ( ( SV276 = SV1133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5617]) ).
thf(6333,plain,
! [SV278: $i,SV1134: $i,SV1885: $i] :
( ( ( c_lessequals @ SV1885 @ SV1134 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV278 ) @ SV1134 ) @ SV1885 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV278 ) @ ( c_HOL_Ominus__class_Ominus @ SV1134 @ SV1885 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5618]) ).
thf(6334,plain,
! [SV1135: $i,SV279: $i,SV1886: $i] :
( ( ( c_lessequals @ SV1886 @ SV279 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV279 ) @ SV1135 ) @ SV1886 @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV279 @ SV1886 @ tc_nat ) ) @ SV1135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5619]) ).
thf(6335,plain,
! [SV2636: $i,SV2401: $i,SV1887: $i,SV1136: $i,SV280: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV280 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1136 @ SV1887 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SV2401 @ SV2636 @ SV280 ) @ SV280 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1136 @ SV2401 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SV1887 @ SV2636 @ SV280 ) @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5620]) ).
thf(6336,plain,
! [SV2637: $i,SV2402: $i,SV1888: $i,SV1137: $i,SV281: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV281 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1137 @ SV1888 @ SV281 ) @ ( c_HOL_Otimes__class_Otimes @ SV2402 @ SV2637 @ SV281 ) @ SV281 )
= ( c_HOL_Otimes__class_Otimes @ SV1137 @ ( c_HOL_Otimes__class_Otimes @ SV1888 @ ( c_HOL_Otimes__class_Otimes @ SV2402 @ SV2637 @ SV281 ) @ SV281 ) @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5621]) ).
thf(6337,plain,
! [SV2638: $i,SV2403: $i,SV1889: $i,SV1138: $i,SV282: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV282 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1138 @ SV1889 @ SV282 ) @ ( c_HOL_Otimes__class_Otimes @ SV2403 @ SV2638 @ SV282 ) @ SV282 )
= ( c_HOL_Otimes__class_Otimes @ SV2403 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1138 @ SV1889 @ SV282 ) @ SV2638 @ SV282 ) @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5622]) ).
thf(6338,plain,
! [SV283: $i,SV1139: $i,SV1890: $i] :
( ( ( c_lessequals @ SV1890 @ SV1139 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_HOL_Ominus__class_Ominus @ SV1139 @ SV1890 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV283 ) @ SV1890 ) @ SV1139 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5623]) ).
thf(6339,plain,
! [SV1140: $i,SV1891: $i,SV284: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV284 @ SV1891 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV284 @ SV1140 @ tc_nat ) @ SV1891 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5624]) ).
thf(6340,plain,
! [SV1142: $i,SV1893: $i,SV286: $i] :
( ( ( c_Lambda_Obeta @ SV286 @ SV1893 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV286 @ SV1142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1893 @ SV1142 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5626]) ).
thf(6341,plain,
! [SV1894: $i,SV1144: $i,SV288: $i] :
( ( ( class_Orderings_Opreorder @ SV288 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1144 @ SV1894 @ SV288 )
| ( c_lessequals @ SV1894 @ SV1144 @ SV288 )
| ~ ( c_lessequals @ SV1144 @ SV1894 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5627]) ).
thf(6342,plain,
! [SV291: $i,SV1145: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1145 @ SV1145 @ SV291 )
= $false )
| ( ( class_Orderings_Oorder @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5628]) ).
thf(6343,plain,
! [SV292: $i,SV1146: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1146 @ SV1146 @ SV292 )
= $false )
| ( ( class_Orderings_Olinorder @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5629]) ).
thf(6344,plain,
! [SV293: $i,SV1147: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1147 @ SV1147 @ SV293 )
= $false )
| ( ( class_Orderings_Opreorder @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5630]) ).
thf(6345,plain,
! [SV1895: $i,SV1151: $i,SV297: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV297 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV297 ) @ SV1151 ) @ SV1895 ) @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1895 @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1151 @ SV297 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5633]) ).
thf(6346,plain,
! [SV1896: $i,SV1156: $i,SV302: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV302 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV1156 @ SV1896 @ SV302 ) @ SV302 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV302 ) @ SV1156 ) @ ( c_List_Olistsum @ SV1896 @ SV302 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5634]) ).
thf(6347,plain,
! [SV1897: $i,SV1157: $i,SV303: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV303 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1157 @ SV1897 @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV1897 @ SV1157 @ SV303 )
| ( SV1897 = SV1157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5635]) ).
thf(6348,plain,
! [SV1898: $i,SV1158: $i,SV304: $i] :
( ( ( class_Orderings_Olinorder @ SV304 )
= $false )
| ( ( ( SV1158 = SV1898 )
| ( c_HOL_Oord__class_Oless @ SV1898 @ SV1158 @ SV304 )
| ( c_HOL_Oord__class_Oless @ SV1158 @ SV1898 @ SV304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5636]) ).
thf(6349,plain,
! [SV305: $i,SV1159: $i] :
( ( ( c_lessequals @ SV1159 @ SV305 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV305 @ SV1159 @ tc_nat ) )
= $true )
| ( ( SV305 = SV1159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5637]) ).
thf(6350,plain,
! [SV307: $i,SV1899: $i,SV1161: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1161 @ SV1899 @ tc_nat )
= $true )
| ( ( ( SV1899 = SV1161 )
| ( c_HOL_Oord__class_Oless @ SV1899 @ SV1161 @ tc_nat ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV307 @ SV1161 ) @ SV1899 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5639]) ).
thf(6351,plain,
! [SV2639: $i,SV2405: $i,SV1900: $i,SV1162: $i,SV308: $i] :
( ( ( SV308 = SV1162 )
| ~ ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2405 ) @ SV2639 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1162 )
| ~ ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2405 ) @ SV2639 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5640]) ).
thf(6352,plain,
! [SV1901: $i,SV1164: $i,SV310: $i] :
( ( ( class_Orderings_Oorder @ SV310 )
= $false )
| ( ( ( SV1164 = SV1901 )
| ~ ( c_lessequals @ SV1901 @ SV1164 @ SV310 )
| ~ ( c_lessequals @ SV1164 @ SV1901 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5642]) ).
thf(6353,plain,
! [SV1902: $i,SV1165: $i,SV311: $i] :
( ( ( class_Orderings_Olinorder @ SV311 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1165 @ SV1902 @ SV311 )
| ( c_HOL_Oord__class_Oless @ SV1902 @ SV1165 @ SV311 )
| ( SV1902 = SV1165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5643]) ).
thf(6354,plain,
! [SV1903: $i,SV1166: $i,SV312: $i] :
( ( ( class_Orderings_Oorder @ SV312 )
= $false )
| ( ( ( SV1166 = SV1903 )
| ~ ( c_lessequals @ SV1903 @ SV1166 @ SV312 )
| ~ ( c_lessequals @ SV1166 @ SV1903 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5644]) ).
thf(6355,plain,
! [SV1904: $i,SV1167: $i,SV313: $i] :
( ( ( class_Orderings_Oorder @ SV313 )
= $false )
| ( ( ( SV1167 = SV1904 )
| ~ ( c_lessequals @ SV1167 @ SV1904 @ SV313 )
| ~ ( c_lessequals @ SV1904 @ SV1167 @ SV313 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5645]) ).
thf(6356,plain,
! [SV1906: $i,SV1169: $i,SV315: $i] :
( ( ( class_Orderings_Olinorder @ SV315 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1169 @ SV1906 @ SV315 )
| ( SV1906 = SV1169 )
| ( c_HOL_Oord__class_Oless @ SV1906 @ SV1169 @ SV315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5647]) ).
thf(6357,plain,
! [SV1907: $i,SV1170: $i,SV316: $i] :
( ( ( class_Orderings_Olinorder @ SV316 )
= $false )
| ( ( ( SV1170 = SV1907 )
| ( c_HOL_Oord__class_Oless @ SV1170 @ SV1907 @ SV316 )
| ( c_HOL_Oord__class_Oless @ SV1907 @ SV1170 @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5648]) ).
thf(6358,plain,
! [SV1908: $i,SV1171: $i,SV317: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV317 )
= $false )
| ( ( ( c_lessequals @ SV1171 @ SV1908 @ SV317 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1908 @ SV317 ) @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5649]) ).
thf(6359,plain,
! [SV1909: $i,SV1172: $i,SV318: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV318 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1172 @ SV1909 @ SV318 ) @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV318 )
| ~ ( c_lessequals @ SV1172 @ SV1909 @ SV318 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5650]) ).
thf(6360,plain,
! [SV2640: $i,SV2407: $i,SV1910: $i,SV1174: $i,SV320: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV1174 ) @ SV1910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV2407 ) @ SV2640 ) @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SV1910 @ SV2640 @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SV2407 @ SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5652]) ).
thf(6361,plain,
! [SV2408: $i,SV1911: $i,SV1175: $i,SV321: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV1175 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1911 ) @ SV2408 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1175 @ SV2408 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV321 @ SV1911 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5653]) ).
thf(6362,plain,
! [SV1912: $i,SV1178: $i,SV324: $i] :
( ( ( class_Orderings_Oorder @ SV324 )
= $false )
| ( ( ( c_lessequals @ SV1178 @ SV1912 @ SV324 )
| ~ ( c_HOL_Oord__class_Oless @ SV1178 @ SV1912 @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5656]) ).
thf(6363,plain,
! [SV1913: $i,SV1179: $i,SV325: $i] :
( ( ( class_Orderings_Opreorder @ SV325 )
= $false )
| ( ( ( c_lessequals @ SV1179 @ SV1913 @ SV325 )
| ~ ( c_HOL_Oord__class_Oless @ SV1179 @ SV1913 @ SV325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5657]) ).
thf(6364,plain,
! [SV2409: $i,SV1914: $i,SV1180: $i,SV326: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV326 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1180 @ SV1914 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ SV1180 @ ( c_Orderings_Oord__class_Omin @ SV1914 @ SV2409 @ SV326 ) @ SV326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5658]) ).
thf(6365,plain,
! [SV2410: $i,SV1915: $i,SV1181: $i,SV327: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV327 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1181 @ SV1915 @ SV327 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_Orderings_Oord__class_Omin @ SV2410 @ SV1915 @ SV327 ) @ SV327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5659]) ).
thf(6366,plain,
! [SV2411: $i,SV1916: $i,SV1182: $i,SV328: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV328 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1182 @ SV1916 @ SV328 ) @ SV2411 @ SV328 )
| ~ ( c_HOL_Oord__class_Oless @ SV1182 @ SV2411 @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5660]) ).
thf(6367,plain,
! [SV2412: $i,SV1917: $i,SV1183: $i,SV329: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV329 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1183 @ SV1917 @ SV329 ) @ SV2412 @ SV329 )
| ~ ( c_HOL_Oord__class_Oless @ SV1917 @ SV2412 @ SV329 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5661]) ).
thf(6368,plain,
! [SV330: $i,SV1918: $i,SV1184: $i] :
( ( ( ~ ( c_lessequals @ SV1184 @ SV1918 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1184 @ SV330 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV330 @ SV1184 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1918 @ SV1184 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV330 @ SV1918 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5662]) ).
thf(6369,plain,
! [SV1920: $i,SV1186: $i,SV332: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV332 ) @ SV1186 ) @ SV1920 ) @ SV332 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1920 @ SV332 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1186 @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5663]) ).
thf(6370,plain,
! [SV1921: $i,SV1187: $i,SV333: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV333 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV333 ) @ SV1187 ) @ SV1921 ) @ SV333 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1921 @ SV333 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1187 @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5664]) ).
thf(6371,plain,
! [SV1922: $i,SV334: $i,SV1188: $i] :
( ( ( ~ ( c_lessequals @ SV1188 @ SV334 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV334 @ SV1922 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV334 @ SV1188 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1922 @ SV1188 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5665]) ).
thf(6372,plain,
! [SV1923: $i,SV1189: $i,SV335: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV335 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1189 @ SV1923 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
| ~ ( c_lessequals @ SV1923 @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV1189 @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5666]) ).
thf(6373,plain,
! [SV1924: $i,SV1190: $i,SV336: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV336 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1190 @ SV1924 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV1924 @ SV336 )
| ~ ( c_lessequals @ SV1190 @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5667]) ).
thf(6374,plain,
! [SV1925: $i,SV1191: $i,SV337: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV337 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1191 @ SV1925 @ SV337 ) @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
| ~ ( c_lessequals @ SV1925 @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV1191 @ SV337 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5668]) ).
thf(6375,plain,
! [SV1926: $i,SV1192: $i,SV338: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV338 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1192 @ SV1926 @ SV338 ) @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV1926 @ SV338 )
| ~ ( c_lessequals @ SV1192 @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5669]) ).
thf(6376,plain,
! [SV1927: $i,SV1193: $i,SV339: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV339 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1193 @ SV1927 @ SV339 ) @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
| ~ ( c_lessequals @ SV1927 @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV1193 @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5670]) ).
thf(6377,plain,
! [SV1928: $i,SV1194: $i,SV340: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV340 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1928 @ SV340 ) @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV1928 @ SV340 )
| ~ ( c_lessequals @ SV1194 @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5671]) ).
thf(6378,plain,
! [SV1929: $i,SV1195: $i,SV341: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV341 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1195 @ SV1929 @ SV341 ) @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
| ~ ( c_lessequals @ SV1195 @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV1929 @ SV341 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5672]) ).
thf(6379,plain,
! [SV342: $i,SV1196: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1196 @ SV1196 @ SV342 ) @ ( c_HOL_Ozero__class_Ozero @ SV342 ) @ SV342 )
= $false )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV342 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5673]) ).
thf(6380,plain,
! [SV343: $i,SV1930: $i,SV1197: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1197 @ SV1930 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV343 ) @ SV1197 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV343 ) @ SV1930 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5674]) ).
thf(6381,plain,
! [SV1198: $i,SV344: $i,SV1931: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1931 ) @ SV344 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1931 ) @ SV1198 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV344 @ SV1198 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5675]) ).
thf(6382,plain,
! [SV1199: $i,SV345: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV345 @ SV1199 @ tc_nat )
= $false )
| ( ( ( c_Suc @ SV345 )
= SV1199 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV345 ) @ SV1199 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5676]) ).
thf(6383,plain,
! [SV346: $i,SV1200: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV1200 ) @ SV346 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV346 @ SV1200 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5677]) ).
thf(6384,plain,
! [SV2415: $i,SV1934: $i,SV1204: $i,SV350: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV350 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ ( c_Orderings_Oord__class_Omin @ SV1204 @ SV1934 @ SV350 ) ) @ SV2415 )
= ( c_Orderings_Oord__class_Omin @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV1204 ) @ SV2415 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV1934 ) @ SV2415 ) @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5680]) ).
thf(6385,plain,
! [SV351: $i,SV1205: $i,SV1935: $i] :
( ( ( c_lessequals @ SV1935 @ SV1205 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV351 @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1205 ) @ SV351 ) @ SV1935 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5681]) ).
thf(6386,plain,
! [SV2641: $i,SV2416: $i,SV1936: $i,SV1206: $i,SV352: $i] :
( ( ! [SY6967: $i,SY6968: $i,SY6969: $i,SY6970: $i] :
( ( ( hAPP @ ( hAPP @ SV352 @ ( hAPP @ ( hAPP @ SV1206 @ SV1936 ) @ SV2416 ) ) @ SV2641 )
= ( hAPP @ ( hAPP @ SV1206 @ ( hAPP @ ( hAPP @ SV352 @ SV1936 ) @ SV2641 ) ) @ ( hAPP @ ( hAPP @ SV352 @ SV2416 ) @ SV2641 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY6967 @ SV1206 @ SV352 @ SY6968 @ SY6969 @ SY6970 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5682]) ).
thf(6387,plain,
! [SV2642: $i,SV2417: $i,SV1937: $i,SV1207: $i,SV353: $i] :
( ( ! [SY6971: $i,SY6972: $i,SY6973: $i,SY6974: $i] :
( ( ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ ( hAPP @ ( hAPP @ SV1937 @ SV2417 ) @ SV2642 ) )
= ( hAPP @ ( hAPP @ SV1937 @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2417 ) ) @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2642 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1937 @ SV353 @ SY6971 @ SY6972 @ SY6973 @ SY6974 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5683]) ).
thf(6388,plain,
! [SV2643: $i,SV2418: $i,SV1938: $i,SV1208: $i,SV354: $i] :
( ( ! [SY6975: $i,SY6976: $i,SY6977: $i] :
( ( ( hAPP @ ( hAPP @ SV354 @ SV1208 ) @ SV1938 )
= ( hAPP @ ( hAPP @ SV354 @ SV1938 ) @ SV1208 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2418 @ SV354 @ SV2643 @ SY6975 @ SY6976 @ SY6977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5684]) ).
thf(6389,plain,
! [SV2644: $i,SV2419: $i,SV1939: $i,SV1209: $i,SV355: $i] :
( ( ! [SY6978: $i,SY6979: $i,SY6980: $i,SY6981: $i] :
( ( ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ ( hAPP @ ( hAPP @ SV355 @ SV1939 ) @ SV2419 ) )
= ( hAPP @ ( hAPP @ SV355 @ ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ SV1939 ) ) @ SV2419 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2644 @ SV355 @ SY6978 @ SY6979 @ SY6980 @ SY6981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5685]) ).
thf(6390,plain,
! [SV2645: $i,SV2420: $i,SV1940: $i,SV1210: $i,SV356: $i] :
( ( ! [SY6982: $i,SY6983: $i] :
( ( ( hAPP @ ( hAPP @ SV356 @ SV1210 ) @ SV1940 )
= SV1940 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2420 @ SV356 @ SV2645 @ SY6982 @ SV1210 @ SY6983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5686]) ).
thf(6391,plain,
! [SV2646: $i,SV2421: $i,SV1941: $i,SV1211: $i,SV357: $i] :
( ( ! [SY6984: $i,SY6985: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV1211 ) @ SV1941 )
= SV1211 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2421 @ SV357 @ SV2646 @ SV1211 @ SY6984 @ SY6985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5687]) ).
thf(6392,plain,
! [SV2647: $i,SV2422: $i,SV1942: $i,SV1212: $i,SV358: $i] :
( ( ! [SY6986: $i,SY6987: $i,SY6988: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV1212 ) @ SV1942 )
= ( hAPP @ ( hAPP @ SV358 @ SV1942 ) @ SV1212 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV358 @ SV2422 @ SV2647 @ SY6986 @ SY6987 @ SY6988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5688]) ).
thf(6393,plain,
! [SV2648: $i,SV2423: $i,SV1943: $i,SV1213: $i,SV359: $i] :
( ( ! [SY6989: $i,SY6990: $i,SY6991: $i,SY6992: $i] :
( ( ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ ( hAPP @ ( hAPP @ SV359 @ SV1943 ) @ SV2423 ) )
= ( hAPP @ ( hAPP @ SV359 @ ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ SV1943 ) ) @ SV2423 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV359 @ SV2648 @ SY6989 @ SY6990 @ SY6991 @ SY6992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5689]) ).
thf(6394,plain,
! [SV2649: $i,SV2424: $i,SV1944: $i,SV1214: $i,SV360: $i] :
( ( ! [SY6993: $i,SY6994: $i] :
( ( ( hAPP @ ( hAPP @ SV360 @ SV1214 ) @ SV1944 )
= SV1944 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV360 @ SV2424 @ SV2649 @ SV1214 @ SY6993 @ SY6994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5690]) ).
thf(6395,plain,
! [SV2650: $i,SV2425: $i,SV1945: $i,SV1215: $i,SV361: $i] :
( ( ! [SY6995: $i,SY6996: $i,SY6997: $i,SY6998: $i] :
( ( ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ ( hAPP @ ( hAPP @ SV361 @ SV1945 ) @ SV2425 ) )
= ( hAPP @ ( hAPP @ SV361 @ ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ SV1945 ) ) @ SV2425 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV361 @ SV2650 @ SY6995 @ SY6996 @ SY6997 @ SY6998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5691]) ).
thf(6396,plain,
! [SV2651: $i,SV2426: $i,SV1946: $i,SV1216: $i,SV362: $i] :
( ( ! [SY6999: $i,SY7000: $i,SY7001: $i] :
( ( ( hAPP @ ( hAPP @ SV362 @ SV1216 ) @ SV1946 )
= ( hAPP @ ( hAPP @ SV362 @ SV1946 ) @ SV1216 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV362 @ SV2426 @ SV2651 @ SY6999 @ SY7000 @ SY7001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5692]) ).
thf(6397,plain,
! [SV2652: $i,SV2427: $i,SV1947: $i,SV1217: $i,SV363: $i] :
( ( ! [SY7002: $i,SY7003: $i,SY7004: $i,SY7005: $i] :
( ( ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV1947 ) ) @ SV2427 )
= ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV2427 ) ) @ SV1947 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV363 @ SV2652 @ SY7002 @ SY7003 @ SY7004 @ SY7005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5693]) ).
thf(6398,plain,
! [SV2653: $i,SV2428: $i,SV1948: $i,SV1218: $i,SV364: $i] :
( ( ! [SY7006: $i,SY7007: $i,SY7008: $i,SY7009: $i] :
( ( ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ SV2428 ) )
= ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ SV2428 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV364 @ SV2653 @ SY7006 @ SY7007 @ SY7008 @ SY7009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5694]) ).
thf(6399,plain,
! [SV2654: $i,SV2429: $i,SV1949: $i,SV1219: $i,SV365: $i] :
( ( ! [SY7010: $i,SY7011: $i,SY7012: $i,SY7013: $i] :
( ( ( hAPP @ ( hAPP @ SV365 @ ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ SV1949 ) ) @ SV2429 )
= ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ ( hAPP @ ( hAPP @ SV365 @ SV1949 ) @ SV2429 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV365 @ SV2654 @ SY7010 @ SY7011 @ SY7012 @ SY7013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5695]) ).
thf(6400,plain,
! [SV2655: $i,SV2430: $i,SV1950: $i,SV1220: $i,SV366: $i] :
( ( ! [SY7014: $i,SY7015: $i,SY7016: $i,SY7017: $i,SY7018: $i] :
( ( ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV1950 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV2430 ) @ SV2655 ) )
= ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV2430 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV1950 ) @ SV2655 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV366 @ SY7014 @ SY7015 @ SY7016 @ SY7017 @ SY7018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5696]) ).
thf(6401,plain,
! [SV2656: $i,SV2431: $i,SV1951: $i,SV1221: $i,SV367: $i] :
( ( ! [SY7019: $i,SY7020: $i,SY7021: $i,SY7022: $i] :
( ( ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ SV2431 ) )
= ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ SV2431 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2656 @ SV367 @ SY7019 @ SY7020 @ SY7021 @ SY7022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5697]) ).
thf(6402,plain,
! [SV2657: $i,SV2432: $i,SV1952: $i,SV1222: $i,SV368: $i] :
( ( ! [SY7023: $i,SY7024: $i,SY7025: $i,SY7026: $i] :
( ( ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ ( hAPP @ ( hAPP @ SV368 @ SV1952 ) @ SV2432 ) )
= ( hAPP @ ( hAPP @ SV368 @ ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ SV1952 ) ) @ SV2432 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2657 @ SV368 @ SY7023 @ SY7024 @ SY7025 @ SY7026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5698]) ).
thf(6403,plain,
! [SV2658: $i,SV2433: $i,SV1953: $i,SV1223: $i,SV369: $i] :
( ( ! [SY7027: $i,SY7028: $i,SY7029: $i,SY7030: $i] :
( ( ( hAPP @ ( hAPP @ SV369 @ ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ SV1953 ) ) @ SV2433 )
= ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ ( hAPP @ ( hAPP @ SV369 @ SV1953 ) @ SV2433 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2658 @ SV369 @ SY7027 @ SY7028 @ SY7029 @ SY7030 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5699]) ).
thf(6404,plain,
! [SV2659: $i,SV2434: $i,SV1954: $i,SV1224: $i,SV370: $i] :
( ( ! [SY7031: $i,SY7032: $i,SY7033: $i,SY7034: $i] :
( ( ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV1954 ) ) @ SV2434 )
= ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV2434 ) ) @ SV1954 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2659 @ SV370 @ SY7031 @ SY7032 @ SY7033 @ SY7034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5700]) ).
thf(6405,plain,
! [SV2660: $i,SV2435: $i,SV1955: $i,SV1225: $i,SV371: $i] :
( ( ! [SY7035: $i,SY7036: $i,SY7037: $i,SY7038: $i,SY7039: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ SV2660 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ SV2660 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY7035 @ SV371 @ SY7036 @ SY7037 @ SY7038 @ SY7039 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5701]) ).
thf(6406,plain,
! [SV2661: $i,SV2436: $i,SV1956: $i,SV1226: $i,SV372: $i] :
( ( ! [SY7040: $i,SY7041: $i,SY7042: $i,SY7043: $i,SY7044: $i] :
( ( ( hAPP @ ( hAPP @ SV372 @ ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ SV1956 ) ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) )
= ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ ( hAPP @ ( hAPP @ SV372 @ SV1956 ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY7040 @ SV372 @ SY7041 @ SY7042 @ SY7043 @ SY7044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5702]) ).
thf(6407,plain,
! [SV2662: $i,SV2437: $i,SV1957: $i,SV1227: $i,SV373: $i] :
( ( ! [SY7045: $i,SY7046: $i,SY7047: $i,SY7048: $i,SY7049: $i] :
( ( ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV1957 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV2437 ) @ SV2662 ) )
= ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV2437 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV1957 ) @ SV2662 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY7045 @ SV373 @ SY7046 @ SY7047 @ SY7048 @ SY7049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5703]) ).
thf(6408,plain,
! [SV2663: $i,SV2438: $i,SV1958: $i,SV1228: $i,SV374: $i] :
( ( ! [SY7050: $i,SY7051: $i] :
( ( ( hAPP @ ( hAPP @ SV374 @ SV1228 ) @ SV1958 )
= SV1228 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2438 @ SV374 @ SV2663 @ SY7050 @ SV1958 @ SY7051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5704]) ).
thf(6409,plain,
! [SV2664: $i,SV2439: $i,SV1959: $i,SV1229: $i,SV375: $i] :
( ( ! [SY7052: $i,SY7053: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV1229 ) @ SV1959 )
= SV1959 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2439 @ SV375 @ SV2664 @ SY7052 @ SV1229 @ SY7053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5705]) ).
thf(6410,plain,
! [SV2665: $i,SV2440: $i,SV1960: $i,SV1230: $i,SV376: $i] :
( ( ! [SY7054: $i,SY7055: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ SV1230 ) @ SV1960 )
= SV1960 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2440 @ SV376 @ SV2665 @ SV1960 @ SY7054 @ SY7055 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5706]) ).
thf(6411,plain,
! [SV2666: $i,SV2441: $i,SV1961: $i,SV1231: $i,SV377: $i] :
( ( ! [SY7056: $i,SY7057: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SV1231 ) @ SV1961 )
= SV1231 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2441 @ SV377 @ SV2666 @ SV1231 @ SY7056 @ SY7057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5707]) ).
thf(6412,plain,
! [SV2667: $i,SV2442: $i,SV1962: $i,SV1232: $i,SV378: $i] :
( ( ! [SY7058: $i,SY7059: $i,SY7060: $i,SY7061: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ ( hAPP @ ( hAPP @ SV1232 @ SV1962 ) @ SV2442 ) ) @ SV2667 )
= ( hAPP @ ( hAPP @ SV1232 @ ( hAPP @ ( hAPP @ SV378 @ SV1962 ) @ SV2667 ) ) @ ( hAPP @ ( hAPP @ SV378 @ SV2442 ) @ SV2667 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1232 @ SV378 @ SY7058 @ SY7059 @ SY7060 @ SY7061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5708]) ).
thf(6413,plain,
! [SV2668: $i,SV2443: $i,SV1963: $i,SV1233: $i,SV379: $i] :
( ( ! [SY7062: $i,SY7063: $i,SY7064: $i] :
( ( ( hAPP @ ( hAPP @ SV379 @ SV1233 ) @ SV1963 )
= ( hAPP @ ( hAPP @ SV379 @ SV1963 ) @ SV1233 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2443 @ SV379 @ SV2668 @ SY7062 @ SY7063 @ SY7064 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5709]) ).
thf(6414,plain,
! [SV2669: $i,SV2444: $i,SV1964: $i,SV1234: $i,SV380: $i] :
( ( ! [SY7065: $i,SY7066: $i] :
( ( ( hAPP @ ( hAPP @ SV380 @ SV1234 ) @ SV1964 )
= SV1234 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV380 @ SV2444 @ SV2669 @ SV1964 @ SY7065 @ SY7066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5710]) ).
thf(6415,plain,
! [SV2670: $i,SV2445: $i,SV1965: $i,SV1235: $i,SV381: $i] :
( ( ! [SY7067: $i,SY7068: $i] :
( ( ( hAPP @ ( hAPP @ SV381 @ SV1235 ) @ SV1965 )
= SV1965 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV381 @ SV2445 @ SV2670 @ SV1235 @ SY7067 @ SY7068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5711]) ).
thf(6416,plain,
! [SV2671: $i,SV2446: $i,SV1966: $i,SV1236: $i,SV382: $i] :
( ( ! [SY7069: $i,SY7070: $i] :
( ( ( hAPP @ ( hAPP @ SV382 @ SV1236 ) @ SV1236 )
= ( hAPP @ ( hAPP @ SV1966 @ ( hAPP @ ( hAPP @ SV382 @ SV2446 ) @ SV2446 ) ) @ SV1236 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV382 @ SV1966 @ SV2671 @ SY7069 @ SV2446 @ SY7070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5712]) ).
thf(6417,plain,
! [SV2672: $i,SV2447: $i,SV1967: $i,SV1237: $i,SV383: $i] :
( ( ! [SY7071: $i,SY7072: $i,SY7073: $i] :
( ( ( hAPP @ ( hAPP @ SV383 @ SV1237 ) @ ( hAPP @ ( hAPP @ SV1967 @ SV2447 ) @ SV1237 ) )
= ( hAPP @ ( hAPP @ SV1967 @ ( hAPP @ ( hAPP @ SV383 @ SV2447 ) @ SV2672 ) ) @ SV1237 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV383 @ SV1967 @ SY7071 @ SY7072 @ SV2672 @ SY7073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5713]) ).
thf(6418,plain,
! [SV2673: $i,SV2448: $i,SV1968: $i,SV1238: $i,SV384: $i] :
( ( ! [SY7074: $i,SY7075: $i,SY7076: $i] :
( ( ( hAPP @ ( hAPP @ SV384 @ ( hAPP @ ( hAPP @ SV1238 @ SV1968 ) @ SV2448 ) ) @ SV2448 )
= ( hAPP @ ( hAPP @ SV1238 @ ( hAPP @ ( hAPP @ SV384 @ SV1968 ) @ SV2673 ) ) @ SV2448 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV384 @ SV1238 @ SY7074 @ SY7075 @ SV2673 @ SY7076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5714]) ).
thf(6419,plain,
! [SV2674: $i,SV2449: $i,SV1969: $i,SV1239: $i,SV385: $i] :
( ( ! [SY7077: $i,SY7078: $i,SY7079: $i,SY7080: $i] :
( ( ( hAPP @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ SV1239 @ SV1969 ) @ SV2449 ) ) @ ( hAPP @ ( hAPP @ SV1239 @ SV2674 ) @ SV2449 ) )
= ( hAPP @ ( hAPP @ SV1239 @ ( hAPP @ ( hAPP @ SV385 @ SV1969 ) @ SV2674 ) ) @ SV2449 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV385 @ SV1239 @ SY7077 @ SY7078 @ SY7079 @ SY7080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5715]) ).
thf(6420,plain,
! [SV2450: $i,SV1970: $i,SV1240: $i,SV386: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV386 @ ( c_Type_Otype_Otype__case @ SV1240 @ SV1970 @ ( c_Type_Otype_OAtom @ SV2450 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV386 @ ( hAPP @ SV1240 @ SV2450 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5716]) ).
thf(6421,plain,
! [SV2451: $i,SV1971: $i,SV1241: $i,SV387: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV387 @ ( c_Type_Otype_Otype__case @ SV1241 @ SV1971 @ ( c_Type_Otype_OAtom @ SV2451 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV387 @ ( hAPP @ SV1241 @ SV2451 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5717]) ).
thf(6422,plain,
! [SV389: $i,SV1973: $i,SV1243: $i] :
( ( ( c_lessequals @ SV1243 @ SV1973 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV389 ) @ SV1243 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV389 ) @ SV1973 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5718]) ).
thf(6423,plain,
! [SV1244: $i,SV390: $i,SV1974: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1974 ) @ SV390 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1974 ) @ SV1244 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV390 @ SV1244 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5719]) ).
thf(6424,plain,
! [SV1975: $i,SV1245: $i,SV391: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV391 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV391 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV391 ) @ ( c_HOL_Otimes__class_Otimes @ SV1245 @ SV1245 @ SV391 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1975 @ SV1975 @ SV391 ) ) @ SV391 )
| ( SV1245
= ( c_HOL_Ozero__class_Ozero @ SV391 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5720]) ).
thf(6425,plain,
! [SV1976: $i,SV1246: $i,SV392: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV392 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV392 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV392 ) @ ( c_HOL_Otimes__class_Otimes @ SV1246 @ SV1246 @ SV392 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1976 @ SV1976 @ SV392 ) ) @ SV392 )
| ( SV1976
= ( c_HOL_Ozero__class_Ozero @ SV392 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5721]) ).
thf(6426,plain,
! [SV2675: $i,SV2452: $i,SV1977: $i,SV1247: $i,SV394: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV394 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1247 ) @ SV1977 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV2452 ) @ SV2675 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1247 ) @ SV2452 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1977 ) @ SV2675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5722]) ).
thf(6427,plain,
! [SV395: $i,SV1978: $i,SV1248: $i] :
( ( ( c_Lambda_Obeta @ SV1248 @ SV1978 )
= $false )
| ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV395 ) @ SV1248 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV395 ) @ SV1978 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5723]) ).
thf(6428,plain,
! [SV1249: $i,SV1979: $i,SV396: $i] :
( ( ( c_Lambda_Obeta @ SV396 @ SV1979 )
= $false )
| ( ( c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV396 ) @ SV1249 ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1979 ) @ SV1249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5724]) ).
thf(6429,plain,
! [SV397: $i,SV1250: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1250 @ SV397 ) @ ( c_HOL_Ozero__class_Ozero @ SV397 ) @ SV397 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV397 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5725]) ).
thf(6430,plain,
! [SV1980: $i,SV1251: $i,SV398: $i] :
( ( ( class_Orderings_Olinorder @ SV398 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1251 @ SV1980 @ SV398 )
= ( c_Orderings_Oord__class_Omax @ SV1980 @ SV1251 @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5726]) ).
thf(6431,plain,
! [SV2454: $i,SV1982: $i,SV1253: $i,SV401: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV401 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV1253 @ SV1982 @ SV401 ) @ ( c_Orderings_Oord__class_Omin @ SV1253 @ SV2454 @ SV401 ) @ SV401 ) @ ( c_Orderings_Oord__class_Omin @ SV1253 @ ( c_Orderings_Oord__class_Omax @ SV1982 @ SV2454 @ SV401 ) @ SV401 ) @ SV401 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5728]) ).
thf(6432,plain,
! [SV1983: $i,SV1255: $i,SV404: $i] :
( ( ( class_Orderings_Olinorder @ SV404 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1255 @ ( c_Orderings_Oord__class_Omin @ SV1255 @ SV1983 @ SV404 ) @ SV404 )
= SV1255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5729]) ).
thf(6433,plain,
! [SV2455: $i,SV1984: $i,SV1256: $i,SV406: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV406 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1256 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1256 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV1984 @ SV406 ) @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV2455 @ SV406 ) @ SV406 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5730]) ).
thf(6434,plain,
! [SV2456: $i,SV1985: $i,SV1257: $i,SV407: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV407 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1257 @ SV1985 @ SV407 )
| ( c_HOL_Oord__class_Oless @ SV1985 @ SV1257 @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2456 @ SV1985 @ SV407 ) @ ( c_HOL_Otimes__class_Otimes @ SV2456 @ SV1257 @ SV407 ) @ SV407 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5731]) ).
thf(6435,plain,
! [SV2457: $i,SV1986: $i,SV1258: $i,SV408: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV408 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1258 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV1258 @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1986 @ SV1258 @ SV408 ) @ ( c_HOL_Otimes__class_Otimes @ SV2457 @ SV1258 @ SV408 ) @ SV408 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5732]) ).
thf(6436,plain,
! [SV2458: $i,SV1987: $i,SV1259: $i,SV409: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV409 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1259 @ SV1987 @ SV409 )
| ( c_HOL_Oord__class_Oless @ SV1987 @ SV1259 @ SV409 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1987 @ SV2458 @ SV409 ) @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SV2458 @ SV409 ) @ SV409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5733]) ).
thf(6437,plain,
! [SV413: $i,SV1263: $i,SV1988: $i] :
( ( ( c_lessequals @ SV1988 @ SV1263 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV413 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV1263 @ SV1988 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV413 ) @ SV1988 ) @ ( c_Suc @ SV1263 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5736]) ).
thf(6438,plain,
! [SV1989: $i,SV1264: $i,SV414: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV414 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1264 @ SV1989 @ SV414 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1264 @ SV1989 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5737]) ).
thf(6439,plain,
! [SV1990: $i,SV1265: $i,SV415: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV415 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SV1990 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 )
| ~ ( c_HOL_Oord__class_Oless @ SV1265 @ SV1990 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5738]) ).
thf(6440,plain,
! [SV1991: $i,SV1266: $i,SV416: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV416 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1266 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1991 @ SV416 ) @ SV416 )
| ~ ( c_HOL_Oord__class_Oless @ SV1266 @ SV1991 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5739]) ).
thf(6441,plain,
! [SV1992: $i,SV1267: $i,SV417: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV417 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1267 @ SV1992 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1267 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1992 @ SV417 ) @ SV417 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5740]) ).
thf(6442,plain,
! [SV420: $i,SV1268: $i,SV1993: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1993 @ SV1268 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV420 @ SV1993 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV420 ) @ SV1268 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5741]) ).
thf(6443,plain,
! [SV2459: $i,SV1994: $i,SV1269: $i,SV421: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV1269 ) @ SV1994 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV2459 ) @ SV1994 ) @ SV421 )
| ~ ( c_lessequals @ SV1269 @ SV2459 @ SV421 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5742]) ).
thf(6444,plain,
! [SV2460: $i,SV1995: $i,SV1270: $i,SV422: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 ) )
= $true )
| ( ( ( c_lessequals @ SV1270 @ SV1995 @ SV422 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1270 ) @ SV2460 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1995 ) @ SV2460 ) @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5743]) ).
thf(6445,plain,
! [SV2461: $i,SV1996: $i,SV1271: $i,SV423: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV423 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SV1996 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SV2461 ) @ SV423 )
| ~ ( c_lessequals @ SV1996 @ SV2461 @ SV423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5744]) ).
thf(6446,plain,
! [SV2462: $i,SV1997: $i,SV1272: $i,SV424: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 ) )
= $true )
| ( ( ( c_lessequals @ SV1272 @ SV1997 @ SV424 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV2462 ) @ SV1272 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV2462 ) @ SV1997 ) @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5745]) ).
thf(6447,plain,
! [SV2463: $i,SV1998: $i,SV1273: $i,SV425: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV425 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV1273 ) @ SV1998 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV2463 ) @ SV1998 ) @ SV425 )
| ~ ( c_lessequals @ SV1273 @ SV2463 @ SV425 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5746]) ).
thf(6448,plain,
! [SV2464: $i,SV1999: $i,SV1274: $i,SV426: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV426 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SV1999 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SV2464 ) @ SV426 )
| ~ ( c_lessequals @ SV1999 @ SV2464 @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5747]) ).
thf(6449,plain,
! [SV1275: $i,SV2000: $i,SV427: $i] :
( ( ( c_lessequals @ SV427 @ SV2000 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV427 ) @ SV1275 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2000 ) @ SV1275 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5748]) ).
thf(6450,plain,
! [SV1276: $i,SV428: $i,SV2001: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2001 ) @ SV428 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2001 ) @ SV1276 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV428 @ SV1276 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5749]) ).
thf(6451,plain,
! [SV429: $i,SV2002: $i,SV1277: $i] :
( ( ( c_lessequals @ SV1277 @ SV2002 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV429 ) @ SV1277 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV429 ) @ SV2002 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5750]) ).
thf(6452,plain,
! [SV2676: $i,SV2465: $i,SV2003: $i,SV1281: $i,SV433: $i] :
( ( ! [SY7081: $i,SY7082: $i,SY7083: $i] :
( ( ( hAPP @ ( hAPP @ SV433 @ SV1281 ) @ ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ SV2465 ) )
= ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ ( c_Suc @ SV2465 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2676 @ SV433 @ SV2003 @ SY7081 @ SY7082 @ SY7083 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5754]) ).
thf(6453,plain,
! [SV2677: $i,SV2466: $i,SV2004: $i,SV1282: $i,SV434: $i] :
( ( ! [SY7084: $i,SY7085: $i,SY7086: $i] :
( ( ( hAPP @ ( hAPP @ SV434 @ ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ SV2466 ) ) @ SV2004 )
= ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ ( c_Suc @ SV2466 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2677 @ SV434 @ SV1282 @ SY7084 @ SY7085 @ SY7086 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5755]) ).
thf(6454,plain,
! [SV2678: $i,SV2467: $i,SV2005: $i,SV1283: $i,SV435: $i] :
( ( ! [SY7087: $i,SY7088: $i,SY7089: $i] :
( ( ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ ( c_Suc @ SV2005 ) )
= ( hAPP @ ( hAPP @ SV2467 @ SV1283 ) @ ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ SV2005 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2678 @ SV2467 @ SV435 @ SY7087 @ SY7088 @ SY7089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5756]) ).
thf(6455,plain,
! [SV2679: $i,SV2468: $i,SV2006: $i,SV1284: $i,SV436: $i] :
( ( ! [SY7090: $i,SY7091: $i,SY7092: $i] :
( ( ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ ( c_Suc @ SV2006 ) )
= ( hAPP @ ( hAPP @ SV2468 @ SV1284 ) @ ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ SV2006 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2679 @ SV2468 @ SV436 @ SY7090 @ SY7091 @ SY7092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5757]) ).
thf(6456,plain,
! [SV1285: $i,SV437: $i,SV2007: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2007 @ SV437 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2007 @ SV1285 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV437 @ SV1285 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5758]) ).
thf(6457,plain,
! [SV1286: $i,SV2008: $i,SV438: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV438 @ SV2008 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1286 @ SV2008 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV438 @ SV1286 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5759]) ).
thf(6458,plain,
! [SV439: $i,SV1287: $i,SV2009: $i] :
( ( ( c_lessequals @ SV2009 @ SV1287 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV439 ) @ ( c_HOL_Ominus__class_Ominus @ SV1287 @ SV2009 @ tc_nat ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV439 ) @ SV1287 ) @ SV2009 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5760]) ).
thf(6459,plain,
! [SV2010: $i,SV440: $i,SV1288: $i] :
( ( ( c_lessequals @ SV1288 @ SV440 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV440 @ SV1288 @ tc_nat ) ) @ SV2010 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV440 ) @ SV2010 ) @ SV1288 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5761]) ).
thf(6460,plain,
! [SV2470: $i,SV2012: $i,SV1290: $i,SV442: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV442 ) )
= $true )
| ( ( ( c_lessequals @ SV1290 @ SV2012 @ SV442 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV442 ) @ SV2012 @ SV442 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1290 @ ( c_Suc @ SV2470 ) @ SV442 ) @ ( c_Power_Opower__class_Opower @ SV2012 @ ( c_Suc @ SV2470 ) @ SV442 ) @ SV442 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5763]) ).
thf(6461,plain,
! [SV2014: $i,SV1292: $i,SV444: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV444 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1292 @ ( c_HOL_Otimes__class_Otimes @ SV1292 @ SV2014 @ SV444 ) @ SV444 )
= ( c_HOL_Otimes__class_Otimes @ SV1292 @ SV2014 @ SV444 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5765]) ).
thf(6462,plain,
! [SV1293: $i,SV445: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV445 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1293 @ SV445 ) @ SV445 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1293 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV445 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5766]) ).
thf(6463,plain,
! [SV446: $i,SV1294: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1294 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1294 @ SV446 ) @ SV446 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV446 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5767]) ).
thf(6464,plain,
! [SV2680: $i,SV2472: $i,SV2015: $i,SV1295: $i,SV447: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SV2472 @ SV2680 @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
| ~ ( c_lessequals @ SV2015 @ SV2680 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SV2472 @ SV447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5768]) ).
thf(6465,plain,
! [SV2681: $i,SV2473: $i,SV2016: $i,SV1296: $i,SV448: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SV2473 @ SV2681 @ SV448 ) @ SV448 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ SV2016 @ SV2681 @ SV448 )
| ~ ( c_lessequals @ SV1296 @ SV2473 @ SV448 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5769]) ).
thf(6466,plain,
! [SV2017: $i,SV1297: $i,SV449: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV449 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1297 @ ( c_Power_Opower__class_Opower @ SV1297 @ SV2017 @ SV449 ) @ SV449 )
= ( c_Power_Opower__class_Opower @ SV1297 @ ( c_Suc @ SV2017 ) @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5770]) ).
thf(6467,plain,
! [SV2018: $i,SV1298: $i,SV450: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV450 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1298 @ SV2018 @ SV450 ) @ SV1298 @ SV450 )
= ( c_Power_Opower__class_Opower @ SV1298 @ ( c_Suc @ SV2018 ) @ SV450 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5771]) ).
thf(6468,plain,
! [SV2019: $i,SV1299: $i,SV451: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV451 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV1299 @ SV451 )
| ( c_lessequals @ SV1299 @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1299 @ SV451 ) @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5772]) ).
thf(6469,plain,
! [SV2020: $i,SV1300: $i,SV452: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV452 )
= $false )
| ( ( ( c_lessequals @ SV1300 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
| ( c_lessequals @ SV2020 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1300 @ SV2020 @ SV452 ) @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5773]) ).
thf(6470,plain,
! [SV2021: $i,SV1301: $i,SV453: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV453 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV1301 @ SV453 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV2021 @ SV453 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1301 @ SV453 ) @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV453 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5774]) ).
thf(6471,plain,
! [SV2022: $i,SV1302: $i,SV454: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV454 )
= $false )
| ( ( ( c_lessequals @ SV1302 @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV1302 @ SV454 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1302 @ SV2022 @ SV454 ) @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5775]) ).
thf(6472,plain,
! [SV2023: $i,SV1303: $i,SV455: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV455 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1303 @ SV2023 @ SV455 ) @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SV1303 @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV2023 @ SV455 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5776]) ).
thf(6473,plain,
! [SV2024: $i,SV1304: $i,SV456: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV456 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1304 @ SV2024 @ SV456 ) @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV2024 @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1304 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5777]) ).
thf(6474,plain,
! [SV2025: $i,SV1305: $i,SV457: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV457 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1305 @ SV2025 @ SV457 ) @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV2025 @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SV1305 @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5778]) ).
thf(6475,plain,
! [SV2474: $i,SV2026: $i,SV1308: $i,SV460: $i] :
( ( ( c_Type_Otypings @ SV460 @ SV1308 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV2026 @ SV460 @ SV2474 @ SV1308 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV460 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV2474 @ SV1308 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2026 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5781]) ).
thf(6476,plain,
! [SV461: $i,SV1309: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1309 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV461 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV461 @ ( c_HOL_Otimes__class_Otimes @ SV1309 @ SV461 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5782]) ).
thf(6477,plain,
! [SV462: $i,SV1310: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1310 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV462 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV462 @ ( c_HOL_Otimes__class_Otimes @ SV462 @ SV1310 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5783]) ).
thf(6478,plain,
! [SV1311: $i,SV2027: $i,SV464: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SV2027 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1311 @ SV2027 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2027 @ SV1311 @ tc_nat )
| ~ ( c_lessequals @ SV2027 @ SV464 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV464 @ SV1311 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5784]) ).
thf(6479,plain,
! [SV1312: $i,SV2028: $i,SV465: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV465 @ SV2028 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1312 @ SV2028 @ tc_nat )
| ~ ( c_lessequals @ SV1312 @ SV465 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV465 @ SV1312 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV2028 @ SV1312 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5785]) ).
thf(6480,plain,
! [SV2475: $i,SV2029: $i,SV1313: $i,SV466: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV466 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1313 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ SV2029 ) @ SV2475 ) @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ SV1313 @ SV2475 @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV2029 @ SV466 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5786]) ).
thf(6481,plain,
! [SV1314: $i,SV2030: $i,SV467: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV467 @ SV2030 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV467 ) @ SV1314 @ SV2030 )
= ( c_Lambda_OdB_OVar @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5787]) ).
thf(6482,plain,
! [SV2031: $i,SV1315: $i,SV468: $i] :
( ( ( c_InductTermi_OIT @ SV468 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV468 @ ( c_Lambda_OdB_OVar @ SV1315 ) @ SV2031 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(6483,plain,
! [SV1316: $i,SV469: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV469 ) @ SV1316 ) @ SV1316 ) @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
= $true )
| ( ( ~ ( c_lessequals @ SV1316 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5789]) ).
thf(6484,plain,
! [SV470: $i,SV1317: $i] :
( ( ( c_lessequals @ SV1317 @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV470 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV470 ) @ SV1317 ) @ SV1317 ) @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV470 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5790]) ).
thf(6485,plain,
! [SV2032: $i,SV1320: $i,SV473: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV473 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1320 @ SV2032 @ tc_nat ) @ SV473 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1320 @ SV473 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV2032 @ SV473 ) @ SV473 ) )
| ~ ( c_lessequals @ SV2032 @ SV1320 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5791]) ).
thf(6486,plain,
! [SV2476: $i,SV2033: $i,SV1321: $i,SV474: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV474 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1321 @ SV2033 @ SV474 ) @ ( c_HOL_Otimes__class_Otimes @ SV2476 @ SV2033 @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SV2033 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SV2476 @ SV1321 @ SV474 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5792]) ).
thf(6487,plain,
! [SV2477: $i,SV2034: $i,SV1322: $i,SV475: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV475 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2034 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2477 @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SV2477 @ SV2034 @ SV475 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5793]) ).
thf(6488,plain,
! [SV2478: $i,SV2035: $i,SV1323: $i,SV476: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__mono @ SV476 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1323 @ SV2035 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SV2478 @ SV2035 @ SV476 ) @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV2035 @ SV476 )
| ~ ( c_lessequals @ SV1323 @ SV2478 @ SV476 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5794]) ).
thf(6489,plain,
! [SV2479: $i,SV2036: $i,SV1324: $i,SV477: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__mono @ SV477 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2036 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2479 @ SV477 ) @ SV477 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV477 ) @ SV1324 @ SV477 )
| ~ ( c_lessequals @ SV2036 @ SV2479 @ SV477 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5795]) ).
thf(6490,plain,
! [SV2480: $i,SV2037: $i,SV1325: $i,SV478: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__mono1 @ SV478 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2037 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2480 @ SV478 ) @ SV478 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV478 ) @ SV1325 @ SV478 )
| ~ ( c_lessequals @ SV2037 @ SV2480 @ SV478 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5796]) ).
thf(6491,plain,
! [SV1327: $i,SV2039: $i,SV480: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV480 @ ( c_HOL_Ominus__class_Ominus @ SV2039 @ SV1327 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV480 ) @ SV1327 ) @ SV2039 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5797]) ).
thf(6492,plain,
! [SV1328: $i,SV2040: $i,SV481: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SV2040 ) @ SV1328 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV481 @ ( c_HOL_Ominus__class_Ominus @ SV1328 @ SV2040 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5798]) ).
thf(6493,plain,
! [SV2481: $i,SV2041: $i,SV1329: $i,SV482: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV482 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SV1329 ) @ SV2041 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SV2481 ) @ SV2041 ) @ SV482 )
| ~ ( c_HOL_Oord__class_Oless @ SV1329 @ SV2481 @ SV482 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5799]) ).
thf(6494,plain,
! [SV2482: $i,SV2042: $i,SV1330: $i,SV483: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV483 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SV1330 ) @ SV2042 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SV2482 ) @ SV2042 ) @ SV483 )
| ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SV2482 @ SV483 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5800]) ).
thf(6495,plain,
! [SV2483: $i,SV2043: $i,SV1331: $i,SV484: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV484 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1331 @ SV2043 @ SV484 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV1331 ) @ SV2483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV2043 ) @ SV2483 ) @ SV484 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5801]) ).
thf(6496,plain,
! [SV2484: $i,SV2044: $i,SV1332: $i,SV485: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV485 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SV2044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SV2484 ) @ SV485 )
| ~ ( c_HOL_Oord__class_Oless @ SV2044 @ SV2484 @ SV485 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5802]) ).
thf(6497,plain,
! [SV2485: $i,SV2045: $i,SV1333: $i,SV486: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV486 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SV2045 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SV2485 ) @ SV486 )
| ~ ( c_HOL_Oord__class_Oless @ SV2045 @ SV2485 @ SV486 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5803]) ).
thf(6498,plain,
! [SV2486: $i,SV2046: $i,SV1334: $i,SV487: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV487 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1334 @ SV2046 @ SV487 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SV2486 ) @ SV1334 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SV2486 ) @ SV2046 ) @ SV487 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5804]) ).
thf(6499,plain,
! [SV1335: $i,SV2047: $i,SV488: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV488 @ SV2047 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV488 ) @ SV1335 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2047 ) @ SV1335 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5805]) ).
thf(6500,plain,
! [SV1336: $i,SV489: $i,SV2048: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2048 ) @ SV489 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2048 ) @ SV1336 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV489 @ SV1336 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5806]) ).
thf(6501,plain,
! [SV490: $i,SV2049: $i,SV1337: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1337 @ SV2049 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV490 ) @ SV1337 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV490 ) @ SV2049 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5807]) ).
thf(6502,plain,
! [SV491: $i,SV1338: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1338 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV491 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV491 @ SV1338 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5808]) ).
thf(6503,plain,
! [SV2487: $i,SV2050: $i,SV1339: $i,SV492: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV492 ) )
= $true )
| ( ( ( c_lessequals @ SV1339 @ SV2050 @ SV492 )
| ~ ( c_lessequals @ SV1339 @ SV2487 @ SV492 )
| ~ ( c_lessequals @ SV2487 @ SV2050 @ SV492 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5809]) ).
thf(6504,plain,
! [SV2488: $i,SV2051: $i,SV1340: $i,SV493: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV493 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1340 @ SV2051 @ SV493 )
| ~ ( c_lessequals @ SV1340 @ SV2488 @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SV2488 @ SV2051 @ SV493 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5810]) ).
thf(6505,plain,
! [SV2489: $i,SV2052: $i,SV1341: $i,SV494: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV494 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1341 @ SV2052 @ SV494 )
| ~ ( c_HOL_Oord__class_Oless @ SV1341 @ SV2489 @ SV494 )
| ~ ( c_lessequals @ SV2489 @ SV2052 @ SV494 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5811]) ).
thf(6506,plain,
! [SV2053: $i,SV1342: $i,SV495: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV495 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1342 ) @ SV2053 ) @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
| ~ ( c_lessequals @ SV2053 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
| ~ ( c_lessequals @ SV1342 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5812]) ).
thf(6507,plain,
! [SV2490: $i,SV2054: $i,SV1343: $i,SV496: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV496 ) )
= $true )
| ( ( ( c_lessequals @ SV1343 @ SV2054 @ SV496 )
| ~ ( c_lessequals @ SV2490 @ SV2054 @ SV496 )
| ~ ( c_lessequals @ SV1343 @ SV2490 @ SV496 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5813]) ).
thf(6508,plain,
! [SV498: $i,SV1344: $i,SV2055: $i] :
( ( ( ~ ( c_lessequals @ SV2055 @ SV1344 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV498 @ SV2055 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV498 @ SV1344 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5814]) ).
thf(6509,plain,
! [SV1346: $i,SV501: $i] :
( ( ( c_lessequals @ SV501 @ ( c_Suc @ SV1346 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV501 @ SV1346 @ tc_nat )
= $true )
| ( ( SV501
= ( c_Suc @ SV1346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5815]) ).
thf(6510,plain,
! [SV503: $i,SV1347: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1347 @ ( c_Suc @ SV503 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV503 @ SV1347 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5816]) ).
thf(6511,plain,
! [SV1349: $i,SV2056: $i,SV505: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV505 @ SV2056 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1349 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV1349 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2056 @ SV1349 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5817]) ).
thf(6512,plain,
! [SV506: $i,SV2057: $i,SV1350: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1350 @ SV2057 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV506 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV1350 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV2057 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5818]) ).
thf(6513,plain,
! [SV2058: $i,SV1351: $i,SV507: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV507 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1351 @ SV2058 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SV1351 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SV2058 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5819]) ).
thf(6514,plain,
! [SV2059: $i,SV508: $i,SV1352: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1352 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV508 @ SV2059 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV508 @ SV1352 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2059 @ SV1352 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5820]) ).
thf(6515,plain,
! [SV1353: $i,SV509: $i,SV2060: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2060 @ SV509 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2060 @ SV1353 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2060 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV509 @ SV1353 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5821]) ).
thf(6516,plain,
! [SV510: $i,SV2061: $i,SV1354: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1354 @ SV2061 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV510 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SV1354 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SV2061 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5822]) ).
thf(6517,plain,
! [SV2491: $i,SV2062: $i,SV1355: $i,SV511: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV511 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1355 @ SV2062 @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV2062 @ SV511 ) @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV1355 @ SV511 ) @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ SV2491 @ ( c_HOL_Ozero__class_Ozero @ SV511 ) @ SV511 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5823]) ).
thf(6518,plain,
! [SV2492: $i,SV2063: $i,SV1356: $i,SV512: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV512 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2063 @ SV512 ) @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2492 @ SV512 ) @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SV2492 @ SV2063 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SV1356 @ ( c_HOL_Ozero__class_Ozero @ SV512 ) @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5824]) ).
thf(6519,plain,
! [SV2493: $i,SV2064: $i,SV1357: $i,SV513: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV513 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1357 @ SV2064 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV1357 @ SV513 ) @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV2064 @ SV513 ) @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV513 ) @ SV2493 @ SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5825]) ).
thf(6520,plain,
! [SV2494: $i,SV2065: $i,SV1358: $i,SV514: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV514 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2065 @ SV514 ) @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2494 @ SV514 ) @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ SV2065 @ SV2494 @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SV1358 @ SV514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5826]) ).
thf(6521,plain,
! [SV2495: $i,SV2066: $i,SV1359: $i,SV515: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV515 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2066 @ SV515 ) @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2495 @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SV1359 @ ( c_HOL_Ozero__class_Ozero @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SV2495 @ SV2066 @ SV515 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5827]) ).
thf(6522,plain,
! [SV2496: $i,SV2067: $i,SV1360: $i,SV516: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV516 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2067 @ SV516 ) @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2496 @ SV516 ) @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV516 ) @ SV1360 @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ SV2067 @ SV2496 @ SV516 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5828]) ).
thf(6523,plain,
! [SV2497: $i,SV2068: $i,SV1361: $i,SV517: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV517 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2068 @ SV517 ) @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2497 @ SV517 ) @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ SV2068 @ SV2497 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1361 @ SV517 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5829]) ).
thf(6524,plain,
! [SV2498: $i,SV2069: $i,SV1362: $i,SV518: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV518 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2069 @ SV518 ) @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2498 @ SV518 ) @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SV2498 @ SV2069 @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SV1362 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5830]) ).
thf(6525,plain,
! [SV2499: $i,SV2070: $i,SV1363: $i,SV519: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV519 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1363 @ SV2070 @ SV519 ) @ ( c_HOL_Otimes__class_Otimes @ SV2499 @ SV2070 @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SV2070 @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SV2499 @ SV1363 @ SV519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5831]) ).
thf(6526,plain,
! [SV2500: $i,SV2071: $i,SV1364: $i,SV520: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV520 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1364 @ SV2071 @ SV520 ) @ ( c_HOL_Otimes__class_Otimes @ SV2500 @ SV2071 @ SV520 ) @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV2071 @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ SV1364 @ SV2500 @ SV520 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5832]) ).
thf(6527,plain,
! [SV2501: $i,SV2072: $i,SV1365: $i,SV521: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV521 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1365 @ SV2072 @ SV521 ) @ ( c_HOL_Otimes__class_Otimes @ SV2501 @ SV2072 @ SV521 ) @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ SV1365 @ SV2501 @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV521 ) @ SV2072 @ SV521 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5833]) ).
thf(6528,plain,
! [SV2502: $i,SV2073: $i,SV1366: $i,SV522: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV522 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1366 @ SV2073 @ SV522 ) @ ( c_HOL_Otimes__class_Otimes @ SV2502 @ SV2073 @ SV522 ) @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SV2502 @ SV1366 @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SV2073 @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV522 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5834]) ).
thf(6529,plain,
! [SV2503: $i,SV2074: $i,SV1367: $i,SV523: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV523 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2074 @ SV523 ) @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2503 @ SV523 ) @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV1367 @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ SV2074 @ SV2503 @ SV523 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5835]) ).
thf(6530,plain,
! [SV2504: $i,SV2076: $i,SV1369: $i,SV525: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV525 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ ( c_Orderings_Oord__class_Omax @ SV1369 @ SV2076 @ SV525 ) ) @ SV2504 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ SV1369 ) @ SV2504 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ SV2076 ) @ SV2504 ) @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5836]) ).
thf(6531,plain,
! [SV2505: $i,SV2077: $i,SV1371: $i,SV527: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV527 @ SV1371 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2077 @ SV2505 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1371 @ SV2505 @ tc_nat )
| ~ ( c_lessequals @ SV527 @ SV2077 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5838]) ).
thf(6532,plain,
! [SV2682: $i,SV2506: $i,SV2078: $i,SV1372: $i,SV529: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV529 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SV2506 @ SV2682 @ SV529 ) @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2506 @ SV529 )
| ~ ( c_lessequals @ SV2078 @ SV2682 @ SV529 )
| ~ ( c_lessequals @ SV1372 @ SV2506 @ SV529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5839]) ).
thf(6533,plain,
! [SV2683: $i,SV2507: $i,SV2079: $i,SV1373: $i,SV530: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV530 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SV2507 @ SV2683 @ SV530 ) @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
| ~ ( c_lessequals @ SV2079 @ SV2683 @ SV530 )
| ~ ( c_lessequals @ SV1373 @ SV2507 @ SV530 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5840]) ).
thf(6534,plain,
! [SV2508: $i,SV2080: $i,SV1374: $i,SV531: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV531 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV1374 @ SV2080 @ SV531 ) @ SV2508 @ SV531 )
= ( c_Orderings_Oord__class_Omax @ SV1374 @ ( c_Orderings_Oord__class_Omax @ SV2080 @ SV2508 @ SV531 ) @ SV531 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5841]) ).
thf(6535,plain,
! [SV2509: $i,SV2081: $i,SV1375: $i,SV532: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV532 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1375 @ ( c_Orderings_Oord__class_Omax @ SV2081 @ SV2509 @ SV532 ) @ SV532 )
= ( c_Orderings_Oord__class_Omax @ SV2081 @ ( c_Orderings_Oord__class_Omax @ SV1375 @ SV2509 @ SV532 ) @ SV532 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5842]) ).
thf(6536,plain,
! [SV2510: $i,SV2082: $i,SV1376: $i,SV534: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV534 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV534 ) @ ( c_HOL_Otimes__class_Otimes @ SV1376 @ SV2082 @ SV534 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2510 @ SV2082 @ SV534 ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV534 ) @ SV1376 ) @ SV2510 ) @ SV2082 @ SV534 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5843]) ).
thf(6537,plain,
! [SV2083: $i,SV1380: $i,SV539: $i] :
( ( ( class_Orderings_Olinorder @ SV539 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1380 @ ( c_Orderings_Oord__class_Omax @ SV1380 @ SV2083 @ SV539 ) @ SV539 )
= ( c_Orderings_Oord__class_Omax @ SV1380 @ SV2083 @ SV539 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5848]) ).
thf(6538,plain,
! [SV2085: $i,SV1382: $i,SV541: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV541 )
= $false )
| ( ( ( c_lessequals @ SV1382 @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV541 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV1382 @ SV541 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV2085 @ SV541 ) @ SV541 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5849]) ).
thf(6539,plain,
! [SV2086: $i,SV1383: $i,SV542: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV542 )
= $false )
| ( ( ( c_lessequals @ SV1383 @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV542 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV2086 @ SV542 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ ( c_HOL_Otimes__class_Otimes @ SV2086 @ SV1383 @ SV542 ) @ SV542 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5850]) ).
thf(6540,plain,
! [SV2087: $i,SV1384: $i,SV543: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV543 )
= $false )
| ( ( ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV543 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV2087 @ SV543 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ ( c_HOL_Otimes__class_Otimes @ SV1384 @ SV2087 @ SV543 ) @ SV543 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5851]) ).
thf(6541,plain,
! [SV2088: $i,SV1385: $i,SV544: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV544 )
= $false )
| ( ( ( c_lessequals @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV544 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV1385 @ SV544 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ ( c_HOL_Otimes__class_Otimes @ SV2088 @ SV1385 @ SV544 ) @ SV544 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5852]) ).
thf(6542,plain,
! [SV2089: $i,SV1388: $i,SV547: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV547 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV547 ) @ SV1388 ) @ SV2089 ) @ SV2089 @ SV547 )
= SV1388 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5853]) ).
thf(6543,plain,
! [SV2684: $i,SV2511: $i,SV2090: $i,SV1389: $i,SV548: $i] :
( ( ! [SY7093: $i] :
( ( c_List_Ofoldl @ SV548 @ SV1389 @ ( c_List_Oappend @ SV2090 @ SV2511 @ SV2684 ) @ SY7093 @ SV2684 )
= ( c_List_Ofoldl @ SV548 @ ( c_List_Ofoldl @ SV548 @ SV1389 @ SV2090 @ SY7093 @ SV2684 ) @ SV2511 @ SY7093 @ SV2684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5854]) ).
thf(6544,plain,
! [SV2685: $i,SV2513: $i,SV2092: $i,SV1391: $i,SV550: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV550 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV1391 ) @ SV2092 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV2513 ) @ SV2685 ) @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SV2092 @ SV2685 @ SV550 )
| ~ ( c_lessequals @ SV1391 @ SV2513 @ SV550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5856]) ).
thf(6545,plain,
! [SV2686: $i,SV2514: $i,SV2093: $i,SV1392: $i,SV551: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV551 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV1392 ) @ SV2093 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV2514 ) @ SV2686 ) @ SV551 )
| ~ ( c_lessequals @ SV2093 @ SV2686 @ SV551 )
| ~ ( c_HOL_Oord__class_Oless @ SV1392 @ SV2514 @ SV551 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5857]) ).
thf(6546,plain,
! [SV1398: $i,SV557: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV557 ) @ SV1398 @ SV557 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV557 ) @ SV1398 ) @ SV1398 ) @ SV557 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV557 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5863]) ).
thf(6547,plain,
! [SV1399: $i,SV558: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV558 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV558 ) @ SV1399 ) @ SV1399 ) @ SV558 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV558 ) @ SV1399 @ SV558 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV558 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5864]) ).
thf(6548,plain,
! [SV559: $i,SV2094: $i,SV1400: $i] :
( ( ( c_Type_Otyping @ SV1400 @ ( c_Lambda_OdB_OAbs @ SV2094 ) @ SV559 )
= $false )
| ( ( SV559
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV559 @ SV1400 @ SV2094 ) ) @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV559 @ SV1400 @ SV2094 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5865]) ).
thf(6549,plain,
! [SV1408: $i,SV567: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV567 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1408 @ SV1408 @ SV567 )
= ( c_HOL_Ozero__class_Ozero @ SV567 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV567 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5873]) ).
thf(6550,plain,
! [SV1415: $i,SV575: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV575 ) )
= $true )
| ( ( SV1415
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1415 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV575 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5880]) ).
thf(6551,plain,
! [SV2515: $i,SV2095: $i,SV1425: $i,SV586: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV586 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1425 @ SV2095 @ SV586 )
| ~ ( c_HOL_Oord__class_Oless @ SV2515 @ SV2095 @ SV586 )
| ~ ( c_lessequals @ SV1425 @ SV2515 @ SV586 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5888]) ).
thf(6552,plain,
! [SV2516: $i,SV2096: $i,SV1426: $i,SV587: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV587 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1426 @ SV2096 @ SV587 )
| ~ ( c_lessequals @ SV2516 @ SV2096 @ SV587 )
| ~ ( c_HOL_Oord__class_Oless @ SV1426 @ SV2516 @ SV587 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5889]) ).
thf(6553,plain,
! [SV2687: $i,SV2517: $i,SV2097: $i,SV1427: $i,SV588: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV588 )
| ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2517 ) @ SV588 )
| ~ ( c_lessequals @ SV2687 @ SV2517 @ SV588 )
| ~ ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2687 ) @ SV588 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5890]) ).
thf(6554,plain,
! [SV591: $i,SV2099: $i,SV1430: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1430 @ SV2099 @ tc_nat ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ominus__class_Ominus @ SV1430 @ SV2099 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5891]) ).
thf(6555,plain,
! [SV2100: $i,SV1432: $i,SV593: $i] :
( ( ( hBOOL @ ( hAPP @ SV593 @ SV1432 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1432 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV593 @ SV2100 ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV593 @ SV2100 ) )
| ( hBOOL @ ( hAPP @ SV593 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5893]) ).
thf(6556,plain,
! [SV2688: $i,SV2518: $i,SV2101: $i,SV1433: $i,SV594: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SV2518 @ SV2688 @ SV594 ) @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV2101 @ SV2688 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SV2518 @ SV594 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5894]) ).
thf(6557,plain,
! [SV1434: $i,SV595: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV595 @ ( c_Suc @ SV1434 ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1434 @ SV595 @ tc_nat ) )
= $true )
| ( ( SV595 = SV1434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5895]) ).
thf(6558,plain,
! [SV1435: $i,SV2102: $i,SV596: $i] :
( ( ( c_lessequals @ SV596 @ SV2102 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV596 @ SV1435 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2102 @ SV1435 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5896]) ).
thf(6559,plain,
! [SV597: $i,SV2103: $i,SV1436: $i] :
( ( ( c_lessequals @ SV1436 @ SV2103 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV597 @ SV1436 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV597 @ SV2103 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5897]) ).
thf(6560,plain,
! [SV598: $i,SV2104: $i,SV1437: $i] :
( ( ( c_lessequals @ SV1437 @ SV2104 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV598 @ SV1437 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV598 @ SV2104 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5898]) ).
thf(6561,plain,
! [SV1438: $i,SV2105: $i,SV599: $i] :
( ( ( c_lessequals @ SV599 @ SV2105 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV599 @ SV1438 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2105 @ SV1438 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5899]) ).
thf(6562,plain,
! [SV2520: $i,SV2107: $i,SV1444: $i,SV606: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV606 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1444 @ ( c_HOL_Ozero__class_Ozero @ SV606 ) @ SV606 )
| ( c_HOL_Oord__class_Oless @ SV2107 @ SV2520 @ SV606 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2107 @ SV1444 @ SV606 ) @ ( c_HOL_Otimes__class_Otimes @ SV2520 @ SV1444 @ SV606 ) @ SV606 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5905]) ).
thf(6563,plain,
! [SV2521: $i,SV2108: $i,SV1445: $i,SV607: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV607 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1445 @ SV2108 @ SV607 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV607 ) @ SV2521 @ SV607 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2108 @ SV2521 @ SV607 ) @ ( c_HOL_Otimes__class_Otimes @ SV1445 @ SV2521 @ SV607 ) @ SV607 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5906]) ).
thf(6564,plain,
! [SV2522: $i,SV2109: $i,SV1446: $i,SV608: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV608 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1446 @ ( c_HOL_Ozero__class_Ozero @ SV608 ) @ SV608 )
| ( c_HOL_Oord__class_Oless @ SV2109 @ SV2522 @ SV608 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2109 @ SV608 ) @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2522 @ SV608 ) @ SV608 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5907]) ).
thf(6565,plain,
! [SV2523: $i,SV2110: $i,SV1447: $i,SV609: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV609 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1447 @ SV2110 @ SV609 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV609 ) @ SV2523 @ SV609 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2523 @ SV2110 @ SV609 ) @ ( c_HOL_Otimes__class_Otimes @ SV2523 @ SV1447 @ SV609 ) @ SV609 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5908]) ).
thf(6566,plain,
! [SV2112: $i,SV1449: $i,SV612: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV612 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1449 ) @ SV2112 ) @ SV612 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV612 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1449 @ SV612 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV2112 @ SV612 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5910]) ).
thf(6567,plain,
! [SV1450: $i,SV613: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV613 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1450 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV613 @ SV1450 @ tc_nat ) @ SV613 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5911]) ).
thf(6568,plain,
! [SV2525: $i,SV2113: $i,SV1451: $i,SV614: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV614 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1451 @ ( c_Orderings_Oord__class_Omin @ SV2113 @ SV2525 @ SV614 ) @ SV614 ) @ ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1451 @ SV2113 @ SV614 ) @ ( c_Orderings_Oord__class_Omax @ SV1451 @ SV2525 @ SV614 ) @ SV614 ) @ SV614 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5912]) ).
thf(6569,plain,
! [SV2526: $i,SV2114: $i,SV1452: $i,SV615: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV615 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV1452 @ SV2114 @ SV615 ) @ SV2526 @ SV615 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1452 @ SV2526 @ SV615 ) @ ( c_Power_Opower__class_Opower @ SV2114 @ SV2526 @ SV615 ) @ SV615 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5913]) ).
thf(6570,plain,
! [SV2527: $i,SV2115: $i,SV1453: $i,SV616: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV616 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV1453 @ SV2115 @ SV616 ) @ SV2527 @ SV616 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1453 @ SV2527 @ SV616 ) @ ( c_Power_Opower__class_Opower @ SV2115 @ SV2527 @ SV616 ) @ SV616 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5914]) ).
thf(6571,plain,
! [SV2116: $i,SV1454: $i,SV617: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV617 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Oappend @ SV1454 @ SV2116 @ SV617 ) @ SV617 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ ( c_List_Olistsum @ SV1454 @ SV617 ) ) @ ( c_List_Olistsum @ SV2116 @ SV617 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5915]) ).
thf(6572,plain,
! [SV2528: $i,SV2117: $i,SV1457: $i,SV620: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV620 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV1457 @ SV2117 @ SV620 ) @ SV2528 @ SV620 )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1457 @ SV2528 @ SV620 ) @ ( c_Orderings_Oord__class_Omax @ SV2117 @ SV2528 @ SV620 ) @ SV620 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5917]) ).
thf(6573,plain,
! [SV2529: $i,SV2118: $i,SV1458: $i,SV621: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV621 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1458 @ ( c_Orderings_Oord__class_Omin @ SV2118 @ SV2529 @ SV621 ) @ SV621 )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1458 @ SV2118 @ SV621 ) @ ( c_Orderings_Oord__class_Omax @ SV1458 @ SV2529 @ SV621 ) @ SV621 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5918]) ).
thf(6574,plain,
! [SV2530: $i,SV2119: $i,SV1459: $i,SV622: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV622 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1459 @ ( c_HOL_Otimes__class_Otimes @ SV2119 @ SV2530 @ tc_nat ) @ SV622 )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV1459 @ SV2119 @ SV622 ) @ SV2530 @ SV622 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5919]) ).
thf(6575,plain,
! [SV2120: $i,SV1460: $i,SV623: $i] :
( ( ( class_Orderings_Oorder @ SV623 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1460 @ SV2120 @ SV623 )
| ( SV2120 = SV1460 )
| ~ ( c_lessequals @ SV1460 @ SV2120 @ SV623 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5920]) ).
thf(6576,plain,
! [SV2121: $i,SV1461: $i,SV624: $i] :
( ( ( class_Orderings_Oorder @ SV624 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1461 @ SV2121 @ SV624 )
| ~ ( c_lessequals @ SV1461 @ SV2121 @ SV624 )
| ( SV2121 = SV1461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5921]) ).
thf(6577,plain,
! [SV1462: $i,SV625: $i] :
( ( ( c_lessequals @ SV625 @ SV1462 @ tc_nat )
= $false )
| ( ( SV625 = SV1462 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV625 @ SV1462 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5922]) ).
thf(6578,plain,
! [SV1463: $i,SV626: $i] :
( ( ( c_lessequals @ SV626 @ SV1463 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV626 @ SV1463 @ tc_nat )
= $true )
| ( ( SV626 = SV1463 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5923]) ).
thf(6579,plain,
! [SV1464: $i,SV627: $i] :
( ( ( c_lessequals @ SV627 @ SV1464 @ tc_nat )
= $false )
| ( ( SV627 = SV1464 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV627 @ SV1464 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5924]) ).
thf(6580,plain,
! [SV2122: $i,SV1465: $i,SV628: $i] :
( ( ( class_Orderings_Oorder @ SV628 )
= $false )
| ( ( ( SV1465 = SV2122 )
| ( c_HOL_Oord__class_Oless @ SV1465 @ SV2122 @ SV628 )
| ~ ( c_lessequals @ SV1465 @ SV2122 @ SV628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5925]) ).
thf(6581,plain,
! [SV2123: $i,SV1466: $i,SV629: $i] :
( ( ( class_Orderings_Oorder @ SV629 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1466 @ SV2123 @ SV629 )
| ( SV1466 = SV2123 )
| ~ ( c_lessequals @ SV1466 @ SV2123 @ SV629 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5926]) ).
thf(6582,plain,
! [SV2124: $i,SV1467: $i,SV630: $i] :
( ( ( class_Orderings_Oorder @ SV630 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1467 @ SV2124 @ SV630 )
| ( SV1467 = SV2124 )
| ~ ( c_lessequals @ SV1467 @ SV2124 @ SV630 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5927]) ).
thf(6583,plain,
! [SV2125: $i,SV1468: $i,SV631: $i] :
( ( ( class_Orderings_Oorder @ SV631 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1468 @ SV2125 @ SV631 )
| ~ ( c_lessequals @ SV1468 @ SV2125 @ SV631 )
| ( SV1468 = SV2125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5928]) ).
thf(6584,plain,
! [SV2126: $i,SV1469: $i,SV632: $i] :
( ( ( class_Orderings_Olinorder @ SV632 )
= $false )
| ( ( ( SV1469 = SV2126 )
| ~ ( c_lessequals @ SV1469 @ SV2126 @ SV632 )
| ( c_HOL_Oord__class_Oless @ SV1469 @ SV2126 @ SV632 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5929]) ).
thf(6585,plain,
! [SV2127: $i,SV1470: $i,SV633: $i] :
( ( ( class_Orderings_Olinorder @ SV633 )
= $false )
| ( ( ( SV1470 = SV2127 )
| ( c_HOL_Oord__class_Oless @ SV1470 @ SV2127 @ SV633 )
| ~ ( c_lessequals @ SV1470 @ SV2127 @ SV633 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5930]) ).
thf(6586,plain,
! [SV2128: $i,SV1471: $i,SV634: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV634 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ ( c_HOL_Otimes__class_Otimes @ SV1471 @ SV2128 @ SV634 ) @ SV634 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV2128 @ SV634 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV1471 @ SV634 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5931]) ).
thf(6587,plain,
! [SV2129: $i,SV1472: $i,SV635: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV635 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ ( c_HOL_Otimes__class_Otimes @ SV1472 @ SV2129 @ SV635 ) @ SV635 )
| ~ ( c_lessequals @ SV2129 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 )
| ~ ( c_lessequals @ SV1472 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5932]) ).
thf(6588,plain,
! [SV2130: $i,SV1473: $i,SV636: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV636 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ ( c_HOL_Otimes__class_Otimes @ SV1473 @ SV2130 @ SV636 ) @ SV636 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV2130 @ SV636 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV1473 @ SV636 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5933]) ).
thf(6589,plain,
! [SV2131: $i,SV1475: $i,SV638: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV638 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ ( c_HOL_Otimes__class_Otimes @ SV1475 @ SV2131 @ SV638 ) @ SV638 )
| ~ ( c_lessequals @ SV2131 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 )
| ~ ( c_lessequals @ SV1475 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5935]) ).
thf(6590,plain,
! [SV2132: $i,SV1476: $i,SV639: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV639 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ ( c_HOL_Otimes__class_Otimes @ SV1476 @ SV2132 @ SV639 ) @ SV639 )
| ~ ( c_lessequals @ SV2132 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 )
| ~ ( c_lessequals @ SV1476 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5936]) ).
thf(6591,plain,
! [SV2133: $i,SV1477: $i,SV640: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV640 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ ( c_HOL_Otimes__class_Otimes @ SV1477 @ SV2133 @ SV640 ) @ SV640 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV2133 @ SV640 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV1477 @ SV640 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5937]) ).
thf(6592,plain,
! [SV2531: $i,SV2134: $i,SV1480: $i,SV644: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV644 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1480 @ SV2134 @ SV644 ) @ SV2531 @ SV644 )
= ( c_HOL_Otimes__class_Otimes @ SV1480 @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV2531 @ SV644 ) @ SV644 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5940]) ).
thf(6593,plain,
! [SV2532: $i,SV2135: $i,SV1481: $i,SV645: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV645 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1481 @ SV2135 @ SV645 ) @ SV2532 @ SV645 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1481 @ SV2532 @ SV645 ) @ SV2135 @ SV645 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5941]) ).
thf(6594,plain,
! [SV2533: $i,SV2136: $i,SV1482: $i,SV646: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV646 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1482 @ SV2136 @ SV646 ) @ SV2533 @ SV646 )
= ( c_HOL_Otimes__class_Otimes @ SV1482 @ ( c_HOL_Otimes__class_Otimes @ SV2136 @ SV2533 @ SV646 ) @ SV646 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5942]) ).
thf(6595,plain,
! [SV2534: $i,SV2137: $i,SV1483: $i,SV647: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV647 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1483 @ ( c_HOL_Otimes__class_Otimes @ SV2137 @ SV2534 @ SV647 ) @ SV647 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1483 @ SV2137 @ SV647 ) @ SV2534 @ SV647 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5943]) ).
thf(6596,plain,
! [SV2535: $i,SV2138: $i,SV1484: $i,SV648: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV648 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1484 @ ( c_HOL_Otimes__class_Otimes @ SV2138 @ SV2535 @ SV648 ) @ SV648 )
= ( c_HOL_Otimes__class_Otimes @ SV2138 @ ( c_HOL_Otimes__class_Otimes @ SV1484 @ SV2535 @ SV648 ) @ SV648 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5944]) ).
thf(6597,plain,
! [SV2540: $i,SV2144: $i,SV1490: $i,SV654: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV654 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1490 @ ( c_HOL_Otimes__class_Otimes @ SV2144 @ SV2540 @ SV654 ) @ SV654 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1490 @ SV2144 @ SV654 ) @ SV2540 @ SV654 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5949]) ).
thf(6598,plain,
! [SV2541: $i,SV2145: $i,SV1491: $i,SV655: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV655 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV655 ) @ SV1491 ) @ SV2145 ) @ SV2541 @ SV655 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV655 ) @ ( c_HOL_Otimes__class_Otimes @ SV1491 @ SV2541 @ SV655 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV2541 @ SV655 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5950]) ).
thf(6599,plain,
! [SV2542: $i,SV2146: $i,SV1492: $i,SV656: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV656 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV656 ) @ SV1492 ) @ SV2146 ) @ SV2542 @ SV656 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV656 ) @ ( c_HOL_Otimes__class_Otimes @ SV1492 @ SV2542 @ SV656 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2146 @ SV2542 @ SV656 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5951]) ).
thf(6600,plain,
! [SV2543: $i,SV2149: $i,SV1495: $i,SV659: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV659 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1495 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV659 ) @ SV2149 ) @ SV2543 ) @ SV659 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV659 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV2149 @ SV659 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV2543 @ SV659 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5952]) ).
thf(6601,plain,
! [SV2150: $i,SV1496: $i,SV660: $i] :
( ( ( class_Orderings_Oorder @ SV660 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1496 @ SV2150 @ SV660 )
| ~ ( c_HOL_Oord__class_Oless @ SV2150 @ SV1496 @ SV660 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5953]) ).
thf(6602,plain,
! [SV2151: $i,SV1497: $i,SV661: $i] :
( ( ( class_Orderings_Olinorder @ SV661 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1497 @ SV2151 @ SV661 )
| ~ ( c_HOL_Oord__class_Oless @ SV2151 @ SV1497 @ SV661 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5954]) ).
thf(6603,plain,
! [SV2152: $i,SV1499: $i,SV663: $i] :
( ( ( class_Orderings_Olinorder @ SV663 )
= $false )
| ( ( ( c_lessequals @ SV1499 @ SV2152 @ SV663 )
| ( c_lessequals @ SV2152 @ SV1499 @ SV663 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5955]) ).
thf(6604,plain,
! [SV2153: $i,SV1500: $i,SV664: $i] :
( ( ( class_Orderings_Opreorder @ SV664 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1500 @ SV2153 @ SV664 )
| ~ ( c_HOL_Oord__class_Oless @ SV2153 @ SV1500 @ SV664 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5956]) ).
thf(6605,plain,
! [SV2154: $i,SV1501: $i,SV665: $i] :
( ( ( class_Orderings_Opreorder @ SV665 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1501 @ SV2154 @ SV665 )
| ~ ( c_HOL_Oord__class_Oless @ SV2154 @ SV1501 @ SV665 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5957]) ).
thf(6606,plain,
! [SV1503: $i,SV667: $i] :
( ( ( hBOOL @ ( hAPP @ SV667 @ SV1503 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV667 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV667 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV667 @ SV1503 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5958]) ).
thf(6607,plain,
! [SV1504: $i,SV669: $i] :
( ( ( hBOOL @ ( hAPP @ SV669 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV669 @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ SV669 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV669 @ SV1504 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5959]) ).
thf(6608,plain,
! [SV1507: $i,SV678: $i] :
( ( ( hBOOL @ ( hAPP @ SV678 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV678 @ ( v_sko__List__Xreplicate__Xinduct__1 @ SV678 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV678 @ SV1507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5960]) ).
thf(6609,plain,
! [SV2158: $i,SV1508: $i,SV679: $i] :
( ( ( hBOOL @ ( hAPP @ SV679 @ ( c_Nat_Onat_Onat__case @ SV1508 @ SV2158 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV679 @ SV1508 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5961]) ).
thf(6610,plain,
! [SV1509: $i,SV680: $i] :
( ( ( hBOOL @ ( hAPP @ SV680 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV680 @ ( v_sko__Nat__Xnat__Xinducts__1 @ SV680 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV680 @ SV1509 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5962]) ).
thf(6611,plain,
! [SV1510: $i,SV683: $i] :
( ( ( hBOOL @ ( hAPP @ SV683 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV683 @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV683 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV683 @ SV1510 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5963]) ).
thf(6612,plain,
! [SV1511: $i,SV686: $i] :
( ( ( hBOOL @ ( hAPP @ SV686 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV686 @ ( v_sko__List__Xupt__Xinduct__1 @ SV686 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV686 @ SV1511 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5964]) ).
thf(6613,plain,
! [SV1513: $i,SV689: $i] :
( ( ( hBOOL @ ( hAPP @ SV689 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV689 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV689 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV689 @ SV1513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5965]) ).
thf(6614,plain,
! [SV2689: $i,SV2544: $i,SV2160: $i,SV1515: $i,SV698: $i] :
( ( ! [SY7094: $i,SY7095: $i] :
( ( ( hAPP @ ( hAPP @ SV698 @ SV1515 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV2160 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2544 @ SV2689 @ SV698 @ SY7094 @ SV2160 @ SY7095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5966]) ).
thf(6615,plain,
! [SV2161: $i,SV1518: $i,SV701: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV701 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SV1518 @ SV2161 @ SV701 @ SV701 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SV1518 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV701 ) @ SV2161 @ ( c_HOL_Ozero__class_Ozero @ SV701 ) @ SV701 @ SV701 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5969]) ).
thf(6616,plain,
! [SV2545: $i,SV2162: $i,SV1519: $i,SV702: $i] :
( ( ( c_Type_Otyping @ SV702 @ SV1519 @ SV2162 )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV2545 @ SV1519 )
| ~ ( c_Type_Otyping @ SV702 @ SV2545 @ SV2162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5970]) ).
thf(6617,plain,
! [SV2163: $i,SV1520: $i,SV703: $i] :
( ( ( c_Type_Otyping @ SV703 @ ( c_Lambda_OdB_OVar @ SV1520 ) @ SV2163 )
= $false )
| ( ( ( hAPP @ SV703 @ SV1520 )
= SV2163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5971]) ).
thf(6618,plain,
! [SV2164: $i,SV1522: $i,SV705: $i] :
( ( ( c_Type_Otyping @ SV705 @ ( c_Lambda_OdB_OAbs @ SV1522 ) @ SV2164 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV705 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xabs__typeE__1__1 @ SV705 @ SV1522 ) @ tc_Type_Otype ) @ SV1522 @ ( c_Type_Osko__Type__Xabs__typeE__1__2 @ SV705 @ SV1522 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5972]) ).
thf(6619,plain,
! [SV1523: $i,SV2165: $i,SV706: $i] :
( ( ( c_Type_Otyping @ SV706 @ ( c_Lambda_OdB_OAbs @ SV2165 ) @ SV1523 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV706 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Type_Osko__Type__Xtyping__elims__3__1 @ SV1523 @ SV706 @ SV2165 ) @ tc_Type_Otype ) @ SV2165 @ ( c_Type_Osko__Type__Xtyping__elims__3__2 @ SV1523 @ SV706 @ SV2165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5973]) ).
thf(6620,plain,
! [SV2546: $i,SV2166: $i,SV1524: $i,SV707: $i] :
( ( ( c_Type_Otyping @ SV707 @ SV1524 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV2166 @ SV707 @ SV1524 @ SV2546 ) ) @ SV2166 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV707 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1524 ) @ SV2546 ) @ SV2166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5974]) ).
thf(6621,plain,
! [SV2690: $i,SV2547: $i,SV2167: $i,SV1525: $i,SV708: $i] :
( ( ( c_Type_Otype_Otype__rec @ SV708 @ SV1525 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2167 ) @ SV2547 ) @ SV2690 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV1525 @ SV2167 ) @ SV2547 ) @ ( c_Type_Otype_Otype__rec @ SV708 @ SV1525 @ SV2167 @ SV2690 ) ) @ ( c_Type_Otype_Otype__rec @ SV708 @ SV1525 @ SV2547 @ SV2690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5975]) ).
thf(6622,plain,
! [SV2691: $i,SV2548: $i,SV2168: $i,SV1526: $i,SV709: $i] :
( ( ( c_Type_Otype_Otype__case @ SV709 @ SV1526 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2168 ) @ SV2548 ) @ SV2691 )
= ( hAPP @ ( hAPP @ SV1526 @ SV2168 ) @ SV2548 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5976]) ).
thf(6623,plain,
! [SV2692: $i,SV2549: $i,SV2169: $i,SV1527: $i,SV710: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV710 @ ( c_Type_Otype_Otype__case @ SV1527 @ SV2169 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2549 ) @ SV2692 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV710 @ ( hAPP @ ( hAPP @ SV2169 @ SV2549 ) @ SV2692 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5977]) ).
thf(6624,plain,
! [SV2693: $i,SV2550: $i,SV2170: $i,SV1528: $i,SV711: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV711 @ ( c_Type_Otype_Otype__case @ SV1528 @ SV2170 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2550 ) @ SV2693 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV711 @ ( hAPP @ ( hAPP @ SV2170 @ SV2550 ) @ SV2693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5978]) ).
thf(6625,plain,
! [SV2694: $i,SV2551: $i,SV2171: $i,SV1529: $i,SV712: $i] :
( ( ! [SY7096: $i] :
( ( c_List_Ofoldr @ SV712 @ ( c_List_Olist_OCons @ SV1529 @ SV2171 @ SV2551 ) @ SV2694 @ SV2551 @ SY7096 )
= ( hAPP @ ( hAPP @ SV712 @ SV1529 ) @ ( c_List_Ofoldr @ SV712 @ SV2171 @ SV2694 @ SV2551 @ SY7096 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5979]) ).
thf(6626,plain,
! [SV2695: $i,SV2552: $i,SV2172: $i,SV1530: $i,SV713: $i] :
( ( ! [SY7097: $i] :
( ( c_List_Ofoldr @ SV713 @ ( c_List_Oappend @ SV1530 @ SV2172 @ SV2552 ) @ SV2695 @ SV2552 @ SY7097 )
= ( c_List_Ofoldr @ SV713 @ SV1530 @ ( c_List_Ofoldr @ SV713 @ SV2172 @ SV2695 @ SV2552 @ SY7097 ) @ SV2552 @ SY7097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5980]) ).
thf(6627,plain,
! [SV1535: $i,SV2176: $i,SV718: $i] :
( ( ( c_Lambda_Obeta @ SV718 @ SV2176 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV718 @ SV1535 ) @ ( c_Lambda_Olift @ SV2176 @ SV1535 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5983]) ).
thf(6628,plain,
! [SV2696: $i,SV2554: $i,SV2177: $i,SV1536: $i,SV719: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV719 @ SV1536 @ SV2177 @ SV2554 ) @ SV2696 )
= ( hAPP @ SV719 @ SV2696 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV2696 @ SV1536 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5984]) ).
thf(6629,plain,
! [SV2555: $i,SV2178: $i,SV1537: $i,SV720: $i] :
( ( ( c_Type_Otyping @ SV720 @ SV1537 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV2178 @ SV720 @ SV1537 @ SV2555 ) @ SV2178 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV720 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1537 @ SV2555 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5985]) ).
thf(6630,plain,
! [SV2697: $i,SV2556: $i,SV2179: $i,SV1538: $i,SV721: $i] :
( ( ( c_Type_Otyping @ SV721 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1538 @ SV2179 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2556 )
| ~ ( c_Type_Otypings @ SV721 @ SV2179 @ SV2697 )
| ~ ( c_Type_Otyping @ SV721 @ SV1538 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV2697 @ SV2556 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5986]) ).
thf(6631,plain,
! [SV2557: $i,SV2180: $i,SV1539: $i,SV722: $i] :
( ( ( c_Type_Otyping @ SV722 @ SV1539 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV2180 @ SV722 @ SV1539 @ SV2557 ) @ SV2180 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV722 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1539 @ SV2557 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5987]) ).
thf(6632,plain,
! [SV1540: $i,SV723: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV723 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV723 )
| ~ ( class_Power_Opower @ SV723 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV723 ) @ SV1540 @ SV723 )
= ( c_HOL_Ozero__class_Ozero @ SV723 ) )
| ( SV1540
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV723 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5988]) ).
thf(6633,plain,
! [SV1541: $i,SV724: $i] :
( ( ( ~ ( class_Power_Opower @ SV724 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV724 ) @ SV1541 @ SV724 )
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1541
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV724 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5989]) ).
thf(6634,plain,
! [SV2698: $i,SV2558: $i,SV2181: $i,SV1542: $i,SV726: $i] :
( ( ( c_Type_Oshift @ ( c_Type_Oshift @ SV726 @ SV1542 @ SV2181 @ SV2558 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2698 @ SV2558 )
= ( c_Type_Oshift @ ( c_Type_Oshift @ SV726 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2698 @ SV2558 ) @ ( c_Suc @ SV1542 ) @ SV2181 @ SV2558 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5990]) ).
thf(6635,plain,
! [SV2699: $i,SV2559: $i,SV2182: $i,SV1543: $i,SV727: $i] :
( ( ( c_Type_Otyping @ SV727 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1543 ) @ SV2182 ) @ SV2559 )
| ~ ( c_Type_Otyping @ SV727 @ SV2182 @ SV2699 )
| ~ ( c_Type_Otyping @ SV727 @ SV1543 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2699 ) @ SV2559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5991]) ).
thf(6636,plain,
! [SV2700: $i,SV2560: $i,SV2183: $i,SV1544: $i,SV728: $i] :
( ( ! [SY7098: $i] :
( ~ ( c_Type_Otyping @ SV728 @ SV1544 @ SV2183 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV728 @ SV2560 @ SV2183 @ tc_Type_Otype ) @ SV2700 @ SY7098 )
| ( c_Type_Otyping @ SV728 @ ( c_Lambda_Osubst @ SV2700 @ SV1544 @ SV2560 ) @ SY7098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5992]) ).
thf(6637,plain,
! [SV2561: $i,SV2184: $i,SV1545: $i,SV729: $i] :
( ( ( c_Type_Otyping @ SV729 @ ( c_Lambda_OdB_OAbs @ SV1545 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2184 ) @ SV2561 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV729 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2184 @ tc_Type_Otype ) @ SV1545 @ SV2561 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5993]) ).
thf(6638,plain,
! [SV2701: $i,SV2562: $i,SV2185: $i,SV1546: $i,SV730: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV730 @ SV1546 @ SV2185 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV2562 @ SV1546 ) @ SV2701 )
| ~ ( c_Type_Otyping @ SV730 @ SV2562 @ SV2701 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5994]) ).
thf(6639,plain,
! [SV2187: $i,SV1552: $i,SV736: $i] :
( ( ( c_fequal @ SV736 @ SV1552 @ SV2187 )
= $false )
| ( ( SV736 = SV1552 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5999]) ).
thf(6640,plain,
! [SV2702: $i,SV2564: $i,SV2188: $i,SV1553: $i,SV737: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV737 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1553 @ SV2188 @ SV737 )
!= ( c_HOL_Ominus__class_Ominus @ SV2564 @ SV2702 @ SV737 ) )
| ( c_lessequals @ SV2188 @ SV1553 @ SV737 )
| ~ ( c_lessequals @ SV2702 @ SV2564 @ SV737 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6000]) ).
thf(6641,plain,
! [SV2703: $i,SV2565: $i,SV2189: $i,SV1554: $i,SV738: $i] :
( ( ( ( c_List_Olist_OCons @ SV738 @ SV1554 @ SV2189 )
!= ( c_List_Olist_OCons @ SV2565 @ SV2703 @ SV2189 ) )
| ( SV738 = SV2565 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6001]) ).
thf(6642,plain,
! [SV2190: $i,SV1555: $i,SV739: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV739 @ SV1555 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV739 @ SV2190 @ tc_nat ) )
= $false )
| ( ( ( SV1555 = SV2190 )
| ( SV739
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6002]) ).
thf(6643,plain,
! [SV2191: $i,SV1556: $i,SV740: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV740 ) @ SV1556 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV740 ) @ SV2191 ) )
= $false )
| ( ( SV1556 = SV2191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6003]) ).
thf(6644,plain,
! [SV2192: $i,SV1557: $i,SV741: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV741 ) @ SV1557 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV741 ) @ SV2192 ) )
= $false )
| ( ( SV1557 = SV2192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6004]) ).
thf(6645,plain,
! [SV2704: $i,SV2566: $i,SV2193: $i,SV1558: $i,SV742: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV1558 @ tc_nat ) ) @ SV2193 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2566 @ SV1558 @ tc_nat ) ) @ SV2704 ) )
| ~ ( c_lessequals @ SV2566 @ SV742 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV742 @ SV2566 @ tc_nat ) @ SV1558 @ tc_nat ) ) @ SV2193 )
= SV2704 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6005]) ).
thf(6646,plain,
! [SV2194: $i,SV1559: $i,SV743: $i] :
( ( ( ( c_List_Oappend @ SV743 @ SV1559 @ SV2194 )
= SV743 )
= $false )
| ( ( SV1559
= ( c_List_Olist_ONil @ SV2194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6006]) ).
thf(6647,plain,
! [SV2567: $i,SV2195: $i,SV1560: $i,SV744: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV744 ) @ SV1560 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV2195 ) @ SV2567 ) )
= $true )
| ( ( SV744 = SV2195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6007]) ).
thf(6648,plain,
! [SV2196: $i,SV1561: $i,SV745: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1561 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV2196 @ SV1561 @ tc_nat ) )
= $false )
| ( ( ( SV1561
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV745 = SV2196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6008]) ).
thf(6649,plain,
! [SV2568: $i,SV2197: $i,SV1563: $i,SV747: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV747 ) @ SV1563 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV2197 ) @ SV2568 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1563 = SV2568 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6010]) ).
thf(6650,plain,
! [SV2198: $i,SV1564: $i,SV748: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV748 ) @ SV1564 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV748 ) @ SV2198 @ tc_nat ) )
= $false )
| ( ( SV1564 = SV2198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6011]) ).
thf(6651,plain,
! [SV749: $i,SV1565: $i] :
( ( ( SV1565
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV1565
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV749 ) @ SV1565 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6012]) ).
thf(6652,plain,
! [SV2705: $i,SV2569: $i,SV2199: $i,SV1566: $i,SV750: $i] :
( ( ! [SY7099: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV750 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV1566 @ SV2199 @ SV750 ) ) @ SV2569 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV2705 @ SV2199 @ SV750 ) ) @ SY7099 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ SV2705 @ SV750 ) @ SV2199 @ SV750 ) ) @ SV2569 )
= SY7099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6013]) ).
thf(6653,plain,
! [SV2570: $i,SV2200: $i,SV1567: $i,SV751: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV751 ) ) @ SV1567 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2200 ) @ SV2570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6014]) ).
thf(6654,plain,
! [SV2571: $i,SV2201: $i,SV1570: $i,SV754: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV754 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SV1570 ) @ SV2201 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SV2571 ) @ SV2201 ) )
| ( SV1570 = SV2571 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6017]) ).
thf(6655,plain,
! [SV2202: $i,SV1571: $i,SV755: $i] :
( ( ( ( c_List_Olist_ONil @ SV755 )
= ( c_List_Oappend @ SV1571 @ SV2202 @ SV755 ) )
= $false )
| ( ( SV2202
= ( c_List_Olist_ONil @ SV755 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6018]) ).
thf(6656,plain,
! [SV756: $i,SV1572: $i] :
( ( ( SV1572
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV1572
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV756 ) @ SV1572 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6019]) ).
thf(6657,plain,
! [SV1573: $i,SV757: $i] :
( ( ( SV757
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1573
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV757 ) @ SV1573 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6020]) ).
thf(6658,plain,
! [SV2572: $i,SV2203: $i,SV1574: $i,SV758: $i] :
( ( ( ( c_List_Oappend @ SV758 @ SV1574 @ SV2203 )
!= ( c_List_Oappend @ SV2572 @ SV1574 @ SV2203 ) )
= $true )
| ( ( SV758 = SV2572 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6021]) ).
thf(6659,plain,
! [SV2573: $i,SV2204: $i,SV1575: $i,SV759: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1575 ) @ SV2204 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV759 @ SV2573 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SV2204 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6022]) ).
thf(6660,plain,
! [SV2706: $i,SV2574: $i,SV2205: $i,SV1576: $i,SV760: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV760 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV2205 @ SV760 )
!= ( c_HOL_Ominus__class_Ominus @ SV2574 @ SV2706 @ SV760 ) )
| ( c_HOL_Oord__class_Oless @ SV2574 @ SV2706 @ SV760 )
| ~ ( c_HOL_Oord__class_Oless @ SV1576 @ SV2205 @ SV760 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6023]) ).
thf(6661,plain,
! [SV2206: $i,SV1577: $i,SV761: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV761 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV1577 @ SV2206 @ SV761 )
!= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
| ( SV1577
= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
| ( SV2206
= ( c_HOL_Ozero__class_Ozero @ SV761 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6024]) ).
thf(6662,plain,
! [SV2575: $i,SV2208: $i,SV1579: $i,SV763: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV763 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1579 @ SV2208 @ SV763 )
!= ( c_Power_Opower__class_Opower @ SV2575 @ SV2208 @ SV763 ) )
| ( SV1579 = SV2575 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2208 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV2575 @ SV763 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6026]) ).
thf(6663,plain,
! [SV2576: $i,SV2209: $i,SV1580: $i,SV764: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV764 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SV2209 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SV2576 ) )
| ( SV2209 = SV2576 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6027]) ).
thf(6664,plain,
! [SV1581: $i,SV765: $i] :
( ( ( SV765
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV765
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV765 ) @ SV1581 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6028]) ).
thf(6665,plain,
! [SV2577: $i,SV2210: $i,SV1582: $i,SV766: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV766 ) @ SV1582 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2210 ) @ SV2577 ) )
= $true )
| ( ( SV1582 = SV2577 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6029]) ).
thf(6666,plain,
! [SV2213: $i,SV1587: $i,SV772: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV772 @ SV1587 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV2213 @ SV1587 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV772 = SV2213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6033]) ).
thf(6667,plain,
! [SV2214: $i,SV1588: $i,SV773: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV773 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV773 )
| ( SV1588
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV773 ) @ SV1588 ) @ SV2214 ) )
| ( SV2214
= ( c_HOL_Ozero__class_Ozero @ SV773 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6034]) ).
thf(6668,plain,
! [SV2707: $i,SV2578: $i,SV2215: $i,SV1589: $i,SV774: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV774 )
| ~ ( class_Int_Onumber__ring @ SV774 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2578 @ SV774 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2707 @ SV774 ) ) )
| ( SV2578 = SV2707 )
| ( SV2215
= ( c_HOL_Ozero__class_Ozero @ SV774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6035]) ).
thf(6669,plain,
! [SV2708: $i,SV2579: $i,SV2216: $i,SV1590: $i,SV775: $i] :
( ( ( ( c_List_Oreplicate @ SV775 @ SV1590 @ SV2216 )
!= ( c_List_Oreplicate @ SV2579 @ SV2708 @ SV2216 ) )
| ( SV775 = SV2579 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6036]) ).
thf(6670,plain,
! [SV776: $i,SV1591: $i] :
( ( ( SV1591
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV776
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV776 ) @ SV1591 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6037]) ).
thf(6671,plain,
! [SV2709: $i,SV2580: $i,SV2217: $i,SV1592: $i,SV778: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV778 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1592 @ SV2217 @ SV778 )
!= ( c_HOL_Ominus__class_Ominus @ SV2580 @ SV2709 @ SV778 ) )
| ( c_HOL_Oord__class_Oless @ SV1592 @ SV2217 @ SV778 )
| ~ ( c_HOL_Oord__class_Oless @ SV2580 @ SV2709 @ SV778 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6038]) ).
thf(6672,plain,
! [SV2218: $i,SV1593: $i,SV779: $i] :
( ( ( class_Orderings_Olinorder @ SV779 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV1593 @ SV2218 @ SV779 )
!= SV2218 )
| ( c_lessequals @ SV1593 @ SV2218 @ SV779 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6039]) ).
thf(6673,plain,
! [SV2710: $i,SV2581: $i,SV2219: $i,SV1594: $i,SV780: $i] :
( ( ( ( c_List_Oappend @ SV780 @ ( c_List_Olist_OCons @ SV1594 @ ( c_List_Olist_ONil @ SV2219 ) @ SV2219 ) @ SV2219 )
!= ( c_List_Oappend @ SV2581 @ ( c_List_Olist_OCons @ SV2710 @ ( c_List_Olist_ONil @ SV2219 ) @ SV2219 ) @ SV2219 ) )
| ( SV1594 = SV2710 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6040]) ).
thf(6674,plain,
! [SV2582: $i,SV2220: $i,SV1596: $i,SV782: $i] :
( ( ( ( c_List_Oappend @ SV782 @ SV1596 @ SV2220 )
!= ( c_List_Oappend @ SV782 @ SV2582 @ SV2220 ) )
= $true )
| ( ( SV1596 = SV2582 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6042]) ).
thf(6675,plain,
! [SV2583: $i,SV2222: $i,SV1598: $i,SV784: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SV1598 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2222 @ SV2583 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SV2583 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2222 @ SV1598 @ tc_nat ) ) )
= $true )
| ( ( ( SV1598 = SV2583 )
| ( SV784 = SV2222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6044]) ).
thf(6676,plain,
! [SV2223: $i,SV1599: $i,SV786: $i] :
( ( ( ( c_List_Olist_ONil @ SV786 )
= ( c_List_Oreplicate @ SV1599 @ SV2223 @ SV786 ) )
= $false )
| ( ( SV1599
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6045]) ).
thf(6677,plain,
! [SV2711: $i,SV2584: $i,SV2224: $i,SV1600: $i,SV787: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV787 )
| ~ ( class_Int_Onumber__ring @ SV787 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2224 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2711 @ SV787 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2711 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2224 @ SV787 ) ) )
| ( SV2224 = SV2711 )
| ( SV1600 = SV2584 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6046]) ).
thf(6678,plain,
! [SV2712: $i,SV2585: $i,SV2225: $i,SV1602: $i,SV789: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV789 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1602 @ SV2225 @ SV789 )
!= ( c_HOL_Ominus__class_Ominus @ SV2585 @ SV2712 @ SV789 ) )
| ( c_lessequals @ SV2712 @ SV2585 @ SV789 )
| ~ ( c_lessequals @ SV2225 @ SV1602 @ SV789 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6048]) ).
thf(6679,plain,
! [SV2226: $i,SV1603: $i,SV790: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV790 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV1603 @ SV2226 @ SV790 )
!= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
| ( SV2226
= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
| ( SV1603
= ( c_HOL_Ozero__class_Ozero @ SV790 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6049]) ).
thf(6680,plain,
! [SV1605: $i,SV792: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV792 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV792 )
| ~ ( class_Power_Opower @ SV792 )
| ( ( c_Power_Opower__class_Opower @ SV1605 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV792 )
!= ( c_HOL_Ozero__class_Ozero @ SV792 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV792 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6051]) ).
thf(6681,plain,
! [SV2227: $i,SV1606: $i,SV793: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV793 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV793 ) @ SV1606 ) @ SV2227 )
!= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV2227 @ SV793 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV1606 @ SV793 )
| ( SV1606
= ( c_HOL_Ozero__class_Ozero @ SV793 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6052]) ).
thf(6682,plain,
! [SV2586: $i,SV2228: $i,SV1607: $i,SV794: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV794 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1607 ) @ SV2228 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV794 @ SV2586 ) )
| ( hBOOL @ ( hAPP @ SV794 @ SV1607 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6053]) ).
thf(6683,plain,
! [SV2229: $i,SV1608: $i,SV795: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV795 @ SV1608 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV2229 @ SV1608 @ tc_nat ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1608 @ SV2229 @ tc_nat )
| ~ ( c_lessequals @ SV1608 @ SV795 @ tc_nat )
| ( SV795 = SV2229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6054]) ).
thf(6684,plain,
! [SV2713: $i,SV2587: $i,SV2230: $i,SV1609: $i,SV796: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV796 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SV2587 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SV2713 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ SV2587 )
= SV2713 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6055]) ).
thf(6685,plain,
! [SV2231: $i,SV1610: $i,SV797: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV797 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV797 ) @ ( c_HOL_Otimes__class_Otimes @ SV1610 @ SV1610 @ SV797 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2231 @ SV2231 @ SV797 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV797 ) )
| ( SV2231
= ( c_HOL_Ozero__class_Ozero @ SV797 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6056]) ).
thf(6686,plain,
! [SV2588: $i,SV2232: $i,SV1611: $i,SV798: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV798 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1611 @ SV1611 @ SV798 )
!= ( c_HOL_Ominus__class_Ominus @ SV2232 @ SV2588 @ SV798 ) )
| ( SV2232 = SV2588 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6057]) ).
thf(6687,plain,
! [SV2714: $i,SV2589: $i,SV2233: $i,SV1612: $i,SV799: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV799 @ SV1612 @ tc_nat ) ) @ SV2233 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2589 @ SV1612 @ tc_nat ) ) @ SV2714 ) )
| ~ ( c_lessequals @ SV799 @ SV2589 @ tc_nat )
| ( SV2233
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2589 @ SV799 @ tc_nat ) @ SV1612 @ tc_nat ) ) @ SV2714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6058]) ).
thf(6688,plain,
! [SV2590: $i,SV2234: $i,SV1613: $i,SV800: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV800 ) @ SV1613 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2234 ) @ SV2590 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2234 @ SV1613 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV800 @ SV2590 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6059]) ).
thf(6689,plain,
! [SV2591: $i,SV2235: $i,SV1614: $i,SV801: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV801 ) @ SV1614 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV2235 ) @ SV2591 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV801 = SV2235 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6060]) ).
thf(6690,plain,
! [SV2236: $i,SV1615: $i,SV802: $i] :
( ( ( ( c_List_Oappend @ SV802 @ SV1615 @ SV2236 )
= ( c_List_Olist_ONil @ SV2236 ) )
= $false )
| ( ( SV1615
= ( c_List_Olist_ONil @ SV2236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6061]) ).
thf(6691,plain,
! [SV2237: $i,SV1616: $i,SV803: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1616 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV803 @ SV2237 @ tc_nat ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV803 @ tc_nat )
| ( SV1616 = SV2237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6062]) ).
thf(6692,plain,
! [SV2238: $i,SV1617: $i,SV804: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV804 ) @ SV1617 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2238 ) @ SV1617 ) )
= $false )
| ( ( SV804 = SV2238 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6063]) ).
thf(6693,plain,
! [SV2715: $i,SV2592: $i,SV2239: $i,SV1619: $i,SV806: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV806 )
| ~ ( class_Int_Onumber__ring @ SV806 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2239 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2715 @ SV806 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2715 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2239 @ SV806 ) ) )
| ( SV2239 = SV2715 )
| ( SV1619 = SV2592 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6065]) ).
thf(6694,plain,
! [SV2593: $i,SV2240: $i,SV1620: $i,SV807: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV807 ) @ SV1620 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2240 ) @ SV2593 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1620 = SV2593 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6066]) ).
thf(6695,plain,
! [SV2716: $i,SV2594: $i,SV2241: $i,SV1621: $i,SV808: $i] :
( ( ! [SY7100: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV808 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV1621 @ SV2241 @ SV808 ) ) @ SV2594 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV2716 @ SV2241 @ SV808 ) ) @ SY7100 ) )
| ( SV2594
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2716 @ SV1621 @ SV808 ) @ SV2241 @ SV808 ) ) @ SY7100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6067]) ).
thf(6696,plain,
! [SV2242: $i,SV1622: $i,SV809: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV809 @ SV1622 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV809 @ SV2242 @ tc_nat ) )
= $false )
| ( ( ( SV809
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1622 = SV2242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6068]) ).
thf(6697,plain,
! [SV2243: $i,SV1623: $i,SV810: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV810 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV810 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1623 @ SV2243 @ SV810 )
!= ( c_HOL_Ozero__class_Ozero @ SV810 ) )
| ( SV1623 = SV2243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6069]) ).
thf(6698,plain,
! [SV2595: $i,SV2244: $i,SV1625: $i,SV812: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1625 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2244 @ SV2595 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV2595 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2244 @ SV1625 @ tc_nat ) ) )
= $true )
| ( ( ( SV1625 = SV2595 )
| ( SV812 = SV2244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6071]) ).
thf(6699,plain,
! [SV814: $i,SV1627: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1627 @ SV814 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1627 = SV814 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV814 @ SV1627 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6072]) ).
thf(6700,plain,
! [SV2245: $i,SV1628: $i,SV815: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV815 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1628 @ SV2245 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV815 )
= SV1628 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6073]) ).
thf(6701,plain,
! [SV2246: $i,SV1629: $i,SV816: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV816 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV1629 @ SV2246 @ SV816 )
!= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
| ( SV2246
= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
| ( SV1629
= ( c_HOL_Ozero__class_Ozero @ SV816 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6074]) ).
thf(6702,plain,
! [SV1630: $i,SV817: $i] :
( ( ( SV817
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV817
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV817 ) @ SV1630 )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6075]) ).
thf(6703,plain,
! [SV2596: $i,SV2247: $i,SV1631: $i,SV818: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV818 ) @ SV1631 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV2247 ) @ SV2596 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6076]) ).
thf(6704,plain,
! [SV2597: $i,SV2248: $i,SV1632: $i,SV819: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV819 ) @ SV1632 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2248 ) @ SV2597 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV819 = SV2248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6077]) ).
thf(6705,plain,
! [SV2598: $i,SV2249: $i,SV1633: $i,SV820: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV820 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SV2249 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SV2598 ) )
| ( SV2249 = SV2598 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6078]) ).
thf(6706,plain,
! [SV2250: $i,SV1634: $i,SV821: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV821 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1634 @ SV821 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV2250 @ SV821 ) )
| ( SV1634 = SV2250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6079]) ).
thf(6707,plain,
! [SV2251: $i,SV1635: $i,SV822: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV822 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV822 ) @ ( c_HOL_Otimes__class_Otimes @ SV1635 @ SV1635 @ SV822 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2251 @ SV2251 @ SV822 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV822 ) )
| ( SV1635
= ( c_HOL_Ozero__class_Ozero @ SV822 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6080]) ).
thf(6708,plain,
! [SV2599: $i,SV2252: $i,SV1636: $i,SV823: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV823 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1636 @ ( c_Suc @ SV2252 ) @ SV823 )
!= ( c_Power_Opower__class_Opower @ SV2599 @ ( c_Suc @ SV2252 ) @ SV823 ) )
| ( SV1636 = SV2599 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV2599 @ SV823 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV1636 @ SV823 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6081]) ).
thf(6709,plain,
! [SV2253: $i,SV1637: $i,SV824: $i] :
( ( ( ( c_List_Oappend @ SV824 @ SV1637 @ SV2253 )
= SV1637 )
= $false )
| ( ( SV824
= ( c_List_Olist_ONil @ SV2253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6082]) ).
thf(6710,plain,
! [SV2255: $i,SV1639: $i,SV826: $i] :
( ( ( SV826
= ( c_List_Oappend @ SV1639 @ SV826 @ SV2255 ) )
= $false )
| ( ( SV1639
= ( c_List_Olist_ONil @ SV2255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6084]) ).
thf(6711,plain,
! [SV2600: $i,SV2258: $i,SV1643: $i,SV830: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV830 ) @ SV1643 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV2258 ) @ SV2600 ) )
= $true )
| ( ( SV1643 = SV2600 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6088]) ).
thf(6712,plain,
! [SV2601: $i,SV2259: $i,SV1644: $i,SV832: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV832 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV832 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2259 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2601 ) )
| ( SV2259 = SV2601 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6089]) ).
thf(6713,plain,
! [SV2260: $i,SV1645: $i,SV833: $i] :
( ( ( ( c_List_Oreplicate @ SV833 @ SV1645 @ SV2260 )
= ( c_List_Olist_ONil @ SV2260 ) )
= $false )
| ( ( SV833
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6090]) ).
thf(6714,plain,
! [SV2261: $i,SV1646: $i,SV834: $i] :
( ( ( class_Orderings_Olinorder @ SV834 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omin @ SV1646 @ SV2261 @ SV834 )
!= SV1646 )
| ( c_lessequals @ SV1646 @ SV2261 @ SV834 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6091]) ).
thf(6715,plain,
! [SV835: $i,SV1647: $i] :
( ( ( SV1647
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV835
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV835 @ SV1647 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6092]) ).
thf(6716,plain,
! [SV2262: $i,SV1648: $i,SV836: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV836 @ SV1648 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV2262 ) )
= $false )
| ( ( SV836
= ( c_Lambda_OdB_OAbs @ SV2262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6093]) ).
thf(6717,plain,
! [SV2717: $i,SV2602: $i,SV2263: $i,SV1649: $i,SV837: $i] :
( ( ( ( c_List_Oreplicate @ SV837 @ SV1649 @ SV2263 )
!= ( c_List_Oreplicate @ SV2602 @ SV2717 @ SV2263 ) )
| ( SV1649 = SV2717 )
| ( SV837
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6094]) ).
thf(6718,plain,
! [SV2718: $i,SV2603: $i,SV2264: $i,SV1650: $i,SV838: $i] :
( ( ! [SY7101: $i,SY7102: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
| ~ ( c_Type_Otyping @ SY7101 @ SV2603 @ SV1650 )
| ~ ( c_InductTermi_OIT @ SV2603 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY7101 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SY7102 )
| ~ ( c_InductTermi_OIT @ SV2264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6095]) ).
thf(6719,plain,
! [SV2265: $i,SV1651: $i,SV839: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV839 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV839 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV839 )
| ~ ( class_Power_Opower @ SV839 )
| ( ( c_Power_Opower__class_Opower @ SV1651 @ SV2265 @ SV839 )
!= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
| ( SV1651
= ( c_HOL_Ozero__class_Ozero @ SV839 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6096]) ).
thf(6720,plain,
! [SV2266: $i,SV1652: $i,SV840: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV840 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1652 @ SV2266 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV840 )
= SV1652 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6097]) ).
thf(6721,plain,
! [SV2719: $i,SV2604: $i,SV2267: $i,SV1653: $i,SV841: $i] :
( ( ( ( c_List_Oappend @ SV841 @ ( c_List_Olist_OCons @ SV1653 @ ( c_List_Olist_ONil @ SV2267 ) @ SV2267 ) @ SV2267 )
!= ( c_List_Oappend @ SV2604 @ ( c_List_Olist_OCons @ SV2719 @ ( c_List_Olist_ONil @ SV2267 ) @ SV2267 ) @ SV2267 ) )
| ( SV841 = SV2604 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6098]) ).
thf(6722,plain,
! [SV2268: $i,SV1654: $i,SV842: $i] :
( ( ( SV842
= ( c_List_Oappend @ SV842 @ SV1654 @ SV2268 ) )
= $false )
| ( ( SV1654
= ( c_List_Olist_ONil @ SV2268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6099]) ).
thf(6723,plain,
! [SV845: $i,SV1656: $i] :
( ( ( SV1656
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV845
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV845 ) @ SV1656 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6101]) ).
thf(6724,plain,
! [SV2270: $i,SV1657: $i,SV846: $i] :
( ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV846 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1657 @ SV2270 @ SV846 )
!= ( c_HOL_Ozero__class_Ozero @ SV846 ) )
| ( SV1657
= ( c_HOL_Ozero__class_Ozero @ SV846 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6102]) ).
thf(6725,plain,
! [SV2720: $i,SV2605: $i,SV2272: $i,SV1659: $i,SV848: $i] :
( ( ( ( c_List_Olist_OCons @ SV848 @ SV1659 @ SV2272 )
!= ( c_List_Olist_OCons @ SV2605 @ SV2720 @ SV2272 ) )
| ( SV1659 = SV2720 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6104]) ).
thf(6726,plain,
! [SV2273: $i,SV1660: $i,SV849: $i] :
( ( ( ( c_List_Olist_ONil @ SV849 )
= ( c_List_Oappend @ SV1660 @ SV2273 @ SV849 ) )
= $false )
| ( ( SV1660
= ( c_List_Olist_ONil @ SV849 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6105]) ).
thf(6727,plain,
! [SV1662: $i,SV851: $i] :
( ( ( SV851
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1662
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV851 ) @ SV1662 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6107]) ).
thf(6728,plain,
! [SV1663: $i,SV852: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV852 ) @ SV1663 ) @ SV1663 )
!= ( c_HOL_Ozero__class_Ozero @ SV852 ) )
= $true )
| ( ( SV1663
= ( c_HOL_Ozero__class_Ozero @ SV852 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV852 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6108]) ).
thf(6729,plain,
! [SV2606: $i,SV2274: $i,SV1664: $i,SV853: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV853 ) @ SV1664 )
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2274 ) @ SV2606 ) )
= $true )
| ( ( SV853 = SV2274 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6109]) ).
thf(6730,plain,
! [SV2276: $i,SV1666: $i,SV855: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV855 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV855 ) @ SV1666 ) @ SV2276 )
!= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV2276 @ SV855 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV1666 @ SV855 )
| ( SV2276
= ( c_HOL_Ozero__class_Ozero @ SV855 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6111]) ).
thf(6731,plain,
! [SV2277: $i,SV1667: $i,SV856: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV856 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1667 @ SV2277 @ SV856 )
!= ( c_HOL_Ozero__class_Ozero @ SV856 ) )
| ( SV1667 = SV2277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6112]) ).
thf(6732,plain,
! [SV2278: $i,SV1668: $i,SV857: $i] :
( ( ( ( c_List_Oappend @ SV857 @ SV1668 @ SV2278 )
= ( c_List_Olist_ONil @ SV2278 ) )
= $false )
| ( ( SV857
= ( c_List_Olist_ONil @ SV2278 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6113]) ).
thf(6733,plain,
! [SV2607: $i,SV2279: $i,SV1669: $i,SV858: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV858 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1669 @ SV2279 @ SV858 )
!= ( c_HOL_Ominus__class_Ominus @ SV2607 @ SV2607 @ SV858 ) )
| ( SV1669 = SV2279 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6114]) ).
thf(6734,plain,
! [SV2608: $i,SV2281: $i,SV1672: $i,SV861: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SV2281 @ tc_nat ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SV2608 @ tc_nat ) ) )
= $true )
| ( ( ( SV2281 = SV2608 )
| ( SV1672
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6117]) ).
thf(6735,plain,
! [SV2721: $i,SV2609: $i,SV2282: $i,SV1673: $i,SV863: $i] :
( ( ! [SY7103: $i,SY7104: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
| ~ ( c_Type_Otyping @ SY7103 @ SV2609 @ SV863 )
| ~ ( c_InductTermi_OIT @ SV2609 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY7103 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SY7104 )
| ~ ( c_InductTermi_OIT @ SV2282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6118]) ).
thf(6736,plain,
! [SV2283: $i,SV1674: $i,SV864: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV864 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1674 @ SV2283 @ SV864 )
!= ( c_HOL_Ozero__class_Ozero @ SV864 ) )
| ( SV1674 = SV2283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6119]) ).
thf(6737,plain,
! [SV2610: $i,SV2284: $i,SV1675: $i,SV865: $i,SV1: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1 @ SV865 @ tc_nat ) ) @ SV1675 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2284 @ SV865 @ tc_nat ) ) @ SV2610 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1675 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2284 @ SV1 @ tc_nat ) @ SV865 @ tc_nat ) ) @ SV2610 ) @ tc_nat )
| ~ ( c_lessequals @ SV1 @ SV2284 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6120]) ).
thf(6738,plain,
! [SV2611: $i,SV2285: $i,SV1676: $i,SV866: $i,SV2: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV866 @ SV1676 @ tc_nat ) @ SV2285 @ tc_nat ) ) @ SV2611 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV2285 @ tc_nat ) ) @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV866 @ SV2285 @ tc_nat ) ) @ SV2611 ) @ tc_nat )
| ~ ( c_lessequals @ SV1676 @ SV866 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6121]) ).
thf(6739,plain,
! [SV2612: $i,SV2286: $i,SV1677: $i,SV867: $i,SV3: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV3 @ SV867 @ tc_nat ) ) @ SV1677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2286 @ SV867 @ tc_nat ) ) @ SV2612 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV3 @ SV2286 @ tc_nat ) @ SV867 @ tc_nat ) ) @ SV1677 ) @ SV2612 @ tc_nat )
| ~ ( c_lessequals @ SV2286 @ SV3 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6122]) ).
thf(6740,plain,
! [SV2613: $i,SV2287: $i,SV1678: $i,SV868: $i,SV4: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV868 @ tc_nat ) @ SV1678 @ tc_nat ) ) @ SV2287 ) @ SV2613 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV4 @ SV1678 @ tc_nat ) ) @ SV2287 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV868 @ SV1678 @ tc_nat ) ) @ SV2613 ) @ tc_nat )
| ~ ( c_lessequals @ SV868 @ SV4 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6123]) ).
thf(6741,plain,
! [SV2614: $i,SV2288: $i,SV1679: $i,SV869: $i,SV5: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV5 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV869 @ SV1679 @ SV5 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2288 @ SV869 @ SV5 ) @ SV1679 @ SV5 ) ) @ SV2614 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV2288 @ SV1679 @ SV5 ) ) @ SV2614 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6124]) ).
thf(6742,plain,
! [SV872: $i,SV8: $i] :
( ( ( class_Power_Opower @ SV8 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ ( c_Suc @ SV872 ) @ SV8 )
= ( c_HOL_Ozero__class_Ozero @ SV8 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6125]) ).
thf(6743,plain,
! [SV2615: $i,SV2289: $i,SV1680: $i,SV873: $i,SV9: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV2289 @ SV2615 @ SV9 ) @ SV9 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV2289 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1680 @ SV2615 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV873 @ SV2289 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6126]) ).
thf(6744,plain,
! [SV874: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ SV10 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV10 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinduct__1 @ SV10 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV10 @ SV874 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6127]) ).
thf(6745,plain,
! [SV2290: $i,SV1683: $i,SV877: $i,SV13: $i] :
( ( ( class_Orderings_Olinorder @ SV13 )
= $false )
| ( ( ( c_lessequals @ SV877 @ ( c_Orderings_Oord__class_Omin @ SV1683 @ SV2290 @ SV13 ) @ SV13 )
| ~ ( c_lessequals @ SV877 @ SV2290 @ SV13 )
| ~ ( c_lessequals @ SV877 @ SV1683 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6130]) ).
thf(6746,plain,
! [SV2291: $i,SV1684: $i,SV878: $i,SV14: $i] :
( ( ( class_Orderings_Olinorder @ SV14 )
= $false )
| ( ( ( c_lessequals @ SV878 @ ( c_Orderings_Oord__class_Omin @ SV1684 @ SV2291 @ SV14 ) @ SV14 )
| ~ ( c_lessequals @ SV878 @ SV2291 @ SV14 )
| ~ ( c_lessequals @ SV878 @ SV1684 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6131]) ).
thf(6747,plain,
! [SV2292: $i,SV1685: $i,SV879: $i,SV15: $i] :
( ( ( class_Orderings_Olinorder @ SV15 )
= $false )
| ( ( ( c_lessequals @ SV879 @ ( c_Orderings_Oord__class_Omin @ SV1685 @ SV2292 @ SV15 ) @ SV15 )
| ~ ( c_lessequals @ SV879 @ SV2292 @ SV15 )
| ~ ( c_lessequals @ SV879 @ SV1685 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6132]) ).
thf(6748,plain,
! [SV2616: $i,SV2293: $i,SV1686: $i,SV880: $i,SV16: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV16 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SV880 @ SV1686 @ SV16 ) ) @ SV2293 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SV2616 @ SV1686 @ SV16 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV880 @ SV2616 @ SV16 ) @ SV1686 @ SV16 ) ) @ SV2293 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6133]) ).
thf(6749,plain,
! [SV1687: $i,SV881: $i,SV17: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SV881 @ SV1687 @ SV17 ) @ SV17 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV881 @ SV17 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6134]) ).
thf(6750,plain,
! [SV2294: $i,SV1688: $i,SV883: $i,SV19: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV19 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV883 @ SV1688 @ SV19 ) @ SV2294 @ SV19 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV883 @ SV2294 @ SV19 ) @ ( c_HOL_Ominus__class_Ominus @ SV1688 @ SV2294 @ SV19 ) @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6135]) ).
thf(6751,plain,
! [SV2295: $i,SV1689: $i,SV884: $i,SV20: $i] :
( ( ( class_Orderings_Olinorder @ SV20 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV884 @ SV1689 @ SV20 ) @ SV2295 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SV1689 @ SV2295 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SV884 @ SV2295 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6136]) ).
thf(6752,plain,
! [SV2296: $i,SV1691: $i,SV886: $i,SV22: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV22 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV22 )
| ( c_HOL_Oord__class_Oless @ SV886 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1691 ) @ SV2296 ) @ SV22 )
| ~ ( c_lessequals @ SV886 @ SV2296 @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV1691 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6138]) ).
thf(6753,plain,
! [SV1692: $i,SV887: $i,SV23: $i] :
( ( ( c_lessequals @ SV23 @ SV887 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1692 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV23 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV887 ) @ SV1692 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6139]) ).
thf(6754,plain,
! [SV24: $i,SV1693: $i,SV888: $i] :
( ( ( c_lessequals @ SV888 @ SV1693 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV888 @ SV24 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1693 @ SV24 ) @ SV24 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6140]) ).
thf(6755,plain,
! [SV1694: $i,SV25: $i,SV889: $i] :
( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV889 @ SV25 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1694 @ SV25 ) @ SV25 )
= $true )
| ( ( ~ ( c_lessequals @ SV889 @ SV1694 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6141]) ).
thf(6756,plain,
! [SV1695: $i,SV890: $i,SV2297: $i,SV26: $i] :
( ( ( c_Lambda_Obeta @ SV26 @ SV2297 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV26 @ SV890 @ SV1695 ) @ ( c_Lambda_Osubst @ SV2297 @ SV890 @ SV1695 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6142]) ).
thf(6757,plain,
! [SV2298: $i,SV1696: $i,SV891: $i,SV27: $i] :
( ( ( class_Orderings_Olinorder @ SV27 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV891 @ ( c_Orderings_Oord__class_Omin @ SV1696 @ SV2298 @ SV27 ) @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV2298 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV1696 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6143]) ).
thf(6758,plain,
! [SV2299: $i,SV1699: $i,SV894: $i,SV30: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV30 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV30 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV1699 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV2299 @ SV30 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV2299 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV1699 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6144]) ).
thf(6759,plain,
! [SV2300: $i,SV1700: $i,SV895: $i,SV31: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV31 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV31 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1700 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV2300 @ SV31 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV2300 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1700 @ SV31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6145]) ).
thf(6760,plain,
! [SV897: $i,SV34: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV34 ) @ SV897 ) @ SV897 ) @ SV34 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV897 @ SV34 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6146]) ).
thf(6761,plain,
! [SV898: $i,SV35: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV898 @ SV35 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV35 ) @ SV898 ) @ SV898 ) @ SV35 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6147]) ).
thf(6762,plain,
! [SV2617: $i,SV2301: $i,SV1703: $i,SV901: $i,SV38: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV38 @ SV901 @ tc_nat ) ) @ SV1703 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2301 @ SV901 @ tc_nat ) ) @ SV2617 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1703 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2301 @ SV38 @ tc_nat ) @ SV901 @ tc_nat ) ) @ SV2617 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV38 @ SV2301 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6150]) ).
thf(6763,plain,
! [SV2618: $i,SV2302: $i,SV1704: $i,SV902: $i,SV39: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV39 @ SV902 @ tc_nat ) ) @ SV1704 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2302 @ SV902 @ tc_nat ) ) @ SV2618 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SV2302 @ tc_nat ) @ SV902 @ tc_nat ) ) @ SV1704 ) @ SV2618 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2302 @ SV39 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6151]) ).
thf(6764,plain,
! [SV2303: $i,SV1710: $i,SV908: $i,SV45: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV45 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV908 @ SV1710 @ SV45 ) @ SV2303 @ SV45 )
= ( c_Power_Opower__class_Opower @ SV908 @ ( c_HOL_Otimes__class_Otimes @ SV1710 @ SV2303 @ tc_nat ) @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6155]) ).
thf(6765,plain,
! [SV909: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ SV46 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV46 @ ( c_Suc @ ( v_sko__Nat__Xnat__Xinducts__1 @ SV46 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV46 @ SV909 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6156]) ).
thf(6766,plain,
! [SV1715: $i,SV51: $i,SV2304: $i,SV914: $i] :
( ( ( ~ ( c_lessequals @ SV914 @ SV2304 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV51 @ SV1715 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV914 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1715 ) @ SV2304 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6161]) ).
thf(6767,plain,
! [SV2619: $i,SV2305: $i,SV1716: $i,SV915: $i,SV52: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV52 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV915 ) @ SV1716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV2305 ) @ SV2619 ) @ SV52 )
| ~ ( c_lessequals @ SV1716 @ SV2619 @ SV52 )
| ~ ( c_lessequals @ SV915 @ SV2305 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6162]) ).
thf(6768,plain,
! [SV59: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) )
= ( c_HOL_Ozero__class_Ozero @ SV59 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6164]) ).
thf(6769,plain,
! [SV1719: $i,SV923: $i,SV62: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV923 ) @ SV1719 ) @ SV62 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1719 @ SV62 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV923 @ SV62 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6166]) ).
thf(6770,plain,
! [SV2306: $i,SV1720: $i,SV924: $i,SV63: $i] :
( ( ( class_Orderings_Opreorder @ SV63 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV924 @ SV1720 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV2306 @ SV1720 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ SV2306 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6167]) ).
thf(6771,plain,
! [SV2307: $i,SV1721: $i,SV925: $i,SV64: $i] :
( ( ( class_Orderings_Oorder @ SV64 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV925 @ SV1721 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV925 @ SV2307 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV2307 @ SV1721 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6168]) ).
thf(6772,plain,
! [SV1722: $i,SV926: $i,SV2308: $i,SV65: $i] :
( ( ( c_Type_Otyping @ SV65 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV2308 ) @ SV926 ) @ SV1722 )
= $false )
| ( ( c_Type_Otyping @ SV65 @ SV926 @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV1722 @ SV65 @ SV2308 @ SV926 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6169]) ).
thf(6773,plain,
! [SV66: $i,SV1723: $i,SV927: $i] :
( ( ( ( c_Orderings_Oord__class_Omax @ SV927 @ SV1723 @ SV66 )
= SV1723 )
= $true )
| ( ( ~ ( c_lessequals @ SV927 @ SV1723 @ SV66 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6170]) ).
thf(6774,plain,
! [SV67: $i,SV1724: $i,SV928: $i] :
( ( ( ( c_Orderings_Oord__class_Omax @ SV928 @ SV1724 @ SV67 )
= SV928 )
= $true )
| ( ( ~ ( c_lessequals @ SV1724 @ SV928 @ SV67 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6171]) ).
thf(6775,plain,
! [SV2309: $i,SV1725: $i,SV929: $i,SV68: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV929 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV1725 ) @ SV2309 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV68 ) @ SV929 ) @ SV1725 ) ) @ SV2309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6172]) ).
thf(6776,plain,
! [SV2310: $i,SV1726: $i,SV930: $i,SV69: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV69 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV930 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV1726 ) @ SV2310 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV1726 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV69 ) @ SV930 ) @ SV2310 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6173]) ).
thf(6777,plain,
! [SV933: $i,SV72: $i,SV1729: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1729 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV72 ) @ tc_nat ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV72 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV72 @ SV1729 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV72 @ SV933 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6174]) ).
thf(6778,plain,
! [SV937: $i,SV1730: $i,SV76: $i] :
( ( ( c_lessequals @ SV76 @ ( c_HOL_Ominus__class_Ominus @ SV1730 @ SV937 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV937 @ SV1730 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV76 ) @ SV937 ) @ SV1730 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6175]) ).
thf(6779,plain,
! [SV938: $i,SV1731: $i,SV77: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV77 ) @ SV1731 ) @ SV938 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1731 @ SV938 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV77 @ ( c_HOL_Ominus__class_Ominus @ SV938 @ SV1731 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6176]) ).
thf(6780,plain,
! [SV2311: $i,SV1732: $i,SV939: $i,SV78: $i] :
( ( ( class_Orderings_Olinorder @ SV78 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV939 @ SV1732 @ SV78 ) @ SV2311 @ SV78 )
| ~ ( c_lessequals @ SV1732 @ SV2311 @ SV78 )
| ~ ( c_lessequals @ SV939 @ SV2311 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6177]) ).
thf(6781,plain,
! [SV2312: $i,SV1733: $i,SV940: $i,SV79: $i] :
( ( ( class_Orderings_Olinorder @ SV79 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV940 @ SV1733 @ SV79 ) @ SV2312 @ SV79 )
| ~ ( c_lessequals @ SV1733 @ SV2312 @ SV79 )
| ~ ( c_lessequals @ SV940 @ SV2312 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6178]) ).
thf(6782,plain,
! [SV2313: $i,SV1734: $i,SV941: $i,SV80: $i] :
( ( ( class_Orderings_Olinorder @ SV80 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV941 @ SV1734 @ SV80 ) @ SV2313 @ SV80 )
| ~ ( c_lessequals @ SV1734 @ SV2313 @ SV80 )
| ~ ( c_lessequals @ SV941 @ SV2313 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6179]) ).
thf(6783,plain,
! [SV2722: $i,SV2620: $i,SV2315: $i,SV1738: $i,SV951: $i,SV90: $i] :
( ( ! [SY7105: $i,SY7106: $i,SY7107: $i] :
( ( ( hAPP @ ( hAPP @ SV90 @ ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ SV1738 ) ) @ SV2315 )
= ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ ( c_HOL_Otimes__class_Otimes @ SV1738 @ SV2315 @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2620 @ SV2722 @ SV90 @ SY7105 @ SY7106 @ SY7107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6182]) ).
thf(6784,plain,
! [SV2316: $i,SV1739: $i,SV952: $i,SV91: $i] :
( ( ( class_Orderings_Olinorder @ SV91 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV952 @ SV1739 @ SV91 ) @ SV2316 @ SV91 )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV952 @ SV2316 @ SV91 ) @ ( c_Orderings_Oord__class_Omin @ SV1739 @ SV2316 @ SV91 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6183]) ).
thf(6785,plain,
! [SV2317: $i,SV1740: $i,SV953: $i,SV92: $i] :
( ( ( class_Orderings_Olinorder @ SV92 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV953 @ ( c_Orderings_Oord__class_Omax @ SV1740 @ SV2317 @ SV92 ) @ SV92 )
= ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV953 @ SV1740 @ SV92 ) @ ( c_Orderings_Oord__class_Omin @ SV953 @ SV2317 @ SV92 ) @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6184]) ).
thf(6786,plain,
! [SV2318: $i,SV1741: $i,SV954: $i,SV93: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV93 )
| ( c_lessequals @ SV954 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV1741 ) @ SV2318 ) @ SV93 )
| ~ ( c_lessequals @ SV954 @ SV2318 @ SV93 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV1741 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6185]) ).
thf(6787,plain,
! [SV2319: $i,SV1742: $i,SV955: $i,SV94: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV94 )
| ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV1742 ) @ SV2319 ) @ SV94 )
| ~ ( c_lessequals @ SV955 @ SV1742 @ SV94 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV2319 @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6186]) ).
thf(6788,plain,
! [SV956: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ SV95 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV95 @ ( c_Suc @ ( v_sko__List__Xupt__Xinduct__1 @ SV95 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV95 @ SV956 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6187]) ).
thf(6789,plain,
! [SV957: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ SV96 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV96 @ ( c_Suc @ ( v_sko__List__Xreplicate__Xinduct__1 @ SV96 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV96 @ SV957 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6188]) ).
thf(6790,plain,
! [SV2723: $i,SV2621: $i,SV2320: $i,SV1748: $i,SV967: $i,SV106: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV106 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV967 @ SV1748 @ SV106 ) ) @ SV2320 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV2621 @ SV1748 @ SV106 ) ) @ SV2723 ) @ SV106 )
| ~ ( c_lessequals @ SV2320 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2621 @ SV967 @ SV106 ) @ SV1748 @ SV106 ) ) @ SV2723 ) @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6194]) ).
thf(6791,plain,
! [SV2724: $i,SV2622: $i,SV2321: $i,SV1749: $i,SV968: $i,SV107: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV107 )
| ( c_lessequals @ SV968 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SV2321 @ SV107 ) @ SV2622 @ SV107 ) ) @ SV2724 ) @ SV107 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV2321 @ SV2622 @ SV107 ) ) @ SV968 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV1749 @ SV2622 @ SV107 ) ) @ SV2724 ) @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6195]) ).
thf(6792,plain,
! [SV2725: $i,SV2623: $i,SV2322: $i,SV1750: $i,SV969: $i,SV108: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV108 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV969 @ SV1750 @ SV108 ) ) @ SV2322 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV2623 @ SV1750 @ SV108 ) ) @ SV2725 ) @ SV108 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV969 @ SV2623 @ SV108 ) @ SV1750 @ SV108 ) ) @ SV2322 ) @ SV2725 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6196]) ).
thf(6793,plain,
! [SV2726: $i,SV2624: $i,SV2323: $i,SV1751: $i,SV970: $i,SV109: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV109 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV970 @ SV1751 @ SV109 ) @ SV2323 @ SV109 ) ) @ SV2624 ) @ SV2726 @ SV109 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV970 @ SV2323 @ SV109 ) ) @ SV2624 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV1751 @ SV2323 @ SV109 ) ) @ SV2726 ) @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6197]) ).
thf(6794,plain,
! [SV2324: $i,SV1756: $i,SV977: $i,SV116: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV116 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV977 ) @ SV1756 ) @ SV2324 @ SV116 @ SV116 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV977 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV1756 @ SV2324 @ SV116 @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6202]) ).
thf(6795,plain,
! [SV978: $i,SV117: $i,SV1757: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1757 @ SV117 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1757 @ SV978 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV978 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV1757 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6203]) ).
thf(6796,plain,
! [SV979: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ SV118 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV118 @ ( c_Suc @ ( c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1 @ SV118 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV118 @ SV979 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6204]) ).
thf(6797,plain,
! [SV2325: $i,SV1758: $i,SV980: $i,SV119: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV119 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV980 @ SV1758 @ SV119 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV2325 @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV980 @ SV2325 @ SV119 ) @ ( c_HOL_Otimes__class_Otimes @ SV1758 @ SV2325 @ SV119 ) @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6205]) ).
thf(6798,plain,
! [SV2326: $i,SV1759: $i,SV981: $i,SV120: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV120 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV981 @ SV1759 @ SV120 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV2326 @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV981 @ SV120 ) @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV1759 @ SV120 ) @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6206]) ).
thf(6799,plain,
! [SV2327: $i,SV1760: $i,SV982: $i,SV121: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring @ SV121 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV982 @ SV1760 @ SV121 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV2327 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV982 @ SV2327 @ SV121 ) @ ( c_HOL_Otimes__class_Otimes @ SV1760 @ SV2327 @ SV121 ) @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6207]) ).
thf(6800,plain,
! [SV2328: $i,SV1761: $i,SV983: $i,SV122: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring @ SV122 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV983 @ SV1761 @ SV122 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV2328 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV983 @ SV122 ) @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV1761 @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6208]) ).
thf(6801,plain,
! [SV2329: $i,SV1763: $i,SV985: $i,SV124: $i] :
( ( ( class_Orderings_Olinorder @ SV124 )
= $false )
| ( ( ( c_lessequals @ SV985 @ SV1763 @ SV124 )
| ( c_lessequals @ SV985 @ SV2329 @ SV124 )
| ~ ( c_lessequals @ SV985 @ ( c_Orderings_Oord__class_Omax @ SV2329 @ SV1763 @ SV124 ) @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6210]) ).
thf(6802,plain,
! [SV2330: $i,SV1764: $i,SV986: $i,SV125: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV125 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV986 @ SV1764 @ SV125 ) @ ( c_Power_Opower__class_Opower @ SV986 @ SV2330 @ SV125 ) @ SV125 )
= ( c_Power_Opower__class_Opower @ SV986 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1764 ) @ SV2330 ) @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6211]) ).
thf(6803,plain,
! [SV2727: $i,SV2625: $i,SV2331: $i,SV1765: $i,SV989: $i,SV128: $i] :
( ( ! [SY7108: $i,SY7109: $i,SY7110: $i] :
( ( ( hAPP @ ( hAPP @ SV128 @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2331 ) ) @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2625 ) )
= ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2331 ) @ SV2625 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2727 @ SV128 @ SV989 @ SY7108 @ SY7109 @ SY7110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6213]) ).
thf(6804,plain,
! [SV2332: $i,SV1766: $i,SV990: $i,SV129: $i] :
( ( ( c_lessequals @ SV129 @ SV990 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SV1766 @ tc_nat ) ) @ SV2332 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV129 @ SV1766 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV990 @ SV129 @ tc_nat ) @ SV1766 @ tc_nat ) ) @ SV2332 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6214]) ).
thf(6805,plain,
! [SV2333: $i,SV1767: $i,SV991: $i,SV131: $i] :
( ( ( class_Orderings_Olinorder @ SV131 )
= $false )
| ( ( ( c_lessequals @ SV991 @ SV1767 @ SV131 )
| ~ ( c_lessequals @ SV991 @ ( c_Orderings_Oord__class_Omin @ SV2333 @ SV1767 @ SV131 ) @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6215]) ).
thf(6806,plain,
! [SV2334: $i,SV1768: $i,SV992: $i,SV132: $i] :
( ( ( class_Orderings_Olinorder @ SV132 )
= $false )
| ( ( ( c_lessequals @ SV992 @ SV1768 @ SV132 )
| ~ ( c_lessequals @ SV992 @ ( c_Orderings_Oord__class_Omin @ SV1768 @ SV2334 @ SV132 ) @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6216]) ).
thf(6807,plain,
! [SV2335: $i,SV1769: $i,SV993: $i,SV133: $i] :
( ( ( class_Orderings_Olinorder @ SV133 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV993 @ SV1769 @ SV133 ) @ SV2335 @ SV133 )
| ~ ( c_lessequals @ SV1769 @ SV2335 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6217]) ).
thf(6808,plain,
! [SV2336: $i,SV1770: $i,SV994: $i,SV134: $i] :
( ( ( class_Orderings_Olinorder @ SV134 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV994 @ SV1770 @ SV134 ) @ SV2336 @ SV134 )
| ~ ( c_lessequals @ SV994 @ SV2336 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6218]) ).
thf(6809,plain,
! [SV2337: $i,SV1771: $i,SV995: $i,SV135: $i] :
( ( ( class_Orderings_Olinorder @ SV135 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV995 @ SV1771 @ SV135 ) @ SV2337 @ SV135 )
| ~ ( c_lessequals @ SV1771 @ SV2337 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6219]) ).
thf(6810,plain,
! [SV2338: $i,SV1772: $i,SV996: $i,SV136: $i] :
( ( ( class_Orderings_Olinorder @ SV136 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV996 @ SV1772 @ SV136 ) @ SV2338 @ SV136 )
| ~ ( c_lessequals @ SV996 @ SV2338 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6220]) ).
thf(6811,plain,
! [SV2339: $i,SV1773: $i,SV997: $i,SV137: $i] :
( ( ( class_Orderings_Olinorder @ SV137 )
= $false )
| ( ( ( c_lessequals @ SV997 @ SV1773 @ SV137 )
| ~ ( c_lessequals @ SV997 @ ( c_Orderings_Oord__class_Omin @ SV2339 @ SV1773 @ SV137 ) @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6221]) ).
thf(6812,plain,
! [SV2340: $i,SV1774: $i,SV998: $i,SV138: $i] :
( ( ( class_Orderings_Olinorder @ SV138 )
= $false )
| ( ( ( c_lessequals @ SV998 @ SV1774 @ SV138 )
| ~ ( c_lessequals @ SV998 @ ( c_Orderings_Oord__class_Omin @ SV1774 @ SV2340 @ SV138 ) @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6222]) ).
thf(6813,plain,
! [SV2728: $i,SV2626: $i,SV2341: $i,SV1776: $i,SV1000: $i,SV140: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV140 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1776 @ SV140 ) ) @ SV2341 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV2626 @ SV1776 @ SV140 ) ) @ SV2728 ) @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV2341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2626 @ SV1000 @ SV140 ) @ SV1776 @ SV140 ) ) @ SV2728 ) @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6224]) ).
thf(6814,plain,
! [SV2729: $i,SV2627: $i,SV2342: $i,SV1777: $i,SV1001: $i,SV141: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV141 )
| ( c_HOL_Oord__class_Oless @ SV1001 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1777 @ SV2342 @ SV141 ) @ SV2627 @ SV141 ) ) @ SV2729 ) @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV2342 @ SV2627 @ SV141 ) ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV1777 @ SV2627 @ SV141 ) ) @ SV2729 ) @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6225]) ).
thf(6815,plain,
! [SV2730: $i,SV2628: $i,SV2343: $i,SV1778: $i,SV1002: $i,SV142: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV142 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1778 @ SV142 ) ) @ SV2343 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV2628 @ SV1778 @ SV142 ) ) @ SV2730 ) @ SV142 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1002 @ SV2628 @ SV142 ) @ SV1778 @ SV142 ) ) @ SV2343 ) @ SV2730 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6226]) ).
thf(6816,plain,
! [SV2731: $i,SV2629: $i,SV2344: $i,SV1779: $i,SV1003: $i,SV143: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV143 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1003 @ SV1779 @ SV143 ) @ SV2344 @ SV143 ) ) @ SV2629 ) @ SV2731 @ SV143 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1003 @ SV2344 @ SV143 ) ) @ SV2629 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1779 @ SV2344 @ SV143 ) ) @ SV2731 ) @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6227]) ).
thf(6817,plain,
! [SV2345: $i,SV1780: $i,SV1004: $i,SV144: $i] :
( ( ( class_Orderings_Olinorder @ SV144 )
= $false )
| ( ( ( c_lessequals @ SV1004 @ SV1780 @ SV144 )
| ( c_lessequals @ SV2345 @ SV1780 @ SV144 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV2345 @ SV1004 @ SV144 ) @ SV1780 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6228]) ).
thf(6818,plain,
! [SV2346: $i,SV1781: $i,SV1005: $i,SV145: $i] :
( ( ( c_lessequals @ SV145 @ SV1005 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV145 @ SV1781 @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1005 @ SV145 @ tc_nat ) @ SV1781 @ tc_nat ) ) @ SV2346 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1005 @ SV1781 @ tc_nat ) ) @ SV2346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6229]) ).
thf(6819,plain,
! [SV146: $i,SV1006: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV146 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV1006 ) @ SV1006 ) @ ( c_HOL_Ozero__class_Ozero @ SV146 ) @ SV146 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6230]) ).
thf(6820,plain,
! [SV1007: $i,SV147: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1007 ) @ SV1007 ) @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1007 @ ( c_HOL_Ozero__class_Ozero @ SV147 ) @ SV147 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6231]) ).
thf(6821,plain,
! [SV1008: $i,SV148: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV1008 ) @ SV1008 ) @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV148 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1008 @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV148 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6232]) ).
thf(6822,plain,
! [SV149: $i,SV1009: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1009 @ ( c_HOL_Ozero__class_Ozero @ SV149 ) @ SV149 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV149 ) @ SV1009 ) @ SV1009 ) @ ( c_HOL_Ozero__class_Ozero @ SV149 ) @ SV149 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6233]) ).
thf(6823,plain,
! [SV1782: $i,SV1010: $i,SV150: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1010 @ SV150 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1782 @ SV150 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ ( c_HOL_Otimes__class_Otimes @ SV1010 @ SV1782 @ SV150 ) @ SV150 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6234]) ).
thf(6824,plain,
! [SV1783: $i,SV1011: $i,SV151: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1011 @ SV151 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1783 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ ( c_HOL_Otimes__class_Otimes @ SV1783 @ SV1011 @ SV151 ) @ SV151 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6235]) ).
thf(6825,plain,
! [SV1784: $i,SV1012: $i,SV152: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SV1784 @ SV152 ) @ SV152 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1784 @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1012 @ SV152 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6236]) ).
thf(6826,plain,
! [SV1785: $i,SV1013: $i,SV153: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV1013 @ SV1785 @ SV153 ) @ SV153 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1785 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1013 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6237]) ).
thf(6827,plain,
! [SV1014: $i,SV154: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV154 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1014 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV154 @ SV1014 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6238]) ).
thf(6828,plain,
! [SV2347: $i,SV1786: $i,SV1015: $i,SV155: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV155 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1786 @ SV155 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV1786 @ SV155 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1015 @ SV2347 @ SV155 ) @ ( c_Power_Opower__class_Opower @ SV1786 @ SV2347 @ SV155 ) @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6239]) ).
thf(6829,plain,
! [SV2348: $i,SV1787: $i,SV1016: $i,SV156: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV156 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1016 ) @ SV1787 ) ) @ SV2348 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV156 ) @ SV1787 ) @ SV2348 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6240]) ).
thf(6830,plain,
! [SV2349: $i,SV1788: $i,SV1017: $i,SV157: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV157 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1017 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1788 ) @ SV2349 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1788 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV157 ) @ SV1017 ) @ SV2349 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6241]) ).
thf(6831,plain,
! [SV2350: $i,SV1789: $i,SV1018: $i,SV158: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV158 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1018 ) @ SV1789 ) ) @ SV2350 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1018 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV158 ) @ SV1789 ) @ SV2350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6242]) ).
thf(6832,plain,
! [SV2351: $i,SV1790: $i,SV1019: $i,SV159: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV159 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1019 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1790 ) @ SV2351 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV159 ) @ SV1019 ) @ SV1790 ) ) @ SV2351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6243]) ).
thf(6833,plain,
! [SV2352: $i,SV1791: $i,SV1020: $i,SV160: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV160 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV1020 ) @ SV1791 ) ) @ SV2352 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV160 ) @ SV1020 ) @ SV2352 ) ) @ SV1791 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6244]) ).
thf(6834,plain,
! [SV2353: $i,SV1792: $i,SV1021: $i,SV161: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV161 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1021 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1792 ) @ SV2353 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1792 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV161 ) @ SV1021 ) @ SV2353 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6245]) ).
thf(6835,plain,
! [SV2354: $i,SV1793: $i,SV1022: $i,SV162: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV162 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1022 ) @ SV1793 ) ) @ SV2354 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1022 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV162 ) @ SV1793 ) @ SV2354 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6246]) ).
thf(6836,plain,
! [SV2355: $i,SV1794: $i,SV1024: $i,SV164: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV164 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV1024 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1794 ) @ SV2355 ) @ SV164 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1024 @ SV1794 @ SV164 ) @ ( c_Power_Opower__class_Opower @ SV1024 @ SV2355 @ SV164 ) @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6248]) ).
thf(6837,plain,
! [SV175: $i,SV1803: $i,SV1035: $i] :
( ( ( ( c_Orderings_Oord__class_Omin @ SV1035 @ SV1803 @ SV175 )
= SV1035 )
= $true )
| ( ( ~ ( c_lessequals @ SV1035 @ SV1803 @ SV175 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6255]) ).
thf(6838,plain,
! [SV176: $i,SV1804: $i,SV1036: $i] :
( ( ( ( c_Orderings_Oord__class_Omin @ SV1036 @ SV1804 @ SV176 )
= SV1804 )
= $true )
| ( ( ~ ( c_lessequals @ SV1804 @ SV1036 @ SV176 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6256]) ).
thf(6839,plain,
! [SV2356: $i,SV1805: $i,SV1037: $i,SV177: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV177 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ SV1037 @ SV1805 @ SV177 ) @ SV2356 @ SV177 )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ SV1037 @ SV2356 @ SV177 ) @ ( c_HOL_Ominus__class_Ominus @ SV1805 @ SV2356 @ SV177 ) @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6257]) ).
thf(6840,plain,
! [SV1806: $i,SV1038: $i,SV2357: $i,SV178: $i] :
( ( ( c_Type_Otyping @ SV178 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV2357 @ SV1038 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1806 )
= $false )
| ( ( c_Type_Otypings @ SV178 @ SV1038 @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV1806 @ SV178 @ SV2357 @ SV1038 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6258]) ).
thf(6841,plain,
! [SV179: $i,SV1807: $i,SV1039: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1039 @ SV1807 @ SV179 )
= $true )
| ( ( c_lessequals @ SV1807 @ SV1039 @ SV179 )
= $true )
| ( ( class_Orderings_Olinorder @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6259]) ).
thf(6842,plain,
! [SV180: $i,SV1040: $i] :
( ( ( c_lessequals @ SV1040 @ SV1040 @ SV180 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1040 @ SV1040 @ SV180 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6260]) ).
thf(6843,plain,
! [SV182: $i,SV1808: $i,SV1042: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SV1808 @ SV182 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1808 @ SV1042 @ SV182 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6262]) ).
thf(6844,plain,
! [SV183: $i,SV1809: $i,SV1043: $i] :
( ( ( c_lessequals @ SV1043 @ SV1809 @ SV183 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1809 @ SV1043 @ SV183 )
= $true )
| ( ( class_Orderings_Olinorder @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6263]) ).
thf(6845,plain,
! [SV184: $i,SV1810: $i,SV1044: $i] :
( ( ( ~ ( c_lessequals @ SV1044 @ SV1810 @ SV184 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1810 @ SV1044 @ SV184 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6264]) ).
thf(6846,plain,
! [SV185: $i,SV1811: $i,SV1045: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1045 @ SV1811 @ SV185 )
= $true )
| ( ( c_lessequals @ SV1811 @ SV1045 @ SV185 )
= $true )
| ( ( class_Orderings_Olinorder @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6265]) ).
thf(6847,plain,
! [SV186: $i,SV1812: $i,SV1046: $i] :
( ( ( ~ ( c_lessequals @ SV1046 @ SV1812 @ SV186 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1812 @ SV1046 @ SV186 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6266]) ).
thf(6848,plain,
! [SV2358: $i,SV1813: $i,SV1050: $i,SV190: $i] :
( ( ( class_Orderings_Olinorder @ SV190 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ SV1050 @ SV1813 @ SV190 ) @ SV2358 @ SV190 )
= ( c_Orderings_Oord__class_Omin @ SV1050 @ ( c_Orderings_Oord__class_Omin @ SV1813 @ SV2358 @ SV190 ) @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6268]) ).
thf(6849,plain,
! [SV2359: $i,SV1814: $i,SV1051: $i,SV191: $i] :
( ( ( class_Orderings_Olinorder @ SV191 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1051 @ ( c_Orderings_Oord__class_Omin @ SV1814 @ SV2359 @ SV191 ) @ SV191 )
= ( c_Orderings_Oord__class_Omin @ SV1814 @ ( c_Orderings_Oord__class_Omin @ SV1051 @ SV2359 @ SV191 ) @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6269]) ).
thf(6850,plain,
! [SV2360: $i,SV1815: $i,SV1052: $i,SV192: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV192 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV192 )
| ( c_HOL_Oord__class_Oless @ SV1052 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV1815 ) @ SV2360 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SV2360 @ SV192 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV1815 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6270]) ).
thf(6851,plain,
! [SV1055: $i,SV1818: $i,SV195: $i] :
( ( ( c_lessequals @ SV195 @ SV1818 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1055 @ SV1818 @ tc_nat )
| ~ ( c_lessequals @ SV1055 @ SV195 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV195 @ SV1055 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1818 @ SV1055 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6273]) ).
thf(6852,plain,
! [SV1056: $i,SV1819: $i,SV196: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV196 @ SV1819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1056 @ SV1819 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1819 @ SV1056 @ tc_nat )
| ~ ( c_lessequals @ SV1819 @ SV196 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV196 @ SV1056 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6274]) ).
thf(6853,plain,
! [SV2361: $i,SV1821: $i,SV1059: $i,SV199: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV199 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1821 @ SV199 ) @ ( c_Power_Opower__class_Opower @ SV2361 @ SV1821 @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV1059 @ SV199 )
| ~ ( c_lessequals @ SV1059 @ SV2361 @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6275]) ).
thf(6854,plain,
! [SV2732: $i,SV2630: $i,SV2362: $i,SV1825: $i,SV1063: $i,SV203: $i] :
( ( ( c_List_Ofoldl @ SV203 @ SV1063 @ ( c_List_Olist_OCons @ SV1825 @ SV2362 @ SV2630 ) @ SV2732 @ SV2630 )
= ( c_List_Ofoldl @ SV203 @ ( hAPP @ ( hAPP @ SV203 @ SV1063 ) @ SV1825 ) @ SV2362 @ SV2732 @ SV2630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6279]) ).
thf(6855,plain,
! [SV1066: $i,SV206: $i,SV1827: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1827 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV206 @ SV1827 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1066 @ SV1827 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV206 @ SV1066 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6280]) ).
thf(6856,plain,
! [SV1067: $i,SV207: $i,SV1828: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1828 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1828 @ SV207 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1828 @ SV1067 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV207 @ SV1067 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6281]) ).
thf(6857,plain,
! [SV1068: $i,SV208: $i,SV1829: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1829 @ SV208 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1829 @ SV1068 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1829 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV208 @ SV1068 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6282]) ).
thf(6858,plain,
! [SV209: $i,SV1830: $i,SV1069: $i] :
( ( ( c_lessequals @ SV1069 @ SV1830 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV209 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SV1069 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SV1830 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6283]) ).
thf(6859,plain,
! [SV2364: $i,SV1831: $i,SV1070: $i,SV210: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV210 )
= $false )
| ( ( ( c_lessequals @ SV1070 @ SV1831 @ SV210 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1831 @ SV210 ) @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1070 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SV2364 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6284]) ).
thf(6860,plain,
! [SV2365: $i,SV1832: $i,SV1071: $i,SV211: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV211 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV1832 @ SV211 ) @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV2365 @ SV211 ) @ SV211 )
| ~ ( c_lessequals @ SV2365 @ SV1832 @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6285]) ).
thf(6861,plain,
! [SV2366: $i,SV1833: $i,SV1072: $i,SV212: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV212 )
= $false )
| ( ( ( c_lessequals @ SV1072 @ SV1833 @ SV212 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1072 @ SV212 ) @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1833 @ SV212 ) @ SV212 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SV2366 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6286]) ).
thf(6862,plain,
! [SV2367: $i,SV1834: $i,SV1073: $i,SV213: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV213 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV1834 @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV2367 @ SV213 ) @ SV213 )
| ~ ( c_lessequals @ SV1834 @ SV2367 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV1073 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6287]) ).
thf(6863,plain,
! [SV2368: $i,SV1835: $i,SV1074: $i,SV214: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV214 )
= $false )
| ( ( ( c_lessequals @ SV1074 @ SV1835 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV2368 @ SV214 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1074 @ SV214 ) @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1835 @ SV214 ) @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6288]) ).
thf(6864,plain,
! [SV2369: $i,SV1836: $i,SV1075: $i,SV215: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV215 )
= $false )
| ( ( ( c_lessequals @ SV1075 @ SV1836 @ SV215 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV2369 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1075 @ SV2369 @ SV215 ) @ ( c_HOL_Otimes__class_Otimes @ SV1836 @ SV2369 @ SV215 ) @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6289]) ).
thf(6865,plain,
! [SV216: $i,SV1076: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1076 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV216 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV216 @ SV1076 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6290]) ).
thf(6866,plain,
! [SV2370: $i,SV1839: $i,SV1079: $i,SV221: $i] :
( ( ( class_Orderings_Olinorder @ SV221 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1079 @ ( c_Orderings_Oord__class_Omax @ SV1839 @ SV2370 @ SV221 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ SV1079 @ SV1839 @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6291]) ).
thf(6867,plain,
! [SV2371: $i,SV1840: $i,SV1080: $i,SV222: $i] :
( ( ( class_Orderings_Olinorder @ SV222 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1080 @ ( c_Orderings_Oord__class_Omax @ SV1840 @ SV2371 @ SV222 ) @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ SV1080 @ SV2371 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6292]) ).
thf(6868,plain,
! [SV2372: $i,SV1841: $i,SV1081: $i,SV223: $i] :
( ( ( class_Orderings_Olinorder @ SV223 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1081 @ ( c_Orderings_Oord__class_Omax @ SV1841 @ SV2372 @ SV223 ) @ SV223 )
| ~ ( c_HOL_Oord__class_Oless @ SV1081 @ SV1841 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6293]) ).
thf(6869,plain,
! [SV2373: $i,SV1842: $i,SV1082: $i,SV224: $i] :
( ( ( class_Orderings_Olinorder @ SV224 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1082 @ ( c_Orderings_Oord__class_Omax @ SV1842 @ SV2373 @ SV224 ) @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ SV1082 @ SV2373 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6294]) ).
thf(6870,plain,
! [SV2374: $i,SV1843: $i,SV1083: $i,SV225: $i] :
( ( ( class_Orderings_Olinorder @ SV225 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1083 @ SV1843 @ SV225 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SV2374 @ SV225 ) @ SV1843 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6295]) ).
thf(6871,plain,
! [SV2375: $i,SV1844: $i,SV1084: $i,SV226: $i] :
( ( ( class_Orderings_Olinorder @ SV226 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1084 @ SV1844 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV2375 @ SV1084 @ SV226 ) @ SV1844 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6296]) ).
thf(6872,plain,
! [SV2631: $i,SV2377: $i,SV1847: $i,SV1087: $i,SV230: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV230 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SV1087 @ SV1847 @ SV230 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SV2377 @ SV1847 @ SV230 ) ) @ SV2631 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ SV1087 ) @ SV2377 ) @ SV1847 @ SV230 ) ) @ SV2631 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6298]) ).
thf(6873,plain,
! [SV1848: $i,SV1091: $i,SV234: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV1091 ) @ SV1848 ) @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1848 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV1091 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6299]) ).
thf(6874,plain,
! [SV2378: $i,SV1849: $i,SV1092: $i,SV235: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV235 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1092 @ SV1849 @ SV235 ) @ ( c_Power_Opower__class_Opower @ SV2378 @ SV1849 @ SV235 ) @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1849 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV235 ) @ SV1092 @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SV2378 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6300]) ).
thf(6875,plain,
! [SV1850: $i,SV236: $i,SV1093: $i] :
( ( ( SV1093
= ( c_HOL_Ozero__class_Ozero @ SV236 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ ( c_HOL_Otimes__class_Otimes @ SV1093 @ SV1093 @ SV236 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1850 @ SV1850 @ SV236 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV236 ) @ SV236 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6301]) ).
thf(6876,plain,
! [SV1851: $i,SV237: $i,SV1094: $i] :
( ( ( SV1094
= ( c_HOL_Ozero__class_Ozero @ SV237 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( c_HOL_Otimes__class_Otimes @ SV1851 @ SV1851 @ SV237 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1094 @ SV1094 @ SV237 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV237 ) @ SV237 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6302]) ).
thf(6877,plain,
! [SV2381: $i,SV1854: $i,SV1097: $i,SV240: $i] :
( ( ( hBOOL @ ( hAPP @ SV240 @ ( c_Nat_Onat_Onat__case @ SV1097 @ SV1854 @ ( c_Suc @ SV2381 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV240 @ ( hAPP @ SV1854 @ SV2381 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6303]) ).
thf(6878,plain,
! [SV2382: $i,SV1855: $i,SV1098: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ SV241 @ ( c_Nat_Onat_Onat__case @ SV1098 @ SV1855 @ ( c_Suc @ SV2382 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV241 @ ( hAPP @ SV1855 @ SV2382 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6304]) ).
thf(6879,plain,
! [SV2383: $i,SV1858: $i,SV1101: $i,SV244: $i] :
( ( ( class_Orderings_Olinorder @ SV244 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1101 @ SV1858 @ SV244 ) @ SV2383 @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ SV1101 @ SV2383 @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6305]) ).
thf(6880,plain,
! [SV2384: $i,SV1859: $i,SV1102: $i,SV245: $i] :
( ( ( class_Orderings_Olinorder @ SV245 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1102 @ SV1859 @ SV245 ) @ SV2384 @ SV245 )
| ~ ( c_HOL_Oord__class_Oless @ SV1859 @ SV2384 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6306]) ).
thf(6881,plain,
! [SV2385: $i,SV1861: $i,SV1104: $i,SV247: $i] :
( ( ( class_Orderings_Olinorder @ SV247 )
= $false )
| ( ( ( c_lessequals @ SV1104 @ SV1861 @ SV247 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2385 @ SV1104 @ SV247 ) @ SV1861 @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6308]) ).
thf(6882,plain,
! [SV2386: $i,SV1862: $i,SV1105: $i,SV248: $i] :
( ( ( class_Orderings_Olinorder @ SV248 )
= $false )
| ( ( ( c_lessequals @ SV1105 @ SV1862 @ SV248 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1105 @ SV2386 @ SV248 ) @ SV1862 @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6309]) ).
thf(6883,plain,
! [SV2387: $i,SV1863: $i,SV1106: $i,SV249: $i] :
( ( ( class_Orderings_Olinorder @ SV249 )
= $false )
| ( ( ( c_lessequals @ SV1106 @ ( c_Orderings_Oord__class_Omax @ SV1863 @ SV2387 @ SV249 ) @ SV249 )
| ~ ( c_lessequals @ SV1106 @ SV2387 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6310]) ).
thf(6884,plain,
! [SV2388: $i,SV1864: $i,SV1107: $i,SV250: $i] :
( ( ( class_Orderings_Olinorder @ SV250 )
= $false )
| ( ( ( c_lessequals @ SV1107 @ ( c_Orderings_Oord__class_Omax @ SV1864 @ SV2388 @ SV250 ) @ SV250 )
| ~ ( c_lessequals @ SV1107 @ SV1864 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6311]) ).
thf(6885,plain,
! [SV2389: $i,SV1865: $i,SV1108: $i,SV251: $i] :
( ( ( class_Orderings_Olinorder @ SV251 )
= $false )
| ( ( ( c_lessequals @ SV1108 @ ( c_Orderings_Oord__class_Omax @ SV1865 @ SV2389 @ SV251 ) @ SV251 )
| ~ ( c_lessequals @ SV1108 @ SV2389 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6312]) ).
thf(6886,plain,
! [SV2390: $i,SV1866: $i,SV1109: $i,SV252: $i] :
( ( ( class_Orderings_Olinorder @ SV252 )
= $false )
| ( ( ( c_lessequals @ SV1109 @ ( c_Orderings_Oord__class_Omax @ SV1866 @ SV2390 @ SV252 ) @ SV252 )
| ~ ( c_lessequals @ SV1109 @ SV1866 @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6313]) ).
thf(6887,plain,
! [SV2391: $i,SV1867: $i,SV1110: $i,SV253: $i] :
( ( ( class_Orderings_Olinorder @ SV253 )
= $false )
| ( ( ( c_lessequals @ SV1110 @ SV1867 @ SV253 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2391 @ SV1110 @ SV253 ) @ SV1867 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6314]) ).
thf(6888,plain,
! [SV2392: $i,SV1868: $i,SV1111: $i,SV254: $i] :
( ( ( class_Orderings_Olinorder @ SV254 )
= $false )
| ( ( ( c_lessequals @ SV1111 @ SV1868 @ SV254 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1111 @ SV2392 @ SV254 ) @ SV1868 @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6315]) ).
thf(6889,plain,
! [SV1871: $i,SV1114: $i,SV257: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ ( c_Power_Opower__class_Opower @ SV1114 @ SV1871 @ SV257 ) @ SV257 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV1114 @ SV257 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6318]) ).
thf(6890,plain,
! [SV2393: $i,SV1872: $i,SV1115: $i,SV258: $i] :
( ( ( class_Orderings_Olinorder @ SV258 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1115 @ SV1872 @ SV258 )
| ( c_HOL_Oord__class_Oless @ SV1115 @ SV2393 @ SV258 )
| ~ ( c_HOL_Oord__class_Oless @ SV1115 @ ( c_Orderings_Oord__class_Omax @ SV2393 @ SV1872 @ SV258 ) @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6319]) ).
thf(6891,plain,
! [SV1873: $i,SV261: $i,SV1118: $i] :
( ( ( c_InductTermi_OIT @ SV1118 )
= $false )
| ( ( ~ ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV261 @ SV1118 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV261 ) ) @ SV1118 ) @ SV1873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6320]) ).
thf(6892,plain,
! [SV1876: $i,SV1121: $i,SV264: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV264 ) @ ( c_HOL_Otimes__class_Otimes @ SV1121 @ SV1121 @ SV264 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1876 @ SV1876 @ SV264 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV264 )
= $false )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6321]) ).
thf(6893,plain,
! [SV2632: $i,SV2396: $i,SV1877: $i,SV1122: $i,SV265: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV265 @ SV1122 @ tc_nat ) @ SV1877 @ tc_nat ) ) @ SV2396 ) @ SV2632 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV265 @ SV1877 @ tc_nat ) ) @ SV2396 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV1877 @ tc_nat ) ) @ SV2632 ) @ tc_nat )
| ~ ( c_lessequals @ SV1122 @ SV265 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6322]) ).
thf(6894,plain,
! [SV2633: $i,SV2397: $i,SV1878: $i,SV1123: $i,SV266: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV266 @ SV1123 @ tc_nat ) ) @ SV1878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2397 @ SV1123 @ tc_nat ) ) @ SV2633 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV266 @ SV2397 @ tc_nat ) @ SV1123 @ tc_nat ) ) @ SV1878 ) @ SV2633 @ tc_nat )
| ~ ( c_lessequals @ SV2397 @ SV266 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6323]) ).
thf(6895,plain,
! [SV2634: $i,SV2398: $i,SV1879: $i,SV1124: $i,SV267: $i] :
( ( ( c_lessequals @ SV267 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1124 @ SV1879 @ tc_nat ) @ SV2398 @ tc_nat ) ) @ SV2634 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1879 @ SV2398 @ tc_nat ) ) @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1124 @ SV2398 @ tc_nat ) ) @ SV2634 ) @ tc_nat )
| ~ ( c_lessequals @ SV1879 @ SV1124 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6324]) ).
thf(6896,plain,
! [SV2635: $i,SV2399: $i,SV1880: $i,SV1125: $i,SV268: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SV1125 @ tc_nat ) ) @ SV1880 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2399 @ SV1125 @ tc_nat ) ) @ SV2635 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1880 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2399 @ SV268 @ tc_nat ) @ SV1125 @ tc_nat ) ) @ SV2635 ) @ tc_nat )
| ~ ( c_lessequals @ SV268 @ SV2399 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6325]) ).
thf(6897,plain,
! [SV2400: $i,SV1882: $i,SV1127: $i,SV270: $i] :
( ( ( class_Orderings_Olinorder @ SV270 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1127 @ SV1882 @ SV270 )
| ( c_HOL_Oord__class_Oless @ SV2400 @ SV1882 @ SV270 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV2400 @ SV1127 @ SV270 ) @ SV1882 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6327]) ).
thf(6898,plain,
! [SV1883: $i,SV1129: $i,SV272: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1129 ) @ SV1883 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1883 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
| ~ ( c_lessequals @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6328]) ).
thf(6899,plain,
! [SV1884: $i,SV1130: $i,SV273: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV1130 ) @ SV1884 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
= $true )
| ( ( ~ ( c_lessequals @ SV1884 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
| ~ ( c_HOL_Oord__class_Oless @ SV1130 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6329]) ).
thf(6900,plain,
! [SV2636: $i,SV2401: $i,SV1887: $i,SV1136: $i,SV280: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV280 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1136 @ SV1887 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SV2401 @ SV2636 @ SV280 ) @ SV280 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1136 @ SV2401 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SV1887 @ SV2636 @ SV280 ) @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6335]) ).
thf(6901,plain,
! [SV2637: $i,SV2402: $i,SV1888: $i,SV1137: $i,SV281: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV281 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1137 @ SV1888 @ SV281 ) @ ( c_HOL_Otimes__class_Otimes @ SV2402 @ SV2637 @ SV281 ) @ SV281 )
= ( c_HOL_Otimes__class_Otimes @ SV1137 @ ( c_HOL_Otimes__class_Otimes @ SV1888 @ ( c_HOL_Otimes__class_Otimes @ SV2402 @ SV2637 @ SV281 ) @ SV281 ) @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6336]) ).
thf(6902,plain,
! [SV2638: $i,SV2403: $i,SV1889: $i,SV1138: $i,SV282: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV282 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1138 @ SV1889 @ SV282 ) @ ( c_HOL_Otimes__class_Otimes @ SV2403 @ SV2638 @ SV282 ) @ SV282 )
= ( c_HOL_Otimes__class_Otimes @ SV2403 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1138 @ SV1889 @ SV282 ) @ SV2638 @ SV282 ) @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6337]) ).
thf(6903,plain,
! [SV288: $i,SV1894: $i,SV1144: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1144 @ SV1894 @ SV288 )
= $true )
| ( ( ( c_lessequals @ SV1894 @ SV1144 @ SV288 )
| ~ ( c_lessequals @ SV1144 @ SV1894 @ SV288 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6341]) ).
thf(6904,plain,
! [SV1895: $i,SV1151: $i,SV297: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV297 ) @ SV1151 ) @ SV1895 ) @ SV297 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1895 @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1151 @ SV297 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6345]) ).
thf(6905,plain,
! [SV303: $i,SV1897: $i,SV1157: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1157 @ SV1897 @ SV303 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1897 @ SV1157 @ SV303 )
| ( SV1897 = SV1157 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6347]) ).
thf(6906,plain,
! [SV304: $i,SV1898: $i,SV1158: $i] :
( ( ( SV1158 = SV1898 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1898 @ SV1158 @ SV304 )
| ( c_HOL_Oord__class_Oless @ SV1158 @ SV1898 @ SV304 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6348]) ).
thf(6907,plain,
! [SV1159: $i,SV305: $i] :
( ( ( c_lessequals @ SV305 @ SV1159 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1159 @ SV305 @ tc_nat )
= $false )
| ( ( SV305 = SV1159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6349]) ).
thf(6908,plain,
! [SV307: $i,SV1161: $i,SV1899: $i] :
( ( ( SV1899 = SV1161 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1899 @ SV1161 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1161 @ SV1899 @ tc_nat )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV307 @ SV1161 ) @ SV1899 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6350]) ).
thf(6909,plain,
! [SV2639: $i,SV2405: $i,SV1900: $i,SV1162: $i,SV308: $i] :
( ( ( SV308 = SV1162 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2405 ) @ SV2639 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1162 )
| ~ ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2405 ) @ SV2639 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6351]) ).
thf(6910,plain,
! [SV310: $i,SV1901: $i,SV1164: $i] :
( ( ( SV1164 = SV1901 )
= $true )
| ( ( ~ ( c_lessequals @ SV1901 @ SV1164 @ SV310 )
| ~ ( c_lessequals @ SV1164 @ SV1901 @ SV310 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV310 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6352]) ).
thf(6911,plain,
! [SV311: $i,SV1902: $i,SV1165: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1165 @ SV1902 @ SV311 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1902 @ SV1165 @ SV311 )
| ( SV1902 = SV1165 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6353]) ).
thf(6912,plain,
! [SV312: $i,SV1903: $i,SV1166: $i] :
( ( ( SV1166 = SV1903 )
= $true )
| ( ( ~ ( c_lessequals @ SV1903 @ SV1166 @ SV312 )
| ~ ( c_lessequals @ SV1166 @ SV1903 @ SV312 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6354]) ).
thf(6913,plain,
! [SV313: $i,SV1904: $i,SV1167: $i] :
( ( ( SV1167 = SV1904 )
= $true )
| ( ( ~ ( c_lessequals @ SV1167 @ SV1904 @ SV313 )
| ~ ( c_lessequals @ SV1904 @ SV1167 @ SV313 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6355]) ).
thf(6914,plain,
! [SV315: $i,SV1906: $i,SV1169: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1169 @ SV1906 @ SV315 )
= $true )
| ( ( ( SV1906 = SV1169 )
| ( c_HOL_Oord__class_Oless @ SV1906 @ SV1169 @ SV315 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6356]) ).
thf(6915,plain,
! [SV316: $i,SV1907: $i,SV1170: $i] :
( ( ( SV1170 = SV1907 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1170 @ SV1907 @ SV316 )
| ( c_HOL_Oord__class_Oless @ SV1907 @ SV1170 @ SV316 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6357]) ).
thf(6916,plain,
! [SV317: $i,SV1908: $i,SV1171: $i] :
( ( ( c_lessequals @ SV1171 @ SV1908 @ SV317 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1908 @ SV317 ) @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6358]) ).
thf(6917,plain,
! [SV318: $i,SV1909: $i,SV1172: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1172 @ SV1909 @ SV318 ) @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV318 )
= $true )
| ( ( ~ ( c_lessequals @ SV1172 @ SV1909 @ SV318 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6359]) ).
thf(6918,plain,
! [SV2640: $i,SV2407: $i,SV1910: $i,SV1174: $i,SV320: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV1174 ) @ SV1910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV2407 ) @ SV2640 ) @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SV1910 @ SV2640 @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SV2407 @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6360]) ).
thf(6919,plain,
! [SV1911: $i,SV321: $i,SV2408: $i,SV1175: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1175 @ SV2408 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV321 @ SV1911 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV1175 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1911 ) @ SV2408 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6361]) ).
thf(6920,plain,
! [SV324: $i,SV1912: $i,SV1178: $i] :
( ( ( c_lessequals @ SV1178 @ SV1912 @ SV324 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1178 @ SV1912 @ SV324 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6362]) ).
thf(6921,plain,
! [SV325: $i,SV1913: $i,SV1179: $i] :
( ( ( c_lessequals @ SV1179 @ SV1913 @ SV325 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1179 @ SV1913 @ SV325 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6363]) ).
thf(6922,plain,
! [SV2409: $i,SV1914: $i,SV1180: $i,SV326: $i] :
( ( ( class_Orderings_Olinorder @ SV326 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1180 @ SV1914 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ SV1180 @ ( c_Orderings_Oord__class_Omin @ SV1914 @ SV2409 @ SV326 ) @ SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6364]) ).
thf(6923,plain,
! [SV2410: $i,SV1915: $i,SV1181: $i,SV327: $i] :
( ( ( class_Orderings_Olinorder @ SV327 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1181 @ SV1915 @ SV327 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_Orderings_Oord__class_Omin @ SV2410 @ SV1915 @ SV327 ) @ SV327 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6365]) ).
thf(6924,plain,
! [SV2411: $i,SV1916: $i,SV1182: $i,SV328: $i] :
( ( ( class_Orderings_Olinorder @ SV328 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1182 @ SV1916 @ SV328 ) @ SV2411 @ SV328 )
| ~ ( c_HOL_Oord__class_Oless @ SV1182 @ SV2411 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6366]) ).
thf(6925,plain,
! [SV2412: $i,SV1917: $i,SV1183: $i,SV329: $i] :
( ( ( class_Orderings_Olinorder @ SV329 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1183 @ SV1917 @ SV329 ) @ SV2412 @ SV329 )
| ~ ( c_HOL_Oord__class_Oless @ SV1917 @ SV2412 @ SV329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6367]) ).
thf(6926,plain,
! [SV330: $i,SV1918: $i,SV1184: $i] :
( ( ( c_lessequals @ SV1184 @ SV1918 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1184 @ SV330 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV330 @ SV1184 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1918 @ SV1184 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV330 @ SV1918 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6368]) ).
thf(6927,plain,
! [SV1920: $i,SV1186: $i,SV332: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV332 ) @ SV1186 ) @ SV1920 ) @ SV332 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1920 @ SV332 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1186 @ SV332 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6369]) ).
thf(6928,plain,
! [SV1921: $i,SV1187: $i,SV333: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV333 ) @ SV1187 ) @ SV1921 ) @ SV333 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1921 @ SV333 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1187 @ SV333 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV333 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6370]) ).
thf(6929,plain,
! [SV1922: $i,SV334: $i,SV1188: $i] :
( ( ( c_lessequals @ SV1188 @ SV334 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV334 @ SV1922 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV334 @ SV1188 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1922 @ SV1188 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6371]) ).
thf(6930,plain,
! [SV335: $i,SV1923: $i,SV1189: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1189 @ SV1923 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
= $true )
| ( ( ~ ( c_lessequals @ SV1923 @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV1189 @ SV335 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV335 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6372]) ).
thf(6931,plain,
! [SV336: $i,SV1924: $i,SV1190: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1190 @ SV1924 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV1924 @ SV336 )
| ~ ( c_lessequals @ SV1190 @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV336 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6373]) ).
thf(6932,plain,
! [SV337: $i,SV1925: $i,SV1191: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1191 @ SV1925 @ SV337 ) @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
= $true )
| ( ( ~ ( c_lessequals @ SV1925 @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV1191 @ SV337 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV337 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6374]) ).
thf(6933,plain,
! [SV338: $i,SV1926: $i,SV1192: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1192 @ SV1926 @ SV338 ) @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV1926 @ SV338 )
| ~ ( c_lessequals @ SV1192 @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV338 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6375]) ).
thf(6934,plain,
! [SV339: $i,SV1927: $i,SV1193: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1193 @ SV1927 @ SV339 ) @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
= $true )
| ( ( ~ ( c_lessequals @ SV1927 @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV1193 @ SV339 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6376]) ).
thf(6935,plain,
! [SV340: $i,SV1928: $i,SV1194: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1928 @ SV340 ) @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV1928 @ SV340 )
| ~ ( c_lessequals @ SV1194 @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6377]) ).
thf(6936,plain,
! [SV341: $i,SV1929: $i,SV1195: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1195 @ SV1929 @ SV341 ) @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
= $true )
| ( ( ~ ( c_lessequals @ SV1195 @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV1929 @ SV341 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV341 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6378]) ).
thf(6937,plain,
! [SV2415: $i,SV1934: $i,SV1204: $i,SV350: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV350 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ ( c_Orderings_Oord__class_Omin @ SV1204 @ SV1934 @ SV350 ) ) @ SV2415 )
= ( c_Orderings_Oord__class_Omin @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV1204 ) @ SV2415 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV350 ) @ SV1934 ) @ SV2415 ) @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6384]) ).
thf(6938,plain,
! [SV2733: $i,SV2641: $i,SV2416: $i,SV1936: $i,SV1206: $i,SV352: $i] :
( ( ! [SY7111: $i,SY7112: $i,SY7113: $i] :
( ( ( hAPP @ ( hAPP @ SV352 @ ( hAPP @ ( hAPP @ SV1206 @ SV1936 ) @ SV2416 ) ) @ SV2641 )
= ( hAPP @ ( hAPP @ SV1206 @ ( hAPP @ ( hAPP @ SV352 @ SV1936 ) @ SV2641 ) ) @ ( hAPP @ ( hAPP @ SV352 @ SV2416 ) @ SV2641 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2733 @ SV1206 @ SV352 @ SY7111 @ SY7112 @ SY7113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6386]) ).
thf(6939,plain,
! [SV2734: $i,SV2642: $i,SV2417: $i,SV1937: $i,SV1207: $i,SV353: $i] :
( ( ! [SY7114: $i,SY7115: $i,SY7116: $i] :
( ( ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ ( hAPP @ ( hAPP @ SV1937 @ SV2417 ) @ SV2642 ) )
= ( hAPP @ ( hAPP @ SV1937 @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2417 ) ) @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2642 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1937 @ SV353 @ SV2734 @ SY7114 @ SY7115 @ SY7116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6387]) ).
thf(6940,plain,
! [SV2735: $i,SV2643: $i,SV2418: $i,SV1938: $i,SV1208: $i,SV354: $i] :
( ( ! [SY7117: $i,SY7118: $i] :
( ( ( hAPP @ ( hAPP @ SV354 @ SV1208 ) @ SV1938 )
= ( hAPP @ ( hAPP @ SV354 @ SV1938 ) @ SV1208 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2418 @ SV354 @ SV2643 @ SV2735 @ SY7117 @ SY7118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6388]) ).
thf(6941,plain,
! [SV2736: $i,SV2644: $i,SV2419: $i,SV1939: $i,SV1209: $i,SV355: $i] :
( ( ! [SY7119: $i,SY7120: $i,SY7121: $i] :
( ( ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ ( hAPP @ ( hAPP @ SV355 @ SV1939 ) @ SV2419 ) )
= ( hAPP @ ( hAPP @ SV355 @ ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ SV1939 ) ) @ SV2419 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2644 @ SV355 @ SV2736 @ SY7119 @ SY7120 @ SY7121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6389]) ).
thf(6942,plain,
! [SV2737: $i,SV2645: $i,SV2420: $i,SV1940: $i,SV1210: $i,SV356: $i] :
( ( ! [SY7122: $i] :
( ( ( hAPP @ ( hAPP @ SV356 @ SV1210 ) @ SV1940 )
= SV1940 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2420 @ SV356 @ SV2645 @ SV2737 @ SV1210 @ SY7122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6390]) ).
thf(6943,plain,
! [SV2738: $i,SV2646: $i,SV2421: $i,SV1941: $i,SV1211: $i,SV357: $i] :
( ( ! [SY7123: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV1211 ) @ SV1941 )
= SV1211 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2421 @ SV357 @ SV2646 @ SV1211 @ SV2738 @ SY7123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6391]) ).
thf(6944,plain,
! [SV2739: $i,SV2647: $i,SV2422: $i,SV1942: $i,SV1212: $i,SV358: $i] :
( ( ! [SY7124: $i,SY7125: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV1212 ) @ SV1942 )
= ( hAPP @ ( hAPP @ SV358 @ SV1942 ) @ SV1212 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV358 @ SV2422 @ SV2647 @ SV2739 @ SY7124 @ SY7125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6392]) ).
thf(6945,plain,
! [SV2740: $i,SV2648: $i,SV2423: $i,SV1943: $i,SV1213: $i,SV359: $i] :
( ( ! [SY7126: $i,SY7127: $i,SY7128: $i] :
( ( ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ ( hAPP @ ( hAPP @ SV359 @ SV1943 ) @ SV2423 ) )
= ( hAPP @ ( hAPP @ SV359 @ ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ SV1943 ) ) @ SV2423 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV359 @ SV2648 @ SV2740 @ SY7126 @ SY7127 @ SY7128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6393]) ).
thf(6946,plain,
! [SV2741: $i,SV2649: $i,SV2424: $i,SV1944: $i,SV1214: $i,SV360: $i] :
( ( ! [SY7129: $i] :
( ( ( hAPP @ ( hAPP @ SV360 @ SV1214 ) @ SV1944 )
= SV1944 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV360 @ SV2424 @ SV2649 @ SV1214 @ SV2741 @ SY7129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6394]) ).
thf(6947,plain,
! [SV2742: $i,SV2650: $i,SV2425: $i,SV1945: $i,SV1215: $i,SV361: $i] :
( ( ! [SY7130: $i,SY7131: $i,SY7132: $i] :
( ( ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ ( hAPP @ ( hAPP @ SV361 @ SV1945 ) @ SV2425 ) )
= ( hAPP @ ( hAPP @ SV361 @ ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ SV1945 ) ) @ SV2425 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV361 @ SV2650 @ SV2742 @ SY7130 @ SY7131 @ SY7132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6395]) ).
thf(6948,plain,
! [SV2743: $i,SV2651: $i,SV2426: $i,SV1946: $i,SV1216: $i,SV362: $i] :
( ( ! [SY7133: $i,SY7134: $i] :
( ( ( hAPP @ ( hAPP @ SV362 @ SV1216 ) @ SV1946 )
= ( hAPP @ ( hAPP @ SV362 @ SV1946 ) @ SV1216 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV362 @ SV2426 @ SV2651 @ SV2743 @ SY7133 @ SY7134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6396]) ).
thf(6949,plain,
! [SV2744: $i,SV2652: $i,SV2427: $i,SV1947: $i,SV1217: $i,SV363: $i] :
( ( ! [SY7135: $i,SY7136: $i,SY7137: $i] :
( ( ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV1947 ) ) @ SV2427 )
= ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV2427 ) ) @ SV1947 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV363 @ SV2652 @ SV2744 @ SY7135 @ SY7136 @ SY7137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6397]) ).
thf(6950,plain,
! [SV2745: $i,SV2653: $i,SV2428: $i,SV1948: $i,SV1218: $i,SV364: $i] :
( ( ! [SY7138: $i,SY7139: $i,SY7140: $i] :
( ( ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ SV2428 ) )
= ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ SV2428 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV364 @ SV2653 @ SV2745 @ SY7138 @ SY7139 @ SY7140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6398]) ).
thf(6951,plain,
! [SV2746: $i,SV2654: $i,SV2429: $i,SV1949: $i,SV1219: $i,SV365: $i] :
( ( ! [SY7141: $i,SY7142: $i,SY7143: $i] :
( ( ( hAPP @ ( hAPP @ SV365 @ ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ SV1949 ) ) @ SV2429 )
= ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ ( hAPP @ ( hAPP @ SV365 @ SV1949 ) @ SV2429 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV365 @ SV2654 @ SV2746 @ SY7141 @ SY7142 @ SY7143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6399]) ).
thf(6952,plain,
! [SV2747: $i,SV2655: $i,SV2430: $i,SV1950: $i,SV1220: $i,SV366: $i] :
( ( ! [SY7144: $i,SY7145: $i,SY7146: $i,SY7147: $i] :
( ( ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV1950 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV2430 ) @ SV2655 ) )
= ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV2430 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV1950 ) @ SV2655 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV366 @ SV2747 @ SY7144 @ SY7145 @ SY7146 @ SY7147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6400]) ).
thf(6953,plain,
! [SV2748: $i,SV2656: $i,SV2431: $i,SV1951: $i,SV1221: $i,SV367: $i] :
( ( ! [SY7148: $i,SY7149: $i,SY7150: $i] :
( ( ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ SV2431 ) )
= ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ SV2431 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2656 @ SV367 @ SV2748 @ SY7148 @ SY7149 @ SY7150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6401]) ).
thf(6954,plain,
! [SV2749: $i,SV2657: $i,SV2432: $i,SV1952: $i,SV1222: $i,SV368: $i] :
( ( ! [SY7151: $i,SY7152: $i,SY7153: $i] :
( ( ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ ( hAPP @ ( hAPP @ SV368 @ SV1952 ) @ SV2432 ) )
= ( hAPP @ ( hAPP @ SV368 @ ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ SV1952 ) ) @ SV2432 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2657 @ SV368 @ SV2749 @ SY7151 @ SY7152 @ SY7153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6402]) ).
thf(6955,plain,
! [SV2750: $i,SV2658: $i,SV2433: $i,SV1953: $i,SV1223: $i,SV369: $i] :
( ( ! [SY7154: $i,SY7155: $i,SY7156: $i] :
( ( ( hAPP @ ( hAPP @ SV369 @ ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ SV1953 ) ) @ SV2433 )
= ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ ( hAPP @ ( hAPP @ SV369 @ SV1953 ) @ SV2433 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2658 @ SV369 @ SV2750 @ SY7154 @ SY7155 @ SY7156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6403]) ).
thf(6956,plain,
! [SV2751: $i,SV2659: $i,SV2434: $i,SV1954: $i,SV1224: $i,SV370: $i] :
( ( ! [SY7157: $i,SY7158: $i,SY7159: $i] :
( ( ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV1954 ) ) @ SV2434 )
= ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV2434 ) ) @ SV1954 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2659 @ SV370 @ SV2751 @ SY7157 @ SY7158 @ SY7159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6404]) ).
thf(6957,plain,
! [SV2752: $i,SV2660: $i,SV2435: $i,SV1955: $i,SV1225: $i,SV371: $i] :
( ( ! [SY7160: $i,SY7161: $i,SY7162: $i,SY7163: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ SV2660 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ SV2660 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2752 @ SV371 @ SY7160 @ SY7161 @ SY7162 @ SY7163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6405]) ).
thf(6958,plain,
! [SV2753: $i,SV2661: $i,SV2436: $i,SV1956: $i,SV1226: $i,SV372: $i] :
( ( ! [SY7164: $i,SY7165: $i,SY7166: $i,SY7167: $i] :
( ( ( hAPP @ ( hAPP @ SV372 @ ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ SV1956 ) ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) )
= ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ ( hAPP @ ( hAPP @ SV372 @ SV1956 ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2753 @ SV372 @ SY7164 @ SY7165 @ SY7166 @ SY7167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6406]) ).
thf(6959,plain,
! [SV2754: $i,SV2662: $i,SV2437: $i,SV1957: $i,SV1227: $i,SV373: $i] :
( ( ! [SY7168: $i,SY7169: $i,SY7170: $i,SY7171: $i] :
( ( ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV1957 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV2437 ) @ SV2662 ) )
= ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV2437 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV1957 ) @ SV2662 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2754 @ SV373 @ SY7168 @ SY7169 @ SY7170 @ SY7171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6407]) ).
thf(6960,plain,
! [SV2755: $i,SV2663: $i,SV2438: $i,SV1958: $i,SV1228: $i,SV374: $i] :
( ( ! [SY7172: $i] :
( ( ( hAPP @ ( hAPP @ SV374 @ SV1228 ) @ SV1958 )
= SV1228 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2438 @ SV374 @ SV2663 @ SV2755 @ SV1958 @ SY7172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6408]) ).
thf(6961,plain,
! [SV2756: $i,SV2664: $i,SV2439: $i,SV1959: $i,SV1229: $i,SV375: $i] :
( ( ! [SY7173: $i] :
( ( ( hAPP @ ( hAPP @ SV375 @ SV1229 ) @ SV1959 )
= SV1959 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2439 @ SV375 @ SV2664 @ SV2756 @ SV1229 @ SY7173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6409]) ).
thf(6962,plain,
! [SV2757: $i,SV2665: $i,SV2440: $i,SV1960: $i,SV1230: $i,SV376: $i] :
( ( ! [SY7174: $i] :
( ( ( hAPP @ ( hAPP @ SV376 @ SV1230 ) @ SV1960 )
= SV1960 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2440 @ SV376 @ SV2665 @ SV1960 @ SV2757 @ SY7174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6410]) ).
thf(6963,plain,
! [SV2758: $i,SV2666: $i,SV2441: $i,SV1961: $i,SV1231: $i,SV377: $i] :
( ( ! [SY7175: $i] :
( ( ( hAPP @ ( hAPP @ SV377 @ SV1231 ) @ SV1961 )
= SV1231 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2441 @ SV377 @ SV2666 @ SV1231 @ SV2758 @ SY7175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6411]) ).
thf(6964,plain,
! [SV2759: $i,SV2667: $i,SV2442: $i,SV1962: $i,SV1232: $i,SV378: $i] :
( ( ! [SY7176: $i,SY7177: $i,SY7178: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ ( hAPP @ ( hAPP @ SV1232 @ SV1962 ) @ SV2442 ) ) @ SV2667 )
= ( hAPP @ ( hAPP @ SV1232 @ ( hAPP @ ( hAPP @ SV378 @ SV1962 ) @ SV2667 ) ) @ ( hAPP @ ( hAPP @ SV378 @ SV2442 ) @ SV2667 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1232 @ SV378 @ SV2759 @ SY7176 @ SY7177 @ SY7178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6412]) ).
thf(6965,plain,
! [SV2760: $i,SV2668: $i,SV2443: $i,SV1963: $i,SV1233: $i,SV379: $i] :
( ( ! [SY7179: $i,SY7180: $i] :
( ( ( hAPP @ ( hAPP @ SV379 @ SV1233 ) @ SV1963 )
= ( hAPP @ ( hAPP @ SV379 @ SV1963 ) @ SV1233 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2443 @ SV379 @ SV2668 @ SV2760 @ SY7179 @ SY7180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6413]) ).
thf(6966,plain,
! [SV2761: $i,SV2669: $i,SV2444: $i,SV1964: $i,SV1234: $i,SV380: $i] :
( ( ! [SY7181: $i] :
( ( ( hAPP @ ( hAPP @ SV380 @ SV1234 ) @ SV1964 )
= SV1234 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV380 @ SV2444 @ SV2669 @ SV1964 @ SV2761 @ SY7181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6414]) ).
thf(6967,plain,
! [SV2762: $i,SV2670: $i,SV2445: $i,SV1965: $i,SV1235: $i,SV381: $i] :
( ( ! [SY7182: $i] :
( ( ( hAPP @ ( hAPP @ SV381 @ SV1235 ) @ SV1965 )
= SV1965 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV381 @ SV2445 @ SV2670 @ SV1235 @ SV2762 @ SY7182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6415]) ).
thf(6968,plain,
! [SV2763: $i,SV2671: $i,SV2446: $i,SV1966: $i,SV1236: $i,SV382: $i] :
( ( ! [SY7183: $i] :
( ( ( hAPP @ ( hAPP @ SV382 @ SV1236 ) @ SV1236 )
= ( hAPP @ ( hAPP @ SV1966 @ ( hAPP @ ( hAPP @ SV382 @ SV2446 ) @ SV2446 ) ) @ SV1236 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV382 @ SV1966 @ SV2671 @ SV2763 @ SV2446 @ SY7183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6416]) ).
thf(6969,plain,
! [SV2764: $i,SV2672: $i,SV2447: $i,SV1967: $i,SV1237: $i,SV383: $i] :
( ( ! [SY7184: $i,SY7185: $i] :
( ( ( hAPP @ ( hAPP @ SV383 @ SV1237 ) @ ( hAPP @ ( hAPP @ SV1967 @ SV2447 ) @ SV1237 ) )
= ( hAPP @ ( hAPP @ SV1967 @ ( hAPP @ ( hAPP @ SV383 @ SV2447 ) @ SV2672 ) ) @ SV1237 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV383 @ SV1967 @ SV2764 @ SY7184 @ SV2672 @ SY7185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6417]) ).
thf(6970,plain,
! [SV2765: $i,SV2673: $i,SV2448: $i,SV1968: $i,SV1238: $i,SV384: $i] :
( ( ! [SY7186: $i,SY7187: $i] :
( ( ( hAPP @ ( hAPP @ SV384 @ ( hAPP @ ( hAPP @ SV1238 @ SV1968 ) @ SV2448 ) ) @ SV2448 )
= ( hAPP @ ( hAPP @ SV1238 @ ( hAPP @ ( hAPP @ SV384 @ SV1968 ) @ SV2673 ) ) @ SV2448 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV384 @ SV1238 @ SV2765 @ SY7186 @ SV2673 @ SY7187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6418]) ).
thf(6971,plain,
! [SV2766: $i,SV2674: $i,SV2449: $i,SV1969: $i,SV1239: $i,SV385: $i] :
( ( ! [SY7188: $i,SY7189: $i,SY7190: $i] :
( ( ( hAPP @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ SV1239 @ SV1969 ) @ SV2449 ) ) @ ( hAPP @ ( hAPP @ SV1239 @ SV2674 ) @ SV2449 ) )
= ( hAPP @ ( hAPP @ SV1239 @ ( hAPP @ ( hAPP @ SV385 @ SV1969 ) @ SV2674 ) ) @ SV2449 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV385 @ SV1239 @ SV2766 @ SY7188 @ SY7189 @ SY7190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6419]) ).
thf(6972,plain,
! [SV2450: $i,SV1970: $i,SV1240: $i,SV386: $i] :
( ( ( hBOOL @ ( hAPP @ SV386 @ ( c_Type_Otype_Otype__case @ SV1240 @ SV1970 @ ( c_Type_Otype_OAtom @ SV2450 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV386 @ ( hAPP @ SV1240 @ SV2450 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6420]) ).
thf(6973,plain,
! [SV2451: $i,SV1971: $i,SV1241: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ SV387 @ ( c_Type_Otype_Otype__case @ SV1241 @ SV1971 @ ( c_Type_Otype_OAtom @ SV2451 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV387 @ ( hAPP @ SV1241 @ SV2451 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6421]) ).
thf(6974,plain,
! [SV1975: $i,SV1245: $i,SV391: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV391 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV391 ) @ ( c_HOL_Otimes__class_Otimes @ SV1245 @ SV1245 @ SV391 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1975 @ SV1975 @ SV391 ) ) @ SV391 )
= $true )
| ( ( SV1245
= ( c_HOL_Ozero__class_Ozero @ SV391 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6424]) ).
thf(6975,plain,
! [SV1976: $i,SV1246: $i,SV392: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV392 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV392 ) @ ( c_HOL_Otimes__class_Otimes @ SV1246 @ SV1246 @ SV392 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1976 @ SV1976 @ SV392 ) ) @ SV392 )
= $true )
| ( ( SV1976
= ( c_HOL_Ozero__class_Ozero @ SV392 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV392 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6425]) ).
thf(6976,plain,
! [SV2675: $i,SV2452: $i,SV1977: $i,SV1247: $i,SV394: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV394 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1247 ) @ SV1977 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV2452 ) @ SV2675 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1247 ) @ SV2452 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1977 ) @ SV2675 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6426]) ).
thf(6977,plain,
! [SV2454: $i,SV1982: $i,SV1253: $i,SV401: $i] :
( ( ( class_Orderings_Olinorder @ SV401 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV1253 @ SV1982 @ SV401 ) @ ( c_Orderings_Oord__class_Omin @ SV1253 @ SV2454 @ SV401 ) @ SV401 ) @ ( c_Orderings_Oord__class_Omin @ SV1253 @ ( c_Orderings_Oord__class_Omax @ SV1982 @ SV2454 @ SV401 ) @ SV401 ) @ SV401 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6431]) ).
thf(6978,plain,
! [SV2455: $i,SV1984: $i,SV1256: $i,SV406: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV406 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1256 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1256 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV1984 @ SV406 ) @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV2455 @ SV406 ) @ SV406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6433]) ).
thf(6979,plain,
! [SV2456: $i,SV1985: $i,SV1257: $i,SV407: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV407 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1257 @ SV1985 @ SV407 )
| ( c_HOL_Oord__class_Oless @ SV1985 @ SV1257 @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2456 @ SV1985 @ SV407 ) @ ( c_HOL_Otimes__class_Otimes @ SV2456 @ SV1257 @ SV407 ) @ SV407 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6434]) ).
thf(6980,plain,
! [SV2457: $i,SV1986: $i,SV1258: $i,SV408: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV408 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1258 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV1258 @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1986 @ SV1258 @ SV408 ) @ ( c_HOL_Otimes__class_Otimes @ SV2457 @ SV1258 @ SV408 ) @ SV408 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6435]) ).
thf(6981,plain,
! [SV2458: $i,SV1987: $i,SV1259: $i,SV409: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV409 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1259 @ SV1987 @ SV409 )
| ( c_HOL_Oord__class_Oless @ SV1987 @ SV1259 @ SV409 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1987 @ SV2458 @ SV409 ) @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SV2458 @ SV409 ) @ SV409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6436]) ).
thf(6982,plain,
! [SV414: $i,SV1989: $i,SV1264: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1264 @ SV1989 @ SV414 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1264 @ SV1989 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV414 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6438]) ).
thf(6983,plain,
! [SV415: $i,SV1990: $i,SV1265: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SV1990 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1265 @ SV1990 @ SV415 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV415 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6439]) ).
thf(6984,plain,
! [SV1991: $i,SV416: $i,SV1266: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1266 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1991 @ SV416 ) @ SV416 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1266 @ SV1991 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6440]) ).
thf(6985,plain,
! [SV417: $i,SV1992: $i,SV1267: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1267 @ SV1992 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1267 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1992 @ SV417 ) @ SV417 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV417 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6441]) ).
thf(6986,plain,
! [SV420: $i,SV1268: $i,SV1993: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1993 @ SV1268 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV420 @ SV1993 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV420 ) @ SV1268 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6442]) ).
thf(6987,plain,
! [SV2459: $i,SV1994: $i,SV1269: $i,SV421: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV1269 ) @ SV1994 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV2459 ) @ SV1994 ) @ SV421 )
| ~ ( c_lessequals @ SV1269 @ SV2459 @ SV421 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6443]) ).
thf(6988,plain,
! [SV2460: $i,SV1995: $i,SV1270: $i,SV422: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
= $false )
| ( ( ( c_lessequals @ SV1270 @ SV1995 @ SV422 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1270 ) @ SV2460 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1995 ) @ SV2460 ) @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6444]) ).
thf(6989,plain,
! [SV2461: $i,SV1996: $i,SV1271: $i,SV423: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV423 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SV1996 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SV2461 ) @ SV423 )
| ~ ( c_lessequals @ SV1996 @ SV2461 @ SV423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6445]) ).
thf(6990,plain,
! [SV2462: $i,SV1997: $i,SV1272: $i,SV424: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
= $false )
| ( ( ( c_lessequals @ SV1272 @ SV1997 @ SV424 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV2462 ) @ SV1272 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV2462 ) @ SV1997 ) @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6446]) ).
thf(6991,plain,
! [SV2463: $i,SV1998: $i,SV1273: $i,SV425: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV425 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV1273 ) @ SV1998 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV2463 ) @ SV1998 ) @ SV425 )
| ~ ( c_lessequals @ SV1273 @ SV2463 @ SV425 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6447]) ).
thf(6992,plain,
! [SV2464: $i,SV1999: $i,SV1274: $i,SV426: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV426 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SV1999 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SV2464 ) @ SV426 )
| ~ ( c_lessequals @ SV1999 @ SV2464 @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6448]) ).
thf(6993,plain,
! [SV2767: $i,SV2676: $i,SV2465: $i,SV2003: $i,SV1281: $i,SV433: $i] :
( ( ! [SY7191: $i,SY7192: $i] :
( ( ( hAPP @ ( hAPP @ SV433 @ SV1281 ) @ ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ SV2465 ) )
= ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ ( c_Suc @ SV2465 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2676 @ SV433 @ SV2003 @ SV2767 @ SY7191 @ SY7192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6452]) ).
thf(6994,plain,
! [SV2768: $i,SV2677: $i,SV2466: $i,SV2004: $i,SV1282: $i,SV434: $i] :
( ( ! [SY7193: $i,SY7194: $i] :
( ( ( hAPP @ ( hAPP @ SV434 @ ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ SV2466 ) ) @ SV2004 )
= ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ ( c_Suc @ SV2466 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2677 @ SV434 @ SV1282 @ SV2768 @ SY7193 @ SY7194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6453]) ).
thf(6995,plain,
! [SV2769: $i,SV2678: $i,SV2467: $i,SV2005: $i,SV1283: $i,SV435: $i] :
( ( ! [SY7195: $i,SY7196: $i] :
( ( ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ ( c_Suc @ SV2005 ) )
= ( hAPP @ ( hAPP @ SV2467 @ SV1283 ) @ ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ SV2005 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2678 @ SV2467 @ SV435 @ SV2769 @ SY7195 @ SY7196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6454]) ).
thf(6996,plain,
! [SV2770: $i,SV2679: $i,SV2468: $i,SV2006: $i,SV1284: $i,SV436: $i] :
( ( ! [SY7197: $i,SY7198: $i] :
( ( ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ ( c_Suc @ SV2006 ) )
= ( hAPP @ ( hAPP @ SV2468 @ SV1284 ) @ ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ SV2006 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2679 @ SV2468 @ SV436 @ SV2770 @ SY7197 @ SY7198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6455]) ).
thf(6997,plain,
! [SV2470: $i,SV2012: $i,SV1290: $i,SV442: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV442 )
= $false )
| ( ( ( c_lessequals @ SV1290 @ SV2012 @ SV442 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV442 ) @ SV2012 @ SV442 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1290 @ ( c_Suc @ SV2470 ) @ SV442 ) @ ( c_Power_Opower__class_Opower @ SV2012 @ ( c_Suc @ SV2470 ) @ SV442 ) @ SV442 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6460]) ).
thf(6998,plain,
! [SV445: $i,SV1293: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1293 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV445 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1293 @ SV445 ) @ SV445 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV445 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6462]) ).
thf(6999,plain,
! [SV1294: $i,SV446: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1294 @ SV446 ) @ SV446 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1294 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV446 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6463]) ).
thf(7000,plain,
! [SV2680: $i,SV2472: $i,SV2015: $i,SV1295: $i,SV447: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SV2472 @ SV2680 @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
| ~ ( c_lessequals @ SV2015 @ SV2680 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SV2472 @ SV447 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6464]) ).
thf(7001,plain,
! [SV2681: $i,SV2473: $i,SV2016: $i,SV1296: $i,SV448: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SV2473 @ SV2681 @ SV448 ) @ SV448 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ SV2016 @ SV2681 @ SV448 )
| ~ ( c_lessequals @ SV1296 @ SV2473 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6465]) ).
thf(7002,plain,
! [SV2019: $i,SV1299: $i,SV451: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV1299 @ SV451 )
= $true )
| ( ( ( c_lessequals @ SV1299 @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1299 @ SV451 ) @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV451 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6468]) ).
thf(7003,plain,
! [SV2020: $i,SV452: $i,SV1300: $i] :
( ( ( c_lessequals @ SV1300 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
= $true )
| ( ( ( c_lessequals @ SV2020 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1300 @ SV2020 @ SV452 ) @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV452 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6469]) ).
thf(7004,plain,
! [SV2021: $i,SV1301: $i,SV453: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV1301 @ SV453 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV2021 @ SV453 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1301 @ SV453 ) @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV453 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV453 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6470]) ).
thf(7005,plain,
! [SV2022: $i,SV454: $i,SV1302: $i] :
( ( ( c_lessequals @ SV1302 @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV1302 @ SV454 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1302 @ SV2022 @ SV454 ) @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV454 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6471]) ).
thf(7006,plain,
! [SV455: $i,SV2023: $i,SV1303: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1303 @ SV2023 @ SV455 ) @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1303 @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV2023 @ SV455 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV455 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6472]) ).
thf(7007,plain,
! [SV456: $i,SV2024: $i,SV1304: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1304 @ SV2024 @ SV456 ) @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2024 @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1304 @ SV456 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV456 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6473]) ).
thf(7008,plain,
! [SV457: $i,SV2025: $i,SV1305: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1305 @ SV2025 @ SV457 ) @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV2025 @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ SV1305 @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV457 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6474]) ).
thf(7009,plain,
! [SV2026: $i,SV1308: $i,SV2474: $i,SV460: $i] :
( ( ( c_Type_Otyping @ SV460 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV2474 @ SV1308 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2026 )
= $false )
| ( ( c_Type_Otypings @ SV460 @ SV1308 @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV2026 @ SV460 @ SV2474 @ SV1308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6475]) ).
thf(7010,plain,
! [SV1309: $i,SV461: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV461 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1309 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV461 @ ( c_HOL_Otimes__class_Otimes @ SV1309 @ SV461 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6476]) ).
thf(7011,plain,
! [SV1310: $i,SV462: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV462 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1310 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV462 @ ( c_HOL_Otimes__class_Otimes @ SV462 @ SV1310 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6477]) ).
thf(7012,plain,
! [SV1311: $i,SV2027: $i,SV464: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SV2027 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1311 @ SV2027 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV2027 @ SV1311 @ tc_nat )
| ~ ( c_lessequals @ SV2027 @ SV464 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV464 @ SV1311 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6478]) ).
thf(7013,plain,
! [SV1312: $i,SV2028: $i,SV465: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV465 @ SV2028 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1312 @ SV2028 @ tc_nat )
| ~ ( c_lessequals @ SV1312 @ SV465 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV465 @ SV1312 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV2028 @ SV1312 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6479]) ).
thf(7014,plain,
! [SV2475: $i,SV2029: $i,SV1313: $i,SV466: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV466 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1313 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ SV2029 ) @ SV2475 ) @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ SV1313 @ SV2475 @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV2029 @ SV466 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6480]) ).
thf(7015,plain,
! [SV469: $i,SV1316: $i] :
( ( ( c_lessequals @ SV1316 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV469 ) @ SV1316 ) @ SV1316 ) @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6483]) ).
thf(7016,plain,
! [SV1317: $i,SV470: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV470 ) @ SV1317 ) @ SV1317 ) @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV470 )
= $false )
| ( ( c_lessequals @ SV1317 @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV470 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6484]) ).
thf(7017,plain,
! [SV473: $i,SV2032: $i,SV1320: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1320 @ SV2032 @ tc_nat ) @ SV473 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1320 @ SV473 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV2032 @ SV473 ) @ SV473 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2032 @ SV1320 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6485]) ).
thf(7018,plain,
! [SV2476: $i,SV2033: $i,SV1321: $i,SV474: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV474 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1321 @ SV2033 @ SV474 ) @ ( c_HOL_Otimes__class_Otimes @ SV2476 @ SV2033 @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SV2033 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SV2476 @ SV1321 @ SV474 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6486]) ).
thf(7019,plain,
! [SV2477: $i,SV2034: $i,SV1322: $i,SV475: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV475 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2034 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2477 @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SV2477 @ SV2034 @ SV475 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6487]) ).
thf(7020,plain,
! [SV2478: $i,SV2035: $i,SV1323: $i,SV476: $i] :
( ( ( class_Ring__and__Field_Omult__mono @ SV476 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1323 @ SV2035 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SV2478 @ SV2035 @ SV476 ) @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV2035 @ SV476 )
| ~ ( c_lessequals @ SV1323 @ SV2478 @ SV476 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6488]) ).
thf(7021,plain,
! [SV2479: $i,SV2036: $i,SV1324: $i,SV477: $i] :
( ( ( class_Ring__and__Field_Omult__mono @ SV477 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2036 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2479 @ SV477 ) @ SV477 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV477 ) @ SV1324 @ SV477 )
| ~ ( c_lessequals @ SV2036 @ SV2479 @ SV477 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6489]) ).
thf(7022,plain,
! [SV2480: $i,SV2037: $i,SV1325: $i,SV478: $i] :
( ( ( class_Ring__and__Field_Omult__mono1 @ SV478 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2037 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2480 @ SV478 ) @ SV478 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV478 ) @ SV1325 @ SV478 )
| ~ ( c_lessequals @ SV2037 @ SV2480 @ SV478 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6490]) ).
thf(7023,plain,
! [SV2481: $i,SV2041: $i,SV1329: $i,SV482: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV482 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SV1329 ) @ SV2041 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SV2481 ) @ SV2041 ) @ SV482 )
| ~ ( c_HOL_Oord__class_Oless @ SV1329 @ SV2481 @ SV482 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6493]) ).
thf(7024,plain,
! [SV2482: $i,SV2042: $i,SV1330: $i,SV483: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV483 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SV1330 ) @ SV2042 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SV2482 ) @ SV2042 ) @ SV483 )
| ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SV2482 @ SV483 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6494]) ).
thf(7025,plain,
! [SV2483: $i,SV2043: $i,SV1331: $i,SV484: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV484 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1331 @ SV2043 @ SV484 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV1331 ) @ SV2483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV2043 ) @ SV2483 ) @ SV484 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6495]) ).
thf(7026,plain,
! [SV2484: $i,SV2044: $i,SV1332: $i,SV485: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV485 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SV2044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SV2484 ) @ SV485 )
| ~ ( c_HOL_Oord__class_Oless @ SV2044 @ SV2484 @ SV485 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6496]) ).
thf(7027,plain,
! [SV2485: $i,SV2045: $i,SV1333: $i,SV486: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV486 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SV2045 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SV2485 ) @ SV486 )
| ~ ( c_HOL_Oord__class_Oless @ SV2045 @ SV2485 @ SV486 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6497]) ).
thf(7028,plain,
! [SV2486: $i,SV2046: $i,SV1334: $i,SV487: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV487 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1334 @ SV2046 @ SV487 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SV2486 ) @ SV1334 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SV2486 ) @ SV2046 ) @ SV487 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6498]) ).
thf(7029,plain,
! [SV1338: $i,SV491: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV491 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1338 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV491 @ SV1338 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6502]) ).
thf(7030,plain,
! [SV2487: $i,SV2050: $i,SV1339: $i,SV492: $i] :
( ( ( class_Orderings_Oorder @ SV492 )
= $false )
| ( ( ( c_lessequals @ SV1339 @ SV2050 @ SV492 )
| ~ ( c_lessequals @ SV1339 @ SV2487 @ SV492 )
| ~ ( c_lessequals @ SV2487 @ SV2050 @ SV492 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6503]) ).
thf(7031,plain,
! [SV2488: $i,SV2051: $i,SV1340: $i,SV493: $i] :
( ( ( class_Orderings_Oorder @ SV493 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1340 @ SV2051 @ SV493 )
| ~ ( c_lessequals @ SV1340 @ SV2488 @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SV2488 @ SV2051 @ SV493 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6504]) ).
thf(7032,plain,
! [SV2489: $i,SV2052: $i,SV1341: $i,SV494: $i] :
( ( ( class_Orderings_Oorder @ SV494 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1341 @ SV2052 @ SV494 )
| ~ ( c_HOL_Oord__class_Oless @ SV1341 @ SV2489 @ SV494 )
| ~ ( c_lessequals @ SV2489 @ SV2052 @ SV494 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6505]) ).
thf(7033,plain,
! [SV2053: $i,SV1342: $i,SV495: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1342 ) @ SV2053 ) @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
= $true )
| ( ( ~ ( c_lessequals @ SV2053 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
| ~ ( c_lessequals @ SV1342 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV495 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6506]) ).
thf(7034,plain,
! [SV2490: $i,SV2054: $i,SV1343: $i,SV496: $i] :
( ( ( class_Orderings_Opreorder @ SV496 )
= $false )
| ( ( ( c_lessequals @ SV1343 @ SV2054 @ SV496 )
| ~ ( c_lessequals @ SV2490 @ SV2054 @ SV496 )
| ~ ( c_lessequals @ SV1343 @ SV2490 @ SV496 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6507]) ).
thf(7035,plain,
! [SV498: $i,SV1344: $i,SV2055: $i] :
( ( ( c_lessequals @ SV2055 @ SV1344 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV498 @ SV2055 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV498 @ SV1344 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6508]) ).
thf(7036,plain,
! [SV1349: $i,SV2056: $i,SV505: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV505 @ SV2056 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1349 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV1349 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2056 @ SV1349 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6511]) ).
thf(7037,plain,
! [SV506: $i,SV2057: $i,SV1350: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1350 @ SV2057 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV506 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV1350 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV2057 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6512]) ).
thf(7038,plain,
! [SV2058: $i,SV1351: $i,SV507: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV507 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1351 @ SV2058 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SV1351 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SV2058 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6513]) ).
thf(7039,plain,
! [SV2059: $i,SV508: $i,SV1352: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1352 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV508 @ SV2059 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV508 @ SV1352 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2059 @ SV1352 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6514]) ).
thf(7040,plain,
! [SV1353: $i,SV509: $i,SV2060: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2060 @ SV509 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2060 @ SV1353 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2060 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV509 @ SV1353 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6515]) ).
thf(7041,plain,
! [SV510: $i,SV2061: $i,SV1354: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1354 @ SV2061 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV510 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SV1354 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SV2061 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6516]) ).
thf(7042,plain,
! [SV2491: $i,SV2062: $i,SV1355: $i,SV511: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV511 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1355 @ SV2062 @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV2062 @ SV511 ) @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV1355 @ SV511 ) @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ SV2491 @ ( c_HOL_Ozero__class_Ozero @ SV511 ) @ SV511 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6517]) ).
thf(7043,plain,
! [SV2492: $i,SV2063: $i,SV1356: $i,SV512: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV512 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2063 @ SV512 ) @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2492 @ SV512 ) @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SV2492 @ SV2063 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SV1356 @ ( c_HOL_Ozero__class_Ozero @ SV512 ) @ SV512 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6518]) ).
thf(7044,plain,
! [SV2493: $i,SV2064: $i,SV1357: $i,SV513: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV513 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1357 @ SV2064 @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV1357 @ SV513 ) @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV2064 @ SV513 ) @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV513 ) @ SV2493 @ SV513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6519]) ).
thf(7045,plain,
! [SV2494: $i,SV2065: $i,SV1358: $i,SV514: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV514 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2065 @ SV514 ) @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2494 @ SV514 ) @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ SV2065 @ SV2494 @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SV1358 @ SV514 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6520]) ).
thf(7046,plain,
! [SV2495: $i,SV2066: $i,SV1359: $i,SV515: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV515 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2066 @ SV515 ) @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2495 @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SV1359 @ ( c_HOL_Ozero__class_Ozero @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SV2495 @ SV2066 @ SV515 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6521]) ).
thf(7047,plain,
! [SV2496: $i,SV2067: $i,SV1360: $i,SV516: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV516 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2067 @ SV516 ) @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2496 @ SV516 ) @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV516 ) @ SV1360 @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ SV2067 @ SV2496 @ SV516 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6522]) ).
thf(7048,plain,
! [SV2497: $i,SV2068: $i,SV1361: $i,SV517: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV517 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2068 @ SV517 ) @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2497 @ SV517 ) @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ SV2068 @ SV2497 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1361 @ SV517 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6523]) ).
thf(7049,plain,
! [SV2498: $i,SV2069: $i,SV1362: $i,SV518: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV518 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2069 @ SV518 ) @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2498 @ SV518 ) @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SV2498 @ SV2069 @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SV1362 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6524]) ).
thf(7050,plain,
! [SV2499: $i,SV2070: $i,SV1363: $i,SV519: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV519 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1363 @ SV2070 @ SV519 ) @ ( c_HOL_Otimes__class_Otimes @ SV2499 @ SV2070 @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SV2070 @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SV2499 @ SV1363 @ SV519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6525]) ).
thf(7051,plain,
! [SV2500: $i,SV2071: $i,SV1364: $i,SV520: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV520 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1364 @ SV2071 @ SV520 ) @ ( c_HOL_Otimes__class_Otimes @ SV2500 @ SV2071 @ SV520 ) @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV2071 @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ SV1364 @ SV2500 @ SV520 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6526]) ).
thf(7052,plain,
! [SV2501: $i,SV2072: $i,SV1365: $i,SV521: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV521 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1365 @ SV2072 @ SV521 ) @ ( c_HOL_Otimes__class_Otimes @ SV2501 @ SV2072 @ SV521 ) @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ SV1365 @ SV2501 @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV521 ) @ SV2072 @ SV521 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6527]) ).
thf(7053,plain,
! [SV2502: $i,SV2073: $i,SV1366: $i,SV522: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV522 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1366 @ SV2073 @ SV522 ) @ ( c_HOL_Otimes__class_Otimes @ SV2502 @ SV2073 @ SV522 ) @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SV2502 @ SV1366 @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SV2073 @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV522 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6528]) ).
thf(7054,plain,
! [SV2503: $i,SV2074: $i,SV1367: $i,SV523: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV523 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2074 @ SV523 ) @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2503 @ SV523 ) @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV1367 @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ SV2074 @ SV2503 @ SV523 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6529]) ).
thf(7055,plain,
! [SV2504: $i,SV2076: $i,SV1369: $i,SV525: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV525 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ ( c_Orderings_Oord__class_Omax @ SV1369 @ SV2076 @ SV525 ) ) @ SV2504 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ SV1369 ) @ SV2504 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV525 ) @ SV2076 ) @ SV2504 ) @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6530]) ).
thf(7056,plain,
! [SV2077: $i,SV527: $i,SV2505: $i,SV1371: $i] :
( ( ( ~ ( c_lessequals @ SV1371 @ SV2505 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV527 @ SV2077 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV527 @ SV1371 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2077 @ SV2505 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6531]) ).
thf(7057,plain,
! [SV2682: $i,SV2506: $i,SV2078: $i,SV1372: $i,SV529: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV529 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SV2506 @ SV2682 @ SV529 ) @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2506 @ SV529 )
| ~ ( c_lessequals @ SV2078 @ SV2682 @ SV529 )
| ~ ( c_lessequals @ SV1372 @ SV2506 @ SV529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6532]) ).
thf(7058,plain,
! [SV2683: $i,SV2507: $i,SV2079: $i,SV1373: $i,SV530: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV530 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SV2507 @ SV2683 @ SV530 ) @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
| ~ ( c_lessequals @ SV2079 @ SV2683 @ SV530 )
| ~ ( c_lessequals @ SV1373 @ SV2507 @ SV530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6533]) ).
thf(7059,plain,
! [SV2508: $i,SV2080: $i,SV1374: $i,SV531: $i] :
( ( ( class_Orderings_Olinorder @ SV531 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV1374 @ SV2080 @ SV531 ) @ SV2508 @ SV531 )
= ( c_Orderings_Oord__class_Omax @ SV1374 @ ( c_Orderings_Oord__class_Omax @ SV2080 @ SV2508 @ SV531 ) @ SV531 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6534]) ).
thf(7060,plain,
! [SV2509: $i,SV2081: $i,SV1375: $i,SV532: $i] :
( ( ( class_Orderings_Olinorder @ SV532 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1375 @ ( c_Orderings_Oord__class_Omax @ SV2081 @ SV2509 @ SV532 ) @ SV532 )
= ( c_Orderings_Oord__class_Omax @ SV2081 @ ( c_Orderings_Oord__class_Omax @ SV1375 @ SV2509 @ SV532 ) @ SV532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6535]) ).
thf(7061,plain,
! [SV2510: $i,SV2082: $i,SV1376: $i,SV534: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV534 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV534 ) @ ( c_HOL_Otimes__class_Otimes @ SV1376 @ SV2082 @ SV534 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2510 @ SV2082 @ SV534 ) )
= ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV534 ) @ SV1376 ) @ SV2510 ) @ SV2082 @ SV534 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6536]) ).
thf(7062,plain,
! [SV2085: $i,SV541: $i,SV1382: $i] :
( ( ( c_lessequals @ SV1382 @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV541 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV1382 @ SV541 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV2085 @ SV541 ) @ SV541 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV541 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6538]) ).
thf(7063,plain,
! [SV2086: $i,SV542: $i,SV1383: $i] :
( ( ( c_lessequals @ SV1383 @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV542 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV2086 @ SV542 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ ( c_HOL_Otimes__class_Otimes @ SV2086 @ SV1383 @ SV542 ) @ SV542 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV542 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6539]) ).
thf(7064,plain,
! [SV2087: $i,SV543: $i,SV1384: $i] :
( ( ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV543 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV2087 @ SV543 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ ( c_HOL_Otimes__class_Otimes @ SV1384 @ SV2087 @ SV543 ) @ SV543 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV543 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6540]) ).
thf(7065,plain,
! [SV2088: $i,SV544: $i,SV1385: $i] :
( ( ( c_lessequals @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV544 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV1385 @ SV544 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ ( c_HOL_Otimes__class_Otimes @ SV2088 @ SV1385 @ SV544 ) @ SV544 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV544 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6541]) ).
thf(7066,plain,
! [SV2771: $i,SV2684: $i,SV2511: $i,SV2090: $i,SV1389: $i,SV548: $i] :
( ( ( c_List_Ofoldl @ SV548 @ SV1389 @ ( c_List_Oappend @ SV2090 @ SV2511 @ SV2684 ) @ SV2771 @ SV2684 )
= ( c_List_Ofoldl @ SV548 @ ( c_List_Ofoldl @ SV548 @ SV1389 @ SV2090 @ SV2771 @ SV2684 ) @ SV2511 @ SV2771 @ SV2684 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6543]) ).
thf(7067,plain,
! [SV2685: $i,SV2513: $i,SV2092: $i,SV1391: $i,SV550: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV550 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV1391 ) @ SV2092 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV2513 ) @ SV2685 ) @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SV2092 @ SV2685 @ SV550 )
| ~ ( c_lessequals @ SV1391 @ SV2513 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6544]) ).
thf(7068,plain,
! [SV2686: $i,SV2514: $i,SV2093: $i,SV1392: $i,SV551: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV551 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV1392 ) @ SV2093 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV2514 ) @ SV2686 ) @ SV551 )
| ~ ( c_lessequals @ SV2093 @ SV2686 @ SV551 )
| ~ ( c_HOL_Oord__class_Oless @ SV1392 @ SV2514 @ SV551 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6545]) ).
thf(7069,plain,
! [SV1398: $i,SV557: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV557 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV557 ) @ SV1398 ) @ SV1398 ) @ SV557 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV557 ) @ SV1398 @ SV557 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV557 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6546]) ).
thf(7070,plain,
! [SV1399: $i,SV558: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV558 ) @ SV1399 @ SV558 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV558 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV558 ) @ SV1399 ) @ SV1399 ) @ SV558 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV558 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6547]) ).
thf(7071,plain,
! [SV1408: $i,SV567: $i] :
( ( ( class_Int_Onumber__ring @ SV567 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1408 @ SV1408 @ SV567 )
= ( c_HOL_Ozero__class_Ozero @ SV567 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV567 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6549]) ).
thf(7072,plain,
! [SV1415: $i,SV575: $i] :
( ( ( class_Int_Onumber__ring @ SV575 )
= $false )
| ( ( SV1415
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV575 ) @ SV1415 ) @ ( c_HOL_Ozero__class_Ozero @ SV575 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV575 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6550]) ).
thf(7073,plain,
! [SV2515: $i,SV2095: $i,SV1425: $i,SV586: $i] :
( ( ( class_Orderings_Opreorder @ SV586 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1425 @ SV2095 @ SV586 )
| ~ ( c_HOL_Oord__class_Oless @ SV2515 @ SV2095 @ SV586 )
| ~ ( c_lessequals @ SV1425 @ SV2515 @ SV586 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6551]) ).
thf(7074,plain,
! [SV2516: $i,SV2096: $i,SV1426: $i,SV587: $i] :
( ( ( class_Orderings_Opreorder @ SV587 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1426 @ SV2096 @ SV587 )
| ~ ( c_lessequals @ SV2516 @ SV2096 @ SV587 )
| ~ ( c_HOL_Oord__class_Oless @ SV1426 @ SV2516 @ SV587 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6552]) ).
thf(7075,plain,
! [SV2687: $i,SV2517: $i,SV2097: $i,SV1427: $i,SV588: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV588 ) )
= $true )
| ( ( ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2517 ) @ SV588 )
| ~ ( c_lessequals @ SV2687 @ SV2517 @ SV588 )
| ~ ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2687 ) @ SV588 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6553]) ).
thf(7076,plain,
! [SV591: $i,SV2099: $i,SV1430: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1430 @ SV2099 @ tc_nat )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ominus__class_Ominus @ SV1430 @ SV2099 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6554]) ).
thf(7077,plain,
! [SV2100: $i,SV593: $i,SV1432: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1432 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV593 @ SV2100 ) @ tc_nat ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV593 @ SV2100 ) )
| ( hBOOL @ ( hAPP @ SV593 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV593 @ SV1432 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6555]) ).
thf(7078,plain,
! [SV2688: $i,SV2518: $i,SV2101: $i,SV1433: $i,SV594: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SV2518 @ SV2688 @ SV594 ) @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV2101 @ SV2688 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SV2518 @ SV594 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6556]) ).
thf(7079,plain,
! [SV595: $i,SV1434: $i] :
( ( ( c_lessequals @ SV1434 @ SV595 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV595 @ ( c_Suc @ SV1434 ) @ tc_nat )
= $false )
| ( ( SV595 = SV1434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6557]) ).
thf(7080,plain,
! [SV2520: $i,SV2107: $i,SV1444: $i,SV606: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV606 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1444 @ ( c_HOL_Ozero__class_Ozero @ SV606 ) @ SV606 )
| ( c_HOL_Oord__class_Oless @ SV2107 @ SV2520 @ SV606 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2107 @ SV1444 @ SV606 ) @ ( c_HOL_Otimes__class_Otimes @ SV2520 @ SV1444 @ SV606 ) @ SV606 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6562]) ).
thf(7081,plain,
! [SV2521: $i,SV2108: $i,SV1445: $i,SV607: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV607 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1445 @ SV2108 @ SV607 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV607 ) @ SV2521 @ SV607 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2108 @ SV2521 @ SV607 ) @ ( c_HOL_Otimes__class_Otimes @ SV1445 @ SV2521 @ SV607 ) @ SV607 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6563]) ).
thf(7082,plain,
! [SV2522: $i,SV2109: $i,SV1446: $i,SV608: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV608 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1446 @ ( c_HOL_Ozero__class_Ozero @ SV608 ) @ SV608 )
| ( c_HOL_Oord__class_Oless @ SV2109 @ SV2522 @ SV608 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2109 @ SV608 ) @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2522 @ SV608 ) @ SV608 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6564]) ).
thf(7083,plain,
! [SV2523: $i,SV2110: $i,SV1447: $i,SV609: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV609 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1447 @ SV2110 @ SV609 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV609 ) @ SV2523 @ SV609 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2523 @ SV2110 @ SV609 ) @ ( c_HOL_Otimes__class_Otimes @ SV2523 @ SV1447 @ SV609 ) @ SV609 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6565]) ).
thf(7084,plain,
! [SV613: $i,SV1450: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1450 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV613 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV613 @ SV1450 @ tc_nat ) @ SV613 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6567]) ).
thf(7085,plain,
! [SV2525: $i,SV2113: $i,SV1451: $i,SV614: $i] :
( ( ( class_Orderings_Olinorder @ SV614 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1451 @ ( c_Orderings_Oord__class_Omin @ SV2113 @ SV2525 @ SV614 ) @ SV614 ) @ ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1451 @ SV2113 @ SV614 ) @ ( c_Orderings_Oord__class_Omax @ SV1451 @ SV2525 @ SV614 ) @ SV614 ) @ SV614 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6568]) ).
thf(7086,plain,
! [SV2526: $i,SV2114: $i,SV1452: $i,SV615: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV615 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV1452 @ SV2114 @ SV615 ) @ SV2526 @ SV615 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1452 @ SV2526 @ SV615 ) @ ( c_Power_Opower__class_Opower @ SV2114 @ SV2526 @ SV615 ) @ SV615 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6569]) ).
thf(7087,plain,
! [SV2527: $i,SV2115: $i,SV1453: $i,SV616: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV616 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV1453 @ SV2115 @ SV616 ) @ SV2527 @ SV616 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV1453 @ SV2527 @ SV616 ) @ ( c_Power_Opower__class_Opower @ SV2115 @ SV2527 @ SV616 ) @ SV616 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6570]) ).
thf(7088,plain,
! [SV2528: $i,SV2117: $i,SV1457: $i,SV620: $i] :
( ( ( class_Orderings_Olinorder @ SV620 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omin @ SV1457 @ SV2117 @ SV620 ) @ SV2528 @ SV620 )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1457 @ SV2528 @ SV620 ) @ ( c_Orderings_Oord__class_Omax @ SV2117 @ SV2528 @ SV620 ) @ SV620 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6572]) ).
thf(7089,plain,
! [SV2529: $i,SV2118: $i,SV1458: $i,SV621: $i] :
( ( ( class_Orderings_Olinorder @ SV621 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV1458 @ ( c_Orderings_Oord__class_Omin @ SV2118 @ SV2529 @ SV621 ) @ SV621 )
= ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omax @ SV1458 @ SV2118 @ SV621 ) @ ( c_Orderings_Oord__class_Omax @ SV1458 @ SV2529 @ SV621 ) @ SV621 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6573]) ).
thf(7090,plain,
! [SV2530: $i,SV2119: $i,SV1459: $i,SV622: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV622 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV1459 @ ( c_HOL_Otimes__class_Otimes @ SV2119 @ SV2530 @ tc_nat ) @ SV622 )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV1459 @ SV2119 @ SV622 ) @ SV2530 @ SV622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6574]) ).
thf(7091,plain,
! [SV623: $i,SV2120: $i,SV1460: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1460 @ SV2120 @ SV623 )
= $true )
| ( ( ( SV2120 = SV1460 )
| ~ ( c_lessequals @ SV1460 @ SV2120 @ SV623 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV623 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6575]) ).
thf(7092,plain,
! [SV624: $i,SV2121: $i,SV1461: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1461 @ SV2121 @ SV624 )
= $true )
| ( ( ~ ( c_lessequals @ SV1461 @ SV2121 @ SV624 )
| ( SV2121 = SV1461 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV624 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6576]) ).
thf(7093,plain,
! [SV628: $i,SV2122: $i,SV1465: $i] :
( ( ( SV1465 = SV2122 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1465 @ SV2122 @ SV628 )
| ~ ( c_lessequals @ SV1465 @ SV2122 @ SV628 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV628 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6580]) ).
thf(7094,plain,
! [SV629: $i,SV2123: $i,SV1466: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1466 @ SV2123 @ SV629 )
= $true )
| ( ( ( SV1466 = SV2123 )
| ~ ( c_lessequals @ SV1466 @ SV2123 @ SV629 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6581]) ).
thf(7095,plain,
! [SV630: $i,SV2124: $i,SV1467: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1467 @ SV2124 @ SV630 )
= $true )
| ( ( ( SV1467 = SV2124 )
| ~ ( c_lessequals @ SV1467 @ SV2124 @ SV630 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV630 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6582]) ).
thf(7096,plain,
! [SV631: $i,SV2125: $i,SV1468: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1468 @ SV2125 @ SV631 )
= $true )
| ( ( ~ ( c_lessequals @ SV1468 @ SV2125 @ SV631 )
| ( SV1468 = SV2125 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV631 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6583]) ).
thf(7097,plain,
! [SV632: $i,SV2126: $i,SV1469: $i] :
( ( ( SV1469 = SV2126 )
= $true )
| ( ( ~ ( c_lessequals @ SV1469 @ SV2126 @ SV632 )
| ( c_HOL_Oord__class_Oless @ SV1469 @ SV2126 @ SV632 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV632 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6584]) ).
thf(7098,plain,
! [SV633: $i,SV2127: $i,SV1470: $i] :
( ( ( SV1470 = SV2127 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1470 @ SV2127 @ SV633 )
| ~ ( c_lessequals @ SV1470 @ SV2127 @ SV633 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV633 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6585]) ).
thf(7099,plain,
! [SV2128: $i,SV1471: $i,SV634: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ ( c_HOL_Otimes__class_Otimes @ SV1471 @ SV2128 @ SV634 ) @ SV634 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV2128 @ SV634 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV1471 @ SV634 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV634 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6586]) ).
thf(7100,plain,
! [SV2129: $i,SV1472: $i,SV635: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ ( c_HOL_Otimes__class_Otimes @ SV1472 @ SV2129 @ SV635 ) @ SV635 )
= $true )
| ( ( ~ ( c_lessequals @ SV2129 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 )
| ~ ( c_lessequals @ SV1472 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV635 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6587]) ).
thf(7101,plain,
! [SV2130: $i,SV1473: $i,SV636: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ ( c_HOL_Otimes__class_Otimes @ SV1473 @ SV2130 @ SV636 ) @ SV636 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV2130 @ SV636 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV1473 @ SV636 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV636 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6588]) ).
thf(7102,plain,
! [SV2131: $i,SV1475: $i,SV638: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ ( c_HOL_Otimes__class_Otimes @ SV1475 @ SV2131 @ SV638 ) @ SV638 )
= $true )
| ( ( ~ ( c_lessequals @ SV2131 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 )
| ~ ( c_lessequals @ SV1475 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV638 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6589]) ).
thf(7103,plain,
! [SV2132: $i,SV1476: $i,SV639: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ ( c_HOL_Otimes__class_Otimes @ SV1476 @ SV2132 @ SV639 ) @ SV639 )
= $true )
| ( ( ~ ( c_lessequals @ SV2132 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 )
| ~ ( c_lessequals @ SV1476 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV639 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6590]) ).
thf(7104,plain,
! [SV2133: $i,SV1477: $i,SV640: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ ( c_HOL_Otimes__class_Otimes @ SV1477 @ SV2133 @ SV640 ) @ SV640 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV2133 @ SV640 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV1477 @ SV640 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV640 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6591]) ).
thf(7105,plain,
! [SV2531: $i,SV2134: $i,SV1480: $i,SV644: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__mult @ SV644 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1480 @ SV2134 @ SV644 ) @ SV2531 @ SV644 )
= ( c_HOL_Otimes__class_Otimes @ SV1480 @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV2531 @ SV644 ) @ SV644 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6592]) ).
thf(7106,plain,
! [SV2532: $i,SV2135: $i,SV1481: $i,SV645: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV645 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1481 @ SV2135 @ SV645 ) @ SV2532 @ SV645 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1481 @ SV2532 @ SV645 ) @ SV2135 @ SV645 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6593]) ).
thf(7107,plain,
! [SV2533: $i,SV2136: $i,SV1482: $i,SV646: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV646 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1482 @ SV2136 @ SV646 ) @ SV2533 @ SV646 )
= ( c_HOL_Otimes__class_Otimes @ SV1482 @ ( c_HOL_Otimes__class_Otimes @ SV2136 @ SV2533 @ SV646 ) @ SV646 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6594]) ).
thf(7108,plain,
! [SV2534: $i,SV2137: $i,SV1483: $i,SV647: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV647 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1483 @ ( c_HOL_Otimes__class_Otimes @ SV2137 @ SV2534 @ SV647 ) @ SV647 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1483 @ SV2137 @ SV647 ) @ SV2534 @ SV647 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6595]) ).
thf(7109,plain,
! [SV2535: $i,SV2138: $i,SV1484: $i,SV648: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV648 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1484 @ ( c_HOL_Otimes__class_Otimes @ SV2138 @ SV2535 @ SV648 ) @ SV648 )
= ( c_HOL_Otimes__class_Otimes @ SV2138 @ ( c_HOL_Otimes__class_Otimes @ SV1484 @ SV2535 @ SV648 ) @ SV648 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6596]) ).
thf(7110,plain,
! [SV2540: $i,SV2144: $i,SV1490: $i,SV654: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV654 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1490 @ ( c_HOL_Otimes__class_Otimes @ SV2144 @ SV2540 @ SV654 ) @ SV654 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1490 @ SV2144 @ SV654 ) @ SV2540 @ SV654 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6597]) ).
thf(7111,plain,
! [SV2541: $i,SV2145: $i,SV1491: $i,SV655: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV655 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV655 ) @ SV1491 ) @ SV2145 ) @ SV2541 @ SV655 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV655 ) @ ( c_HOL_Otimes__class_Otimes @ SV1491 @ SV2541 @ SV655 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV2541 @ SV655 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6598]) ).
thf(7112,plain,
! [SV2542: $i,SV2146: $i,SV1492: $i,SV656: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ SV656 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV656 ) @ SV1492 ) @ SV2146 ) @ SV2542 @ SV656 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV656 ) @ ( c_HOL_Otimes__class_Otimes @ SV1492 @ SV2542 @ SV656 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2146 @ SV2542 @ SV656 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6599]) ).
thf(7113,plain,
! [SV2543: $i,SV2149: $i,SV1495: $i,SV659: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV659 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1495 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV659 ) @ SV2149 ) @ SV2543 ) @ SV659 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV659 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV2149 @ SV659 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV2543 @ SV659 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6600]) ).
thf(7114,plain,
! [SV660: $i,SV2150: $i,SV1496: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1496 @ SV2150 @ SV660 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2150 @ SV1496 @ SV660 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6601]) ).
thf(7115,plain,
! [SV661: $i,SV2151: $i,SV1497: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1497 @ SV2151 @ SV661 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2151 @ SV1497 @ SV661 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV661 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6602]) ).
thf(7116,plain,
! [SV663: $i,SV2152: $i,SV1499: $i] :
( ( ( c_lessequals @ SV1499 @ SV2152 @ SV663 )
= $true )
| ( ( c_lessequals @ SV2152 @ SV1499 @ SV663 )
= $true )
| ( ( class_Orderings_Olinorder @ SV663 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6603]) ).
thf(7117,plain,
! [SV664: $i,SV2153: $i,SV1500: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1500 @ SV2153 @ SV664 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2153 @ SV1500 @ SV664 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV664 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6604]) ).
thf(7118,plain,
! [SV665: $i,SV2154: $i,SV1501: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1501 @ SV2154 @ SV665 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2154 @ SV1501 @ SV665 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6605]) ).
thf(7119,plain,
! [SV1513: $i,SV689: $i] :
( ( ( hBOOL @ ( hAPP @ SV689 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV689 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV689 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV689 @ SV1513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6613]) ).
thf(7120,plain,
! [SV2772: $i,SV2689: $i,SV2544: $i,SV2160: $i,SV1515: $i,SV698: $i] :
( ( ! [SY7199: $i] :
( ( ( hAPP @ ( hAPP @ SV698 @ SV1515 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV2160 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2544 @ SV2689 @ SV698 @ SV2772 @ SV2160 @ SY7199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6614]) ).
thf(7121,plain,
! [SV2162: $i,SV702: $i,SV1519: $i,SV2545: $i] :
( ( ( ~ ( c_Lambda_Obeta @ SV2545 @ SV1519 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV702 @ SV2545 @ SV2162 ) )
= $true )
| ( ( c_Type_Otyping @ SV702 @ SV1519 @ SV2162 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6616]) ).
thf(7122,plain,
! [SV2166: $i,SV2546: $i,SV1524: $i,SV707: $i] :
( ( ( c_Type_Otyping @ SV707 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1524 ) @ SV2546 ) @ SV2166 )
= $false )
| ( ( c_Type_Otyping @ SV707 @ SV1524 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xtyping__elims__2__1 @ SV2166 @ SV707 @ SV1524 @ SV2546 ) ) @ SV2166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6620]) ).
thf(7123,plain,
! [SV2692: $i,SV2549: $i,SV2169: $i,SV1527: $i,SV710: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV710 @ ( c_Type_Otype_Otype__case @ SV1527 @ SV2169 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2549 ) @ SV2692 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV710 @ ( hAPP @ ( hAPP @ SV2169 @ SV2549 ) @ SV2692 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6623]) ).
thf(7124,plain,
! [SV2693: $i,SV2550: $i,SV2170: $i,SV1528: $i,SV711: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV711 @ ( c_Type_Otype_Otype__case @ SV1528 @ SV2170 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2550 ) @ SV2693 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV711 @ ( hAPP @ ( hAPP @ SV2170 @ SV2550 ) @ SV2693 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6624]) ).
thf(7125,plain,
! [SV2773: $i,SV2694: $i,SV2551: $i,SV2171: $i,SV1529: $i,SV712: $i] :
( ( ( c_List_Ofoldr @ SV712 @ ( c_List_Olist_OCons @ SV1529 @ SV2171 @ SV2551 ) @ SV2694 @ SV2551 @ SV2773 )
= ( hAPP @ ( hAPP @ SV712 @ SV1529 ) @ ( c_List_Ofoldr @ SV712 @ SV2171 @ SV2694 @ SV2551 @ SV2773 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6625]) ).
thf(7126,plain,
! [SV2774: $i,SV2695: $i,SV2552: $i,SV2172: $i,SV1530: $i,SV713: $i] :
( ( ( c_List_Ofoldr @ SV713 @ ( c_List_Oappend @ SV1530 @ SV2172 @ SV2552 ) @ SV2695 @ SV2552 @ SV2774 )
= ( c_List_Ofoldr @ SV713 @ SV1530 @ ( c_List_Ofoldr @ SV713 @ SV2172 @ SV2695 @ SV2552 @ SV2774 ) @ SV2552 @ SV2774 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6626]) ).
thf(7127,plain,
! [SV2696: $i,SV2554: $i,SV2177: $i,SV1536: $i,SV719: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV719 @ SV1536 @ SV2177 @ SV2554 ) @ SV2696 )
= ( hAPP @ SV719 @ SV2696 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2696 @ SV1536 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6628]) ).
thf(7128,plain,
! [SV2178: $i,SV2555: $i,SV1537: $i,SV720: $i] :
( ( ( c_Type_Otyping @ SV720 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1537 @ SV2555 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2178 )
= $false )
| ( ( c_Type_Otyping @ SV720 @ SV1537 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeE__1__1 @ SV2178 @ SV720 @ SV1537 @ SV2555 ) @ SV2178 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6629]) ).
thf(7129,plain,
! [SV2697: $i,SV2556: $i,SV2179: $i,SV1538: $i,SV721: $i] :
( ( ( c_Type_Otyping @ SV721 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1538 @ SV2179 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2556 )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV721 @ SV2179 @ SV2697 )
| ~ ( c_Type_Otyping @ SV721 @ SV1538 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV2697 @ SV2556 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6630]) ).
thf(7130,plain,
! [SV2180: $i,SV2557: $i,SV1539: $i,SV722: $i] :
( ( ( c_Type_Otyping @ SV722 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1539 @ SV2557 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2180 )
= $false )
| ( ( c_Type_Otyping @ SV722 @ SV1539 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ ( c_Type_Osko__Type__Xlist__app__typeD__1__1 @ SV2180 @ SV722 @ SV1539 @ SV2557 ) @ SV2180 @ tc_Type_Otype @ tc_Type_Otype ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6631]) ).
thf(7131,plain,
! [SV1540: $i,SV723: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV723 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV723 )
| ~ ( class_Power_Opower @ SV723 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV723 ) @ SV1540 @ SV723 )
= ( c_HOL_Ozero__class_Ozero @ SV723 ) )
| ( SV1540
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6632]) ).
thf(7132,plain,
! [SV1541: $i,SV724: $i] :
( ( ( class_Power_Opower @ SV724 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV724 ) @ SV1541 @ SV724 )
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1541
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV724 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6633]) ).
thf(7133,plain,
! [SV2699: $i,SV2559: $i,SV2182: $i,SV1543: $i,SV727: $i] :
( ( ( c_Type_Otyping @ SV727 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1543 ) @ SV2182 ) @ SV2559 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV727 @ SV2182 @ SV2699 )
| ~ ( c_Type_Otyping @ SV727 @ SV1543 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2699 ) @ SV2559 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6635]) ).
thf(7134,plain,
! [SV2775: $i,SV2700: $i,SV2560: $i,SV2183: $i,SV1544: $i,SV728: $i] :
( ( ~ ( c_Type_Otyping @ SV728 @ SV1544 @ SV2183 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV728 @ SV2560 @ SV2183 @ tc_Type_Otype ) @ SV2700 @ SV2775 )
| ( c_Type_Otyping @ SV728 @ ( c_Lambda_Osubst @ SV2700 @ SV1544 @ SV2560 ) @ SV2775 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6636]) ).
thf(7135,plain,
! [SV2561: $i,SV1545: $i,SV2184: $i,SV729: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV729 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2184 @ tc_Type_Otype ) @ SV1545 @ SV2561 )
= $false )
| ( ( c_Type_Otyping @ SV729 @ ( c_Lambda_OdB_OAbs @ SV1545 ) @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2184 ) @ SV2561 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6637]) ).
thf(7136,plain,
! [SV2701: $i,SV2562: $i,SV2185: $i,SV1546: $i,SV730: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV730 @ SV1546 @ SV2185 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV2562 @ SV1546 ) @ SV2701 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV730 @ SV2562 @ SV2701 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6638]) ).
thf(7137,plain,
! [SV2702: $i,SV2564: $i,SV2188: $i,SV1553: $i,SV737: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV737 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1553 @ SV2188 @ SV737 )
!= ( c_HOL_Ominus__class_Ominus @ SV2564 @ SV2702 @ SV737 ) )
| ( c_lessequals @ SV2188 @ SV1553 @ SV737 )
| ~ ( c_lessequals @ SV2702 @ SV2564 @ SV737 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6640]) ).
thf(7138,plain,
! [SV2703: $i,SV2565: $i,SV2189: $i,SV1554: $i,SV738: $i] :
( ( ( ( c_List_Olist_OCons @ SV738 @ SV1554 @ SV2189 )
!= ( c_List_Olist_OCons @ SV2565 @ SV2703 @ SV2189 ) )
= $true )
| ( ( SV738 = SV2565 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6641]) ).
thf(7139,plain,
! [SV739: $i,SV2190: $i,SV1555: $i] :
( ( ( SV1555 = SV2190 )
= $true )
| ( ( SV739
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV739 @ SV1555 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV739 @ SV2190 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6642]) ).
thf(7140,plain,
! [SV2704: $i,SV2566: $i,SV2193: $i,SV1558: $i,SV742: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV1558 @ tc_nat ) ) @ SV2193 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2566 @ SV1558 @ tc_nat ) ) @ SV2704 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2566 @ SV742 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV742 @ SV2566 @ tc_nat ) @ SV1558 @ tc_nat ) ) @ SV2193 )
= SV2704 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6645]) ).
thf(7141,plain,
! [SV2567: $i,SV2195: $i,SV1560: $i,SV744: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV744 ) @ SV1560 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV2195 ) @ SV2567 ) )
= $false )
| ( ( SV744 = SV2195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6647]) ).
thf(7142,plain,
! [SV2196: $i,SV745: $i,SV1561: $i] :
( ( ( SV1561
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV745 = SV2196 )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1561 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV2196 @ SV1561 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6648]) ).
thf(7143,plain,
! [SV2568: $i,SV2197: $i,SV1563: $i,SV747: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV747 ) @ SV1563 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV2197 ) @ SV2568 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV1563 = SV2568 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6649]) ).
thf(7144,plain,
! [SV2776: $i,SV2705: $i,SV2569: $i,SV2199: $i,SV1566: $i,SV750: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV750 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV1566 @ SV2199 @ SV750 ) ) @ SV2569 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV2705 @ SV2199 @ SV750 ) ) @ SV2776 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ SV2705 @ SV750 ) @ SV2199 @ SV750 ) ) @ SV2569 )
= SV2776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6652]) ).
thf(7145,plain,
! [SV2571: $i,SV2201: $i,SV1570: $i,SV754: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV754 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SV1570 ) @ SV2201 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SV2571 ) @ SV2201 ) )
| ( SV1570 = SV2571 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6654]) ).
thf(7146,plain,
! [SV2572: $i,SV2203: $i,SV1574: $i,SV758: $i] :
( ( ( ( c_List_Oappend @ SV758 @ SV1574 @ SV2203 )
= ( c_List_Oappend @ SV2572 @ SV1574 @ SV2203 ) )
= $false )
| ( ( SV758 = SV2572 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6658]) ).
thf(7147,plain,
! [SV2573: $i,SV2204: $i,SV1575: $i,SV759: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1575 ) @ SV2204 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ SV759 @ SV2573 ) )
| ( hBOOL @ ( hAPP @ SV759 @ SV2204 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6659]) ).
thf(7148,plain,
! [SV2706: $i,SV2574: $i,SV2205: $i,SV1576: $i,SV760: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV760 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV2205 @ SV760 )
!= ( c_HOL_Ominus__class_Ominus @ SV2574 @ SV2706 @ SV760 ) )
| ( c_HOL_Oord__class_Oless @ SV2574 @ SV2706 @ SV760 )
| ~ ( c_HOL_Oord__class_Oless @ SV1576 @ SV2205 @ SV760 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6660]) ).
thf(7149,plain,
! [SV761: $i,SV2206: $i,SV1577: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV1577 @ SV2206 @ SV761 )
!= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
= $true )
| ( ( ( SV1577
= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
| ( SV2206
= ( c_HOL_Ozero__class_Ozero @ SV761 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV761 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6661]) ).
thf(7150,plain,
! [SV2575: $i,SV2208: $i,SV1579: $i,SV763: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV763 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1579 @ SV2208 @ SV763 )
!= ( c_Power_Opower__class_Opower @ SV2575 @ SV2208 @ SV763 ) )
| ( SV1579 = SV2575 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2208 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV2575 @ SV763 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6662]) ).
thf(7151,plain,
! [SV2576: $i,SV2209: $i,SV1580: $i,SV764: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV764 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SV2209 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SV2576 ) )
| ( SV2209 = SV2576 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6663]) ).
thf(7152,plain,
! [SV2577: $i,SV2210: $i,SV1582: $i,SV766: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV766 ) @ SV1582 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2210 ) @ SV2577 ) )
= $false )
| ( ( SV1582 = SV2577 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6665]) ).
thf(7153,plain,
! [SV2214: $i,SV1588: $i,SV773: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV773 ) )
= $true )
| ( ( ( SV1588
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV773 ) @ SV1588 ) @ SV2214 ) )
| ( SV2214
= ( c_HOL_Ozero__class_Ozero @ SV773 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV773 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6667]) ).
thf(7154,plain,
! [SV2707: $i,SV2578: $i,SV2215: $i,SV1589: $i,SV774: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV774 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV774 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2578 @ SV774 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2707 @ SV774 ) ) )
| ( SV2578 = SV2707 )
| ( SV2215
= ( c_HOL_Ozero__class_Ozero @ SV774 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6668]) ).
thf(7155,plain,
! [SV2708: $i,SV2579: $i,SV2216: $i,SV1590: $i,SV775: $i] :
( ( ( ( c_List_Oreplicate @ SV775 @ SV1590 @ SV2216 )
!= ( c_List_Oreplicate @ SV2579 @ SV2708 @ SV2216 ) )
= $true )
| ( ( SV775 = SV2579 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6669]) ).
thf(7156,plain,
! [SV2709: $i,SV2580: $i,SV2217: $i,SV1592: $i,SV778: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV778 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1592 @ SV2217 @ SV778 )
!= ( c_HOL_Ominus__class_Ominus @ SV2580 @ SV2709 @ SV778 ) )
| ( c_HOL_Oord__class_Oless @ SV1592 @ SV2217 @ SV778 )
| ~ ( c_HOL_Oord__class_Oless @ SV2580 @ SV2709 @ SV778 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6671]) ).
thf(7157,plain,
! [SV779: $i,SV2218: $i,SV1593: $i] :
( ( ( ( c_Orderings_Oord__class_Omax @ SV1593 @ SV2218 @ SV779 )
!= SV2218 )
= $true )
| ( ( c_lessequals @ SV1593 @ SV2218 @ SV779 )
= $true )
| ( ( class_Orderings_Olinorder @ SV779 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6672]) ).
thf(7158,plain,
! [SV2710: $i,SV2581: $i,SV2219: $i,SV1594: $i,SV780: $i] :
( ( ( ( c_List_Oappend @ SV780 @ ( c_List_Olist_OCons @ SV1594 @ ( c_List_Olist_ONil @ SV2219 ) @ SV2219 ) @ SV2219 )
!= ( c_List_Oappend @ SV2581 @ ( c_List_Olist_OCons @ SV2710 @ ( c_List_Olist_ONil @ SV2219 ) @ SV2219 ) @ SV2219 ) )
= $true )
| ( ( SV1594 = SV2710 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6673]) ).
thf(7159,plain,
! [SV2582: $i,SV2220: $i,SV1596: $i,SV782: $i] :
( ( ( ( c_List_Oappend @ SV782 @ SV1596 @ SV2220 )
= ( c_List_Oappend @ SV782 @ SV2582 @ SV2220 ) )
= $false )
| ( ( SV1596 = SV2582 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6674]) ).
thf(7160,plain,
! [SV2583: $i,SV2222: $i,SV1598: $i,SV784: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SV1598 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2222 @ SV2583 @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SV2583 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2222 @ SV1598 @ tc_nat ) ) )
= $false )
| ( ( ( SV1598 = SV2583 )
| ( SV784 = SV2222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6675]) ).
thf(7161,plain,
! [SV2711: $i,SV2584: $i,SV2224: $i,SV1600: $i,SV787: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV787 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV787 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2224 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2711 @ SV787 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2711 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2224 @ SV787 ) ) )
| ( SV2224 = SV2711 )
| ( SV1600 = SV2584 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6677]) ).
thf(7162,plain,
! [SV2712: $i,SV2585: $i,SV2225: $i,SV1602: $i,SV789: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV789 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1602 @ SV2225 @ SV789 )
!= ( c_HOL_Ominus__class_Ominus @ SV2585 @ SV2712 @ SV789 ) )
| ( c_lessequals @ SV2712 @ SV2585 @ SV789 )
| ~ ( c_lessequals @ SV2225 @ SV1602 @ SV789 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6678]) ).
thf(7163,plain,
! [SV790: $i,SV2226: $i,SV1603: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV1603 @ SV2226 @ SV790 )
!= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
= $true )
| ( ( ( SV2226
= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
| ( SV1603
= ( c_HOL_Ozero__class_Ozero @ SV790 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV790 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6679]) ).
thf(7164,plain,
! [SV1605: $i,SV792: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV792 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV792 )
| ~ ( class_Power_Opower @ SV792 )
| ( ( c_Power_Opower__class_Opower @ SV1605 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV792 )
!= ( c_HOL_Ozero__class_Ozero @ SV792 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV792 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6680]) ).
thf(7165,plain,
! [SV2227: $i,SV1606: $i,SV793: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV793 ) @ SV1606 ) @ SV2227 )
!= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV2227 @ SV793 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV1606 @ SV793 )
| ( SV1606
= ( c_HOL_Ozero__class_Ozero @ SV793 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV793 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6681]) ).
thf(7166,plain,
! [SV2586: $i,SV2228: $i,SV1607: $i,SV794: $i] :
( ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV794 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1607 ) @ SV2228 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ SV794 @ SV2586 ) )
| ( hBOOL @ ( hAPP @ SV794 @ SV1607 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6682]) ).
thf(7167,plain,
! [SV795: $i,SV2229: $i,SV1608: $i] :
( ( ( ~ ( c_lessequals @ SV1608 @ SV2229 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1608 @ SV795 @ tc_nat )
| ( SV795 = SV2229 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV795 @ SV1608 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV2229 @ SV1608 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6683]) ).
thf(7168,plain,
! [SV2713: $i,SV2587: $i,SV2230: $i,SV1609: $i,SV796: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV796 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SV2587 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SV2713 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ SV2587 )
= SV2713 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6684]) ).
thf(7169,plain,
! [SV2231: $i,SV1610: $i,SV797: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV797 ) @ ( c_HOL_Otimes__class_Otimes @ SV1610 @ SV1610 @ SV797 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2231 @ SV2231 @ SV797 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV797 ) )
= $true )
| ( ( SV2231
= ( c_HOL_Ozero__class_Ozero @ SV797 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV797 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6685]) ).
thf(7170,plain,
! [SV2588: $i,SV2232: $i,SV1611: $i,SV798: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV798 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1611 @ SV1611 @ SV798 )
!= ( c_HOL_Ominus__class_Ominus @ SV2232 @ SV2588 @ SV798 ) )
| ( SV2232 = SV2588 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6686]) ).
thf(7171,plain,
! [SV2714: $i,SV2589: $i,SV2233: $i,SV1612: $i,SV799: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV799 @ SV1612 @ tc_nat ) ) @ SV2233 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2589 @ SV1612 @ tc_nat ) ) @ SV2714 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV799 @ SV2589 @ tc_nat )
| ( SV2233
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2589 @ SV799 @ tc_nat ) @ SV1612 @ tc_nat ) ) @ SV2714 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6687]) ).
thf(7172,plain,
! [SV2590: $i,SV2234: $i,SV1613: $i,SV800: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV800 ) @ SV1613 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2234 ) @ SV2590 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2234 @ SV1613 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV800 @ SV2590 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6688]) ).
thf(7173,plain,
! [SV2591: $i,SV2235: $i,SV1614: $i,SV801: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV801 ) @ SV1614 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV2235 ) @ SV2591 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV801 = SV2235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6689]) ).
thf(7174,plain,
! [SV2237: $i,SV1616: $i,SV803: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV803 @ tc_nat ) )
= $true )
| ( ( SV1616 = SV2237 )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1616 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV803 @ SV2237 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6691]) ).
thf(7175,plain,
! [SV2715: $i,SV2592: $i,SV2239: $i,SV1619: $i,SV806: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV806 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV806 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2239 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2715 @ SV806 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2715 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2239 @ SV806 ) ) )
| ( SV2239 = SV2715 )
| ( SV1619 = SV2592 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6693]) ).
thf(7176,plain,
! [SV2593: $i,SV2240: $i,SV1620: $i,SV807: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV807 ) @ SV1620 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2240 ) @ SV2593 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV1620 = SV2593 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6694]) ).
thf(7177,plain,
! [SV2777: $i,SV2716: $i,SV2594: $i,SV2241: $i,SV1621: $i,SV808: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV808 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV1621 @ SV2241 @ SV808 ) ) @ SV2594 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV2716 @ SV2241 @ SV808 ) ) @ SV2777 ) )
| ( SV2594
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2716 @ SV1621 @ SV808 ) @ SV2241 @ SV808 ) ) @ SV2777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6695]) ).
thf(7178,plain,
! [SV2242: $i,SV1622: $i,SV809: $i] :
( ( ( SV809
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1622 = SV2242 )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV809 @ SV1622 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV809 @ SV2242 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6696]) ).
thf(7179,plain,
! [SV2243: $i,SV1623: $i,SV810: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV810 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1623 @ SV2243 @ SV810 )
!= ( c_HOL_Ozero__class_Ozero @ SV810 ) )
| ( SV1623 = SV2243 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV810 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6697]) ).
thf(7180,plain,
! [SV2595: $i,SV2244: $i,SV1625: $i,SV812: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1625 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2244 @ SV2595 @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV2595 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2244 @ SV1625 @ tc_nat ) ) )
= $false )
| ( ( ( SV1625 = SV2595 )
| ( SV812 = SV2244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6698]) ).
thf(7181,plain,
! [SV814: $i,SV1627: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1627 @ SV814 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV1627 = SV814 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV814 @ SV1627 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6699]) ).
thf(7182,plain,
! [SV816: $i,SV2246: $i,SV1629: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV1629 @ SV2246 @ SV816 )
!= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
= $true )
| ( ( ( SV2246
= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
| ( SV1629
= ( c_HOL_Ozero__class_Ozero @ SV816 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV816 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6701]) ).
thf(7183,plain,
! [SV2597: $i,SV2248: $i,SV1632: $i,SV819: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV819 ) @ SV1632 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2248 ) @ SV2597 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV819 = SV2248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6704]) ).
thf(7184,plain,
! [SV2598: $i,SV2249: $i,SV1633: $i,SV820: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV820 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SV2249 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SV2598 ) )
| ( SV2249 = SV2598 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6705]) ).
thf(7185,plain,
! [SV2250: $i,SV821: $i,SV1634: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1634 @ SV821 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV2250 @ SV821 ) )
= $true )
| ( ( SV1634 = SV2250 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV821 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6706]) ).
thf(7186,plain,
! [SV2251: $i,SV1635: $i,SV822: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV822 ) @ ( c_HOL_Otimes__class_Otimes @ SV1635 @ SV1635 @ SV822 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2251 @ SV2251 @ SV822 ) )
!= ( c_HOL_Ozero__class_Ozero @ SV822 ) )
= $true )
| ( ( SV1635
= ( c_HOL_Ozero__class_Ozero @ SV822 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV822 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6707]) ).
thf(7187,plain,
! [SV2599: $i,SV2252: $i,SV1636: $i,SV823: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV823 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1636 @ ( c_Suc @ SV2252 ) @ SV823 )
!= ( c_Power_Opower__class_Opower @ SV2599 @ ( c_Suc @ SV2252 ) @ SV823 ) )
| ( SV1636 = SV2599 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV2599 @ SV823 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV1636 @ SV823 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6708]) ).
thf(7188,plain,
! [SV2600: $i,SV2258: $i,SV1643: $i,SV830: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV830 ) @ SV1643 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV2258 ) @ SV2600 ) )
= $false )
| ( ( SV1643 = SV2600 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6711]) ).
thf(7189,plain,
! [SV2601: $i,SV2259: $i,SV1644: $i,SV832: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV832 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV832 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2259 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2601 ) )
| ( SV2259 = SV2601 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6712]) ).
thf(7190,plain,
! [SV834: $i,SV2261: $i,SV1646: $i] :
( ( ( ( c_Orderings_Oord__class_Omin @ SV1646 @ SV2261 @ SV834 )
!= SV1646 )
= $true )
| ( ( c_lessequals @ SV1646 @ SV2261 @ SV834 )
= $true )
| ( ( class_Orderings_Olinorder @ SV834 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6714]) ).
thf(7191,plain,
! [SV2717: $i,SV2602: $i,SV2263: $i,SV1649: $i,SV837: $i] :
( ( ( ( c_List_Oreplicate @ SV837 @ SV1649 @ SV2263 )
!= ( c_List_Oreplicate @ SV2602 @ SV2717 @ SV2263 ) )
= $true )
| ( ( ( SV1649 = SV2717 )
| ( SV837
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6717]) ).
thf(7192,plain,
! [SV2778: $i,SV2718: $i,SV2603: $i,SV2264: $i,SV1650: $i,SV838: $i] :
( ( ! [SY7200: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
| ~ ( c_Type_Otyping @ SV2778 @ SV2603 @ SV1650 )
| ~ ( c_InductTermi_OIT @ SV2603 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2778 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SY7200 )
| ~ ( c_InductTermi_OIT @ SV2264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6718]) ).
thf(7193,plain,
! [SV2265: $i,SV1651: $i,SV839: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV839 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV839 )
| ~ ( class_Power_Opower @ SV839 )
| ( ( c_Power_Opower__class_Opower @ SV1651 @ SV2265 @ SV839 )
!= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
| ( SV1651
= ( c_HOL_Ozero__class_Ozero @ SV839 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV839 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6719]) ).
thf(7194,plain,
! [SV2719: $i,SV2604: $i,SV2267: $i,SV1653: $i,SV841: $i] :
( ( ( ( c_List_Oappend @ SV841 @ ( c_List_Olist_OCons @ SV1653 @ ( c_List_Olist_ONil @ SV2267 ) @ SV2267 ) @ SV2267 )
!= ( c_List_Oappend @ SV2604 @ ( c_List_Olist_OCons @ SV2719 @ ( c_List_Olist_ONil @ SV2267 ) @ SV2267 ) @ SV2267 ) )
= $true )
| ( ( SV841 = SV2604 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6721]) ).
thf(7195,plain,
! [SV846: $i,SV2270: $i,SV1657: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1657 @ SV2270 @ SV846 )
!= ( c_HOL_Ozero__class_Ozero @ SV846 ) )
= $true )
| ( ( SV1657
= ( c_HOL_Ozero__class_Ozero @ SV846 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV846 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6724]) ).
thf(7196,plain,
! [SV2720: $i,SV2605: $i,SV2272: $i,SV1659: $i,SV848: $i] :
( ( ( ( c_List_Olist_OCons @ SV848 @ SV1659 @ SV2272 )
!= ( c_List_Olist_OCons @ SV2605 @ SV2720 @ SV2272 ) )
= $true )
| ( ( SV1659 = SV2720 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6725]) ).
thf(7197,plain,
! [SV1663: $i,SV852: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV852 ) @ SV1663 ) @ SV1663 )
= ( c_HOL_Ozero__class_Ozero @ SV852 ) )
= $false )
| ( ( SV1663
= ( c_HOL_Ozero__class_Ozero @ SV852 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV852 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6728]) ).
thf(7198,plain,
! [SV2606: $i,SV2274: $i,SV1664: $i,SV853: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV853 ) @ SV1664 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2274 ) @ SV2606 ) )
= $false )
| ( ( SV853 = SV2274 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6729]) ).
thf(7199,plain,
! [SV2276: $i,SV1666: $i,SV855: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV855 ) @ SV1666 ) @ SV2276 )
!= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV2276 @ SV855 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV1666 @ SV855 )
| ( SV2276
= ( c_HOL_Ozero__class_Ozero @ SV855 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV855 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6730]) ).
thf(7200,plain,
! [SV856: $i,SV2277: $i,SV1667: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1667 @ SV2277 @ SV856 )
!= ( c_HOL_Ozero__class_Ozero @ SV856 ) )
= $true )
| ( ( SV1667 = SV2277 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV856 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6731]) ).
thf(7201,plain,
! [SV2607: $i,SV2279: $i,SV1669: $i,SV858: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV858 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1669 @ SV2279 @ SV858 )
!= ( c_HOL_Ominus__class_Ominus @ SV2607 @ SV2607 @ SV858 ) )
| ( SV1669 = SV2279 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6733]) ).
thf(7202,plain,
! [SV2608: $i,SV2281: $i,SV1672: $i,SV861: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SV2281 @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SV2608 @ tc_nat ) ) )
= $false )
| ( ( ( SV2281 = SV2608 )
| ( SV1672
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6734]) ).
thf(7203,plain,
! [SV2779: $i,SV2721: $i,SV2609: $i,SV2282: $i,SV1673: $i,SV863: $i] :
( ( ! [SY7201: $i] :
( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
| ~ ( c_Type_Otyping @ SV2779 @ SV2609 @ SV863 )
| ~ ( c_InductTermi_OIT @ SV2609 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2779 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SY7201 )
| ~ ( c_InductTermi_OIT @ SV2282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6735]) ).
thf(7204,plain,
! [SV864: $i,SV2283: $i,SV1674: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1674 @ SV2283 @ SV864 )
!= ( c_HOL_Ozero__class_Ozero @ SV864 ) )
= $true )
| ( ( SV1674 = SV2283 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV864 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6736]) ).
thf(7205,plain,
! [SV2610: $i,SV865: $i,SV1: $i,SV2284: $i,SV1675: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1675 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2284 @ SV1 @ tc_nat ) @ SV865 @ tc_nat ) ) @ SV2610 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1 @ SV2284 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1 @ SV865 @ tc_nat ) ) @ SV1675 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2284 @ SV865 @ tc_nat ) ) @ SV2610 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6737]) ).
thf(7206,plain,
! [SV2611: $i,SV866: $i,SV2: $i,SV2285: $i,SV1676: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV2285 @ tc_nat ) ) @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV866 @ SV2285 @ tc_nat ) ) @ SV2611 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1676 @ SV866 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV2 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV866 @ SV1676 @ tc_nat ) @ SV2285 @ tc_nat ) ) @ SV2611 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6738]) ).
thf(7207,plain,
! [SV2612: $i,SV1677: $i,SV867: $i,SV2286: $i,SV3: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV3 @ SV2286 @ tc_nat ) @ SV867 @ tc_nat ) ) @ SV1677 ) @ SV2612 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2286 @ SV3 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV3 @ SV867 @ tc_nat ) ) @ SV1677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2286 @ SV867 @ tc_nat ) ) @ SV2612 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6739]) ).
thf(7208,plain,
! [SV2613: $i,SV868: $i,SV2287: $i,SV1678: $i,SV4: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV4 @ SV1678 @ tc_nat ) ) @ SV2287 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV868 @ SV1678 @ tc_nat ) ) @ SV2613 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV868 @ SV4 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV868 @ tc_nat ) @ SV1678 @ tc_nat ) ) @ SV2287 ) @ SV2613 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6740]) ).
thf(7209,plain,
! [SV2614: $i,SV2288: $i,SV1679: $i,SV869: $i,SV5: $i] :
( ( ( class_Ring__and__Field_Oring @ SV5 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV869 @ SV1679 @ SV5 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2288 @ SV869 @ SV5 ) @ SV1679 @ SV5 ) ) @ SV2614 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV2288 @ SV1679 @ SV5 ) ) @ SV2614 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6741]) ).
thf(7210,plain,
! [SV2615: $i,SV2289: $i,SV1680: $i,SV873: $i,SV9: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV2289 @ SV2615 @ SV9 ) @ SV9 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV2289 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1680 @ SV2615 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV873 @ SV2289 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6743]) ).
thf(7211,plain,
! [SV13: $i,SV2290: $i,SV1683: $i,SV877: $i] :
( ( ( c_lessequals @ SV877 @ ( c_Orderings_Oord__class_Omin @ SV1683 @ SV2290 @ SV13 ) @ SV13 )
= $true )
| ( ( ~ ( c_lessequals @ SV877 @ SV2290 @ SV13 )
| ~ ( c_lessequals @ SV877 @ SV1683 @ SV13 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6745]) ).
thf(7212,plain,
! [SV14: $i,SV2291: $i,SV1684: $i,SV878: $i] :
( ( ( c_lessequals @ SV878 @ ( c_Orderings_Oord__class_Omin @ SV1684 @ SV2291 @ SV14 ) @ SV14 )
= $true )
| ( ( ~ ( c_lessequals @ SV878 @ SV2291 @ SV14 )
| ~ ( c_lessequals @ SV878 @ SV1684 @ SV14 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6746]) ).
thf(7213,plain,
! [SV15: $i,SV2292: $i,SV1685: $i,SV879: $i] :
( ( ( c_lessequals @ SV879 @ ( c_Orderings_Oord__class_Omin @ SV1685 @ SV2292 @ SV15 ) @ SV15 )
= $true )
| ( ( ~ ( c_lessequals @ SV879 @ SV2292 @ SV15 )
| ~ ( c_lessequals @ SV879 @ SV1685 @ SV15 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6747]) ).
thf(7214,plain,
! [SV2616: $i,SV2293: $i,SV1686: $i,SV880: $i,SV16: $i] :
( ( ( class_Ring__and__Field_Oring @ SV16 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SV880 @ SV1686 @ SV16 ) ) @ SV2293 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ SV2616 @ SV1686 @ SV16 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV880 @ SV2616 @ SV16 ) @ SV1686 @ SV16 ) ) @ SV2293 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6748]) ).
thf(7215,plain,
! [SV1687: $i,SV881: $i,SV17: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV881 @ SV17 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ ( c_Power_Opower__class_Opower @ SV881 @ SV1687 @ SV17 ) @ SV17 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6749]) ).
thf(7216,plain,
! [SV2295: $i,SV20: $i,SV1689: $i,SV884: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV884 @ SV1689 @ SV20 ) @ SV2295 @ SV20 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1689 @ SV2295 @ SV20 )
| ~ ( c_HOL_Oord__class_Oless @ SV884 @ SV2295 @ SV20 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6751]) ).
thf(7217,plain,
! [SV2296: $i,SV1691: $i,SV886: $i,SV22: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV22 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV886 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1691 ) @ SV2296 ) @ SV22 )
| ~ ( c_lessequals @ SV886 @ SV2296 @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV1691 @ SV22 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6752]) ).
thf(7218,plain,
! [SV887: $i,SV23: $i,SV1692: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1692 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV23 @ SV887 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV23 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV887 ) @ SV1692 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6753]) ).
thf(7219,plain,
! [SV1693: $i,SV24: $i,SV888: $i] :
( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV888 @ SV24 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1693 @ SV24 ) @ SV24 )
= $false )
| ( ( c_lessequals @ SV888 @ SV1693 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6754]) ).
thf(7220,plain,
! [SV25: $i,SV1694: $i,SV889: $i] :
( ( ( c_lessequals @ SV889 @ SV1694 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV889 @ SV25 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1694 @ SV25 ) @ SV25 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6755]) ).
thf(7221,plain,
! [SV27: $i,SV2298: $i,SV1696: $i,SV891: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV891 @ ( c_Orderings_Oord__class_Omin @ SV1696 @ SV2298 @ SV27 ) @ SV27 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV2298 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV1696 @ SV27 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6757]) ).
thf(7222,plain,
! [SV2299: $i,SV1699: $i,SV894: $i,SV30: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV30 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV1699 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV2299 @ SV30 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV2299 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV1699 @ SV30 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6758]) ).
thf(7223,plain,
! [SV2300: $i,SV1700: $i,SV895: $i,SV31: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV31 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1700 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV2300 @ SV31 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV2300 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1700 @ SV31 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6759]) ).
thf(7224,plain,
! [SV2617: $i,SV1703: $i,SV901: $i,SV2301: $i,SV38: $i] :
( ( ( c_lessequals @ SV38 @ SV2301 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV38 @ SV901 @ tc_nat ) ) @ SV1703 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2301 @ SV901 @ tc_nat ) ) @ SV2617 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1703 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2301 @ SV38 @ tc_nat ) @ SV901 @ tc_nat ) ) @ SV2617 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6762]) ).
thf(7225,plain,
! [SV2618: $i,SV1704: $i,SV902: $i,SV39: $i,SV2302: $i] :
( ( ( c_lessequals @ SV2302 @ SV39 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV39 @ SV902 @ tc_nat ) ) @ SV1704 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2302 @ SV902 @ tc_nat ) ) @ SV2618 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SV2302 @ tc_nat ) @ SV902 @ tc_nat ) ) @ SV1704 ) @ SV2618 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6763]) ).
thf(7226,plain,
! [SV1715: $i,SV51: $i,SV2304: $i,SV914: $i] :
( ( ( c_lessequals @ SV914 @ SV2304 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV51 @ SV1715 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV914 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1715 ) @ SV2304 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6766]) ).
thf(7227,plain,
! [SV2619: $i,SV2305: $i,SV1716: $i,SV915: $i,SV52: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV52 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV915 ) @ SV1716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV2305 ) @ SV2619 ) @ SV52 )
| ~ ( c_lessequals @ SV1716 @ SV2619 @ SV52 )
| ~ ( c_lessequals @ SV915 @ SV2305 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6767]) ).
thf(7228,plain,
! [SV59: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) )
= ( c_HOL_Ozero__class_Ozero @ SV59 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6768]) ).
thf(7229,plain,
! [SV923: $i,SV1719: $i,SV62: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1719 @ SV62 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV923 @ SV62 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV923 ) @ SV1719 ) @ SV62 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6769]) ).
thf(7230,plain,
! [SV2306: $i,SV63: $i,SV1720: $i,SV924: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV924 @ SV1720 @ SV63 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2306 @ SV1720 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ SV2306 @ SV63 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6770]) ).
thf(7231,plain,
! [SV2307: $i,SV64: $i,SV1721: $i,SV925: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV925 @ SV1721 @ SV64 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV925 @ SV2307 @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV2307 @ SV1721 @ SV64 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6771]) ).
thf(7232,plain,
! [SV66: $i,SV1723: $i,SV927: $i] :
( ( ( c_lessequals @ SV927 @ SV1723 @ SV66 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV927 @ SV1723 @ SV66 )
= SV1723 )
= $true )
| ( ( class_Orderings_Olinorder @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6773]) ).
thf(7233,plain,
! [SV67: $i,SV928: $i,SV1724: $i] :
( ( ( c_lessequals @ SV1724 @ SV928 @ SV67 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV928 @ SV1724 @ SV67 )
= SV928 )
= $true )
| ( ( class_Orderings_Olinorder @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6774]) ).
thf(7234,plain,
! [SV933: $i,SV72: $i,SV1729: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1729 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV72 ) @ tc_nat )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV72 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV72 @ SV1729 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV72 @ SV933 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6777]) ).
thf(7235,plain,
! [SV76: $i,SV1730: $i,SV937: $i] :
( ( ( c_lessequals @ SV937 @ SV1730 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV76 @ ( c_HOL_Ominus__class_Ominus @ SV1730 @ SV937 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV76 ) @ SV937 ) @ SV1730 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6778]) ).
thf(7236,plain,
! [SV77: $i,SV938: $i,SV1731: $i] :
( ( ( c_lessequals @ SV1731 @ SV938 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV77 ) @ SV1731 ) @ SV938 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV77 @ ( c_HOL_Ominus__class_Ominus @ SV938 @ SV1731 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6779]) ).
thf(7237,plain,
! [SV2311: $i,SV78: $i,SV1732: $i,SV939: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV939 @ SV1732 @ SV78 ) @ SV2311 @ SV78 )
= $true )
| ( ( ~ ( c_lessequals @ SV1732 @ SV2311 @ SV78 )
| ~ ( c_lessequals @ SV939 @ SV2311 @ SV78 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6780]) ).
thf(7238,plain,
! [SV2312: $i,SV79: $i,SV1733: $i,SV940: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV940 @ SV1733 @ SV79 ) @ SV2312 @ SV79 )
= $true )
| ( ( ~ ( c_lessequals @ SV1733 @ SV2312 @ SV79 )
| ~ ( c_lessequals @ SV940 @ SV2312 @ SV79 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6781]) ).
thf(7239,plain,
! [SV2313: $i,SV80: $i,SV1734: $i,SV941: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV941 @ SV1734 @ SV80 ) @ SV2313 @ SV80 )
= $true )
| ( ( ~ ( c_lessequals @ SV1734 @ SV2313 @ SV80 )
| ~ ( c_lessequals @ SV941 @ SV2313 @ SV80 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6782]) ).
thf(7240,plain,
! [SV2780: $i,SV2722: $i,SV2620: $i,SV2315: $i,SV1738: $i,SV951: $i,SV90: $i] :
( ( ! [SY7202: $i,SY7203: $i] :
( ( ( hAPP @ ( hAPP @ SV90 @ ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ SV1738 ) ) @ SV2315 )
= ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ ( c_HOL_Otimes__class_Otimes @ SV1738 @ SV2315 @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2620 @ SV2722 @ SV90 @ SV2780 @ SY7202 @ SY7203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6783]) ).
thf(7241,plain,
! [SV2318: $i,SV1741: $i,SV954: $i,SV93: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV93 ) )
= $true )
| ( ( ( c_lessequals @ SV954 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV1741 ) @ SV2318 ) @ SV93 )
| ~ ( c_lessequals @ SV954 @ SV2318 @ SV93 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV1741 @ SV93 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6786]) ).
thf(7242,plain,
! [SV2319: $i,SV1742: $i,SV955: $i,SV94: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV94 ) )
= $true )
| ( ( ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV1742 ) @ SV2319 ) @ SV94 )
| ~ ( c_lessequals @ SV955 @ SV1742 @ SV94 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV2319 @ SV94 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6787]) ).
thf(7243,plain,
! [SV2723: $i,SV2621: $i,SV2320: $i,SV1748: $i,SV967: $i,SV106: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV106 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV967 @ SV1748 @ SV106 ) ) @ SV2320 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV2621 @ SV1748 @ SV106 ) ) @ SV2723 ) @ SV106 )
| ~ ( c_lessequals @ SV2320 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2621 @ SV967 @ SV106 ) @ SV1748 @ SV106 ) ) @ SV2723 ) @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6790]) ).
thf(7244,plain,
! [SV2724: $i,SV2622: $i,SV2321: $i,SV1749: $i,SV968: $i,SV107: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV107 ) )
= $true )
| ( ( ( c_lessequals @ SV968 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SV2321 @ SV107 ) @ SV2622 @ SV107 ) ) @ SV2724 ) @ SV107 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV2321 @ SV2622 @ SV107 ) ) @ SV968 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV1749 @ SV2622 @ SV107 ) ) @ SV2724 ) @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6791]) ).
thf(7245,plain,
! [SV2725: $i,SV2623: $i,SV2322: $i,SV1750: $i,SV969: $i,SV108: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV108 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV969 @ SV1750 @ SV108 ) ) @ SV2322 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV2623 @ SV1750 @ SV108 ) ) @ SV2725 ) @ SV108 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV969 @ SV2623 @ SV108 ) @ SV1750 @ SV108 ) ) @ SV2322 ) @ SV2725 @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6792]) ).
thf(7246,plain,
! [SV2726: $i,SV2624: $i,SV2323: $i,SV1751: $i,SV970: $i,SV109: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV109 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV970 @ SV1751 @ SV109 ) @ SV2323 @ SV109 ) ) @ SV2624 ) @ SV2726 @ SV109 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV970 @ SV2323 @ SV109 ) ) @ SV2624 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV1751 @ SV2323 @ SV109 ) ) @ SV2726 ) @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6793]) ).
thf(7247,plain,
! [SV117: $i,SV978: $i,SV1757: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1757 @ SV978 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1757 @ SV117 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV978 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV1757 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6795]) ).
thf(7248,plain,
! [SV2325: $i,SV119: $i,SV1758: $i,SV980: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV980 @ SV1758 @ SV119 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV2325 @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV980 @ SV2325 @ SV119 ) @ ( c_HOL_Otimes__class_Otimes @ SV1758 @ SV2325 @ SV119 ) @ SV119 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6797]) ).
thf(7249,plain,
! [SV2326: $i,SV120: $i,SV1759: $i,SV981: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV981 @ SV1759 @ SV120 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV2326 @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV981 @ SV120 ) @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV1759 @ SV120 ) @ SV120 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6798]) ).
thf(7250,plain,
! [SV2327: $i,SV121: $i,SV1760: $i,SV982: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV982 @ SV1760 @ SV121 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV2327 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV982 @ SV2327 @ SV121 ) @ ( c_HOL_Otimes__class_Otimes @ SV1760 @ SV2327 @ SV121 ) @ SV121 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6799]) ).
thf(7251,plain,
! [SV2328: $i,SV122: $i,SV1761: $i,SV983: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV983 @ SV1761 @ SV122 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV2328 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV983 @ SV122 ) @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV1761 @ SV122 ) @ SV122 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6800]) ).
thf(7252,plain,
! [SV2329: $i,SV124: $i,SV1763: $i,SV985: $i] :
( ( ( c_lessequals @ SV985 @ SV1763 @ SV124 )
= $true )
| ( ( ( c_lessequals @ SV985 @ SV2329 @ SV124 )
| ~ ( c_lessequals @ SV985 @ ( c_Orderings_Oord__class_Omax @ SV2329 @ SV1763 @ SV124 ) @ SV124 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6801]) ).
thf(7253,plain,
! [SV2781: $i,SV2727: $i,SV2625: $i,SV2331: $i,SV1765: $i,SV989: $i,SV128: $i] :
( ( ! [SY7204: $i,SY7205: $i] :
( ( ( hAPP @ ( hAPP @ SV128 @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2331 ) ) @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2625 ) )
= ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2331 ) @ SV2625 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2727 @ SV128 @ SV989 @ SV2781 @ SY7204 @ SY7205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6803]) ).
thf(7254,plain,
! [SV2333: $i,SV131: $i,SV1767: $i,SV991: $i] :
( ( ( c_lessequals @ SV991 @ SV1767 @ SV131 )
= $true )
| ( ( ~ ( c_lessequals @ SV991 @ ( c_Orderings_Oord__class_Omin @ SV2333 @ SV1767 @ SV131 ) @ SV131 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6805]) ).
thf(7255,plain,
! [SV2334: $i,SV132: $i,SV1768: $i,SV992: $i] :
( ( ( c_lessequals @ SV992 @ SV1768 @ SV132 )
= $true )
| ( ( ~ ( c_lessequals @ SV992 @ ( c_Orderings_Oord__class_Omin @ SV1768 @ SV2334 @ SV132 ) @ SV132 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6806]) ).
thf(7256,plain,
! [SV2335: $i,SV133: $i,SV1769: $i,SV993: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV993 @ SV1769 @ SV133 ) @ SV2335 @ SV133 )
= $true )
| ( ( ~ ( c_lessequals @ SV1769 @ SV2335 @ SV133 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6807]) ).
thf(7257,plain,
! [SV2336: $i,SV134: $i,SV1770: $i,SV994: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV994 @ SV1770 @ SV134 ) @ SV2336 @ SV134 )
= $true )
| ( ( ~ ( c_lessequals @ SV994 @ SV2336 @ SV134 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6808]) ).
thf(7258,plain,
! [SV2337: $i,SV135: $i,SV1771: $i,SV995: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV995 @ SV1771 @ SV135 ) @ SV2337 @ SV135 )
= $true )
| ( ( ~ ( c_lessequals @ SV1771 @ SV2337 @ SV135 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6809]) ).
thf(7259,plain,
! [SV2338: $i,SV136: $i,SV1772: $i,SV996: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV996 @ SV1772 @ SV136 ) @ SV2338 @ SV136 )
= $true )
| ( ( ~ ( c_lessequals @ SV996 @ SV2338 @ SV136 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6810]) ).
thf(7260,plain,
! [SV2339: $i,SV137: $i,SV1773: $i,SV997: $i] :
( ( ( c_lessequals @ SV997 @ SV1773 @ SV137 )
= $true )
| ( ( ~ ( c_lessequals @ SV997 @ ( c_Orderings_Oord__class_Omin @ SV2339 @ SV1773 @ SV137 ) @ SV137 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6811]) ).
thf(7261,plain,
! [SV2340: $i,SV138: $i,SV1774: $i,SV998: $i] :
( ( ( c_lessequals @ SV998 @ SV1774 @ SV138 )
= $true )
| ( ( ~ ( c_lessequals @ SV998 @ ( c_Orderings_Oord__class_Omin @ SV1774 @ SV2340 @ SV138 ) @ SV138 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6812]) ).
thf(7262,plain,
! [SV2728: $i,SV2626: $i,SV2341: $i,SV1776: $i,SV1000: $i,SV140: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV140 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1776 @ SV140 ) ) @ SV2341 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV2626 @ SV1776 @ SV140 ) ) @ SV2728 ) @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV2341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2626 @ SV1000 @ SV140 ) @ SV1776 @ SV140 ) ) @ SV2728 ) @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6813]) ).
thf(7263,plain,
! [SV2729: $i,SV2627: $i,SV2342: $i,SV1777: $i,SV1001: $i,SV141: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV141 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1001 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1777 @ SV2342 @ SV141 ) @ SV2627 @ SV141 ) ) @ SV2729 ) @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV2342 @ SV2627 @ SV141 ) ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV1777 @ SV2627 @ SV141 ) ) @ SV2729 ) @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6814]) ).
thf(7264,plain,
! [SV2730: $i,SV2628: $i,SV2343: $i,SV1778: $i,SV1002: $i,SV142: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV142 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1778 @ SV142 ) ) @ SV2343 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV2628 @ SV1778 @ SV142 ) ) @ SV2730 ) @ SV142 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1002 @ SV2628 @ SV142 ) @ SV1778 @ SV142 ) ) @ SV2343 ) @ SV2730 @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6815]) ).
thf(7265,plain,
! [SV2731: $i,SV2629: $i,SV2344: $i,SV1779: $i,SV1003: $i,SV143: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV143 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1003 @ SV1779 @ SV143 ) @ SV2344 @ SV143 ) ) @ SV2629 ) @ SV2731 @ SV143 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1003 @ SV2344 @ SV143 ) ) @ SV2629 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1779 @ SV2344 @ SV143 ) ) @ SV2731 ) @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6816]) ).
thf(7266,plain,
! [SV2345: $i,SV144: $i,SV1780: $i,SV1004: $i] :
( ( ( c_lessequals @ SV1004 @ SV1780 @ SV144 )
= $true )
| ( ( ( c_lessequals @ SV2345 @ SV1780 @ SV144 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV2345 @ SV1004 @ SV144 ) @ SV1780 @ SV144 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6817]) ).
thf(7267,plain,
! [SV1010: $i,SV1782: $i,SV150: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1782 @ SV150 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ ( c_HOL_Otimes__class_Otimes @ SV1010 @ SV1782 @ SV150 ) @ SV150 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1010 @ SV150 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6823]) ).
thf(7268,plain,
! [SV1011: $i,SV1783: $i,SV151: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1783 @ SV151 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ ( c_HOL_Otimes__class_Otimes @ SV1783 @ SV1011 @ SV151 ) @ SV151 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1011 @ SV151 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6824]) ).
thf(7269,plain,
! [SV1012: $i,SV1784: $i,SV152: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1784 @ SV152 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1012 @ SV152 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SV1784 @ SV152 ) @ SV152 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6825]) ).
thf(7270,plain,
! [SV1013: $i,SV153: $i,SV1785: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1785 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1013 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV1013 @ SV1785 @ SV153 ) @ SV153 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6826]) ).
thf(7271,plain,
! [SV2347: $i,SV155: $i,SV1786: $i,SV1015: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1786 @ SV155 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV1786 @ SV155 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1015 @ SV2347 @ SV155 ) @ ( c_Power_Opower__class_Opower @ SV1786 @ SV2347 @ SV155 ) @ SV155 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6828]) ).
thf(7272,plain,
! [SV175: $i,SV1803: $i,SV1035: $i] :
( ( ( c_lessequals @ SV1035 @ SV1803 @ SV175 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1035 @ SV1803 @ SV175 )
= SV1035 )
= $true )
| ( ( class_Orderings_Olinorder @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6837]) ).
thf(7273,plain,
! [SV176: $i,SV1036: $i,SV1804: $i] :
( ( ( c_lessequals @ SV1804 @ SV1036 @ SV176 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1036 @ SV1804 @ SV176 )
= SV1804 )
= $true )
| ( ( class_Orderings_Olinorder @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6838]) ).
thf(7274,plain,
! [SV180: $i,SV1040: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1040 @ SV1040 @ SV180 )
= $false )
| ( ( c_lessequals @ SV1040 @ SV1040 @ SV180 )
= $false )
| ( ( class_Orderings_Olinorder @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6842]) ).
thf(7275,plain,
! [SV182: $i,SV1808: $i,SV1042: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1042 @ SV1808 @ SV182 )
= $false )
| ( ( ~ ( c_lessequals @ SV1808 @ SV1042 @ SV182 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6843]) ).
thf(7276,plain,
! [SV184: $i,SV1810: $i,SV1044: $i] :
( ( ( c_lessequals @ SV1044 @ SV1810 @ SV184 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1810 @ SV1044 @ SV184 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6845]) ).
thf(7277,plain,
! [SV186: $i,SV1812: $i,SV1046: $i] :
( ( ( c_lessequals @ SV1046 @ SV1812 @ SV186 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1812 @ SV1046 @ SV186 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6847]) ).
thf(7278,plain,
! [SV2360: $i,SV1815: $i,SV1052: $i,SV192: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV192 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1052 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV1815 ) @ SV2360 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SV2360 @ SV192 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV1815 @ SV192 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6850]) ).
thf(7279,plain,
! [SV195: $i,SV1818: $i,SV1055: $i] :
( ( ( ~ ( c_lessequals @ SV1055 @ SV1818 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1055 @ SV195 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV195 @ SV1818 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV195 @ SV1055 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1818 @ SV1055 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6851]) ).
thf(7280,plain,
! [SV196: $i,SV1056: $i,SV1819: $i] :
( ( ( ~ ( c_lessequals @ SV1819 @ SV1056 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1819 @ SV196 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV196 @ SV1819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1056 @ SV1819 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV196 @ SV1056 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6852]) ).
thf(7281,plain,
! [SV2361: $i,SV199: $i,SV1821: $i,SV1059: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1821 @ SV199 ) @ ( c_Power_Opower__class_Opower @ SV2361 @ SV1821 @ SV199 ) @ SV199 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV1059 @ SV199 )
| ~ ( c_lessequals @ SV1059 @ SV2361 @ SV199 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6853]) ).
thf(7282,plain,
! [SV1066: $i,SV1827: $i,SV206: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV206 @ SV1827 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1066 @ SV1827 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1827 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV206 @ SV1066 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6855]) ).
thf(7283,plain,
! [SV1067: $i,SV207: $i,SV1828: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1828 @ SV207 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1828 @ SV1067 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1828 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV207 @ SV1067 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6856]) ).
thf(7284,plain,
! [SV1068: $i,SV208: $i,SV1829: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1829 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1829 @ SV208 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1829 @ SV1068 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV208 @ SV1068 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6857]) ).
thf(7285,plain,
! [SV1830: $i,SV1069: $i,SV209: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV209 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1069 @ SV1830 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SV1069 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV209 @ SV1830 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6858]) ).
thf(7286,plain,
! [SV2364: $i,SV210: $i,SV1831: $i,SV1070: $i] :
( ( ( c_lessequals @ SV1070 @ SV1831 @ SV210 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1831 @ SV210 ) @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1070 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SV2364 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6859]) ).
thf(7287,plain,
! [SV2365: $i,SV211: $i,SV1832: $i,SV1071: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV1832 @ SV211 ) @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV2365 @ SV211 ) @ SV211 )
= $true )
| ( ( ~ ( c_lessequals @ SV2365 @ SV1832 @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6860]) ).
thf(7288,plain,
! [SV2366: $i,SV212: $i,SV1833: $i,SV1072: $i] :
( ( ( c_lessequals @ SV1072 @ SV1833 @ SV212 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1072 @ SV212 ) @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1833 @ SV212 ) @ SV212 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SV2366 @ SV212 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6861]) ).
thf(7289,plain,
! [SV2367: $i,SV213: $i,SV1834: $i,SV1073: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV1834 @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV2367 @ SV213 ) @ SV213 )
= $true )
| ( ( ~ ( c_lessequals @ SV1834 @ SV2367 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV1073 @ SV213 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6862]) ).
thf(7290,plain,
! [SV2368: $i,SV214: $i,SV1835: $i,SV1074: $i] :
( ( ( c_lessequals @ SV1074 @ SV1835 @ SV214 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV2368 @ SV214 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1074 @ SV214 ) @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1835 @ SV214 ) @ SV214 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6863]) ).
thf(7291,plain,
! [SV2369: $i,SV215: $i,SV1836: $i,SV1075: $i] :
( ( ( c_lessequals @ SV1075 @ SV1836 @ SV215 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV2369 @ SV215 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1075 @ SV2369 @ SV215 ) @ ( c_HOL_Otimes__class_Otimes @ SV1836 @ SV2369 @ SV215 ) @ SV215 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6864]) ).
thf(7292,plain,
! [SV221: $i,SV2370: $i,SV1839: $i,SV1079: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1079 @ ( c_Orderings_Oord__class_Omax @ SV1839 @ SV2370 @ SV221 ) @ SV221 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1079 @ SV1839 @ SV221 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6866]) ).
thf(7293,plain,
! [SV222: $i,SV2371: $i,SV1840: $i,SV1080: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1080 @ ( c_Orderings_Oord__class_Omax @ SV1840 @ SV2371 @ SV222 ) @ SV222 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1080 @ SV2371 @ SV222 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6867]) ).
thf(7294,plain,
! [SV223: $i,SV2372: $i,SV1841: $i,SV1081: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1081 @ ( c_Orderings_Oord__class_Omax @ SV1841 @ SV2372 @ SV223 ) @ SV223 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1081 @ SV1841 @ SV223 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6868]) ).
thf(7295,plain,
! [SV224: $i,SV2373: $i,SV1842: $i,SV1082: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1082 @ ( c_Orderings_Oord__class_Omax @ SV1842 @ SV2373 @ SV224 ) @ SV224 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1082 @ SV2373 @ SV224 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6869]) ).
thf(7296,plain,
! [SV2374: $i,SV225: $i,SV1843: $i,SV1083: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1083 @ SV1843 @ SV225 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SV2374 @ SV225 ) @ SV1843 @ SV225 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6870]) ).
thf(7297,plain,
! [SV2375: $i,SV226: $i,SV1844: $i,SV1084: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1084 @ SV1844 @ SV226 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV2375 @ SV1084 @ SV226 ) @ SV1844 @ SV226 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6871]) ).
thf(7298,plain,
! [SV2631: $i,SV2377: $i,SV1847: $i,SV1087: $i,SV230: $i] :
( ( ( class_Ring__and__Field_Osemiring @ SV230 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SV1087 @ SV1847 @ SV230 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ SV2377 @ SV1847 @ SV230 ) ) @ SV2631 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ ( c_HOL_Otimes__class_Otimes @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV230 ) @ SV1087 ) @ SV2377 ) @ SV1847 @ SV230 ) ) @ SV2631 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6872]) ).
thf(7299,plain,
! [SV1091: $i,SV234: $i,SV1848: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1848 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1091 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV1091 ) @ SV1848 ) @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6873]) ).
thf(7300,plain,
! [SV2378: $i,SV235: $i,SV1849: $i,SV1092: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1092 @ SV1849 @ SV235 ) @ ( c_Power_Opower__class_Opower @ SV2378 @ SV1849 @ SV235 ) @ SV235 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1849 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV235 ) @ SV1092 @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SV2378 @ SV235 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6874]) ).
thf(7301,plain,
! [SV1850: $i,SV1093: $i,SV236: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV236 ) @ ( c_HOL_Otimes__class_Otimes @ SV1093 @ SV1093 @ SV236 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1850 @ SV1850 @ SV236 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV236 ) @ SV236 )
= $false )
| ( ( SV1093
= ( c_HOL_Ozero__class_Ozero @ SV236 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6875]) ).
thf(7302,plain,
! [SV1094: $i,SV1851: $i,SV237: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( c_HOL_Otimes__class_Otimes @ SV1851 @ SV1851 @ SV237 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1094 @ SV1094 @ SV237 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV237 ) @ SV237 )
= $false )
| ( ( SV1094
= ( c_HOL_Ozero__class_Ozero @ SV237 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6876]) ).
thf(7303,plain,
! [SV2383: $i,SV244: $i,SV1858: $i,SV1101: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1101 @ SV1858 @ SV244 ) @ SV2383 @ SV244 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1101 @ SV2383 @ SV244 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6879]) ).
thf(7304,plain,
! [SV2384: $i,SV245: $i,SV1859: $i,SV1102: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1102 @ SV1859 @ SV245 ) @ SV2384 @ SV245 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1859 @ SV2384 @ SV245 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6880]) ).
thf(7305,plain,
! [SV2385: $i,SV247: $i,SV1861: $i,SV1104: $i] :
( ( ( c_lessequals @ SV1104 @ SV1861 @ SV247 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2385 @ SV1104 @ SV247 ) @ SV1861 @ SV247 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6881]) ).
thf(7306,plain,
! [SV2386: $i,SV248: $i,SV1862: $i,SV1105: $i] :
( ( ( c_lessequals @ SV1105 @ SV1862 @ SV248 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1105 @ SV2386 @ SV248 ) @ SV1862 @ SV248 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6882]) ).
thf(7307,plain,
! [SV249: $i,SV2387: $i,SV1863: $i,SV1106: $i] :
( ( ( c_lessequals @ SV1106 @ ( c_Orderings_Oord__class_Omax @ SV1863 @ SV2387 @ SV249 ) @ SV249 )
= $true )
| ( ( ~ ( c_lessequals @ SV1106 @ SV2387 @ SV249 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6883]) ).
thf(7308,plain,
! [SV250: $i,SV2388: $i,SV1864: $i,SV1107: $i] :
( ( ( c_lessequals @ SV1107 @ ( c_Orderings_Oord__class_Omax @ SV1864 @ SV2388 @ SV250 ) @ SV250 )
= $true )
| ( ( ~ ( c_lessequals @ SV1107 @ SV1864 @ SV250 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6884]) ).
thf(7309,plain,
! [SV251: $i,SV2389: $i,SV1865: $i,SV1108: $i] :
( ( ( c_lessequals @ SV1108 @ ( c_Orderings_Oord__class_Omax @ SV1865 @ SV2389 @ SV251 ) @ SV251 )
= $true )
| ( ( ~ ( c_lessequals @ SV1108 @ SV2389 @ SV251 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6885]) ).
thf(7310,plain,
! [SV252: $i,SV2390: $i,SV1866: $i,SV1109: $i] :
( ( ( c_lessequals @ SV1109 @ ( c_Orderings_Oord__class_Omax @ SV1866 @ SV2390 @ SV252 ) @ SV252 )
= $true )
| ( ( ~ ( c_lessequals @ SV1109 @ SV1866 @ SV252 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6886]) ).
thf(7311,plain,
! [SV2391: $i,SV253: $i,SV1867: $i,SV1110: $i] :
( ( ( c_lessequals @ SV1110 @ SV1867 @ SV253 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2391 @ SV1110 @ SV253 ) @ SV1867 @ SV253 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV253 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6887]) ).
thf(7312,plain,
! [SV2392: $i,SV254: $i,SV1868: $i,SV1111: $i] :
( ( ( c_lessequals @ SV1111 @ SV1868 @ SV254 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1111 @ SV2392 @ SV254 ) @ SV1868 @ SV254 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV254 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6888]) ).
thf(7313,plain,
! [SV1871: $i,SV1114: $i,SV257: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV1114 @ SV257 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ ( c_Power_Opower__class_Opower @ SV1114 @ SV1871 @ SV257 ) @ SV257 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6889]) ).
thf(7314,plain,
! [SV2393: $i,SV258: $i,SV1872: $i,SV1115: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1115 @ SV1872 @ SV258 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1115 @ SV2393 @ SV258 )
| ~ ( c_HOL_Oord__class_Oless @ SV1115 @ ( c_Orderings_Oord__class_Omax @ SV2393 @ SV1872 @ SV258 ) @ SV258 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6890]) ).
thf(7315,plain,
! [SV1873: $i,SV1118: $i,SV261: $i] :
( ( ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV261 @ SV1118 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( c_InductTermi_OIT @ SV1118 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV261 ) ) @ SV1118 ) @ SV1873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6891]) ).
thf(7316,plain,
! [SV2632: $i,SV1122: $i,SV2396: $i,SV1877: $i,SV265: $i] :
( ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV265 @ SV1877 @ tc_nat ) ) @ SV2396 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV1877 @ tc_nat ) ) @ SV2632 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1122 @ SV265 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV265 @ SV1122 @ tc_nat ) @ SV1877 @ tc_nat ) ) @ SV2396 ) @ SV2632 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6893]) ).
thf(7317,plain,
! [SV2633: $i,SV1878: $i,SV1123: $i,SV2397: $i,SV266: $i] :
( ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV266 @ SV2397 @ tc_nat ) @ SV1123 @ tc_nat ) ) @ SV1878 ) @ SV2633 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2397 @ SV266 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV266 @ SV1123 @ tc_nat ) ) @ SV1878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2397 @ SV1123 @ tc_nat ) ) @ SV2633 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6894]) ).
thf(7318,plain,
! [SV2634: $i,SV1124: $i,SV267: $i,SV2398: $i,SV1879: $i] :
( ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1879 @ SV2398 @ tc_nat ) ) @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1124 @ SV2398 @ tc_nat ) ) @ SV2634 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1879 @ SV1124 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV267 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1124 @ SV1879 @ tc_nat ) @ SV2398 @ tc_nat ) ) @ SV2634 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6895]) ).
thf(7319,plain,
! [SV2635: $i,SV1125: $i,SV268: $i,SV2399: $i,SV1880: $i] :
( ( ( ~ ( c_lessequals @ SV1880 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2399 @ SV268 @ tc_nat ) @ SV1125 @ tc_nat ) ) @ SV2635 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV268 @ SV2399 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SV1125 @ tc_nat ) ) @ SV1880 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2399 @ SV1125 @ tc_nat ) ) @ SV2635 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6896]) ).
thf(7320,plain,
! [SV2400: $i,SV270: $i,SV1882: $i,SV1127: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1127 @ SV1882 @ SV270 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV2400 @ SV1882 @ SV270 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV2400 @ SV1127 @ SV270 ) @ SV1882 @ SV270 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6897]) ).
thf(7321,plain,
! [SV1129: $i,SV272: $i,SV1883: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1883 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1129 ) @ SV1883 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6898]) ).
thf(7322,plain,
! [SV1130: $i,SV273: $i,SV1884: $i] :
( ( ( ~ ( c_lessequals @ SV1884 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1130 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV1130 ) @ SV1884 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6899]) ).
thf(7323,plain,
! [SV2636: $i,SV2401: $i,SV1887: $i,SV1136: $i,SV280: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV280 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1136 @ SV1887 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SV2401 @ SV2636 @ SV280 ) @ SV280 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1136 @ SV2401 @ SV280 ) @ ( c_HOL_Otimes__class_Otimes @ SV1887 @ SV2636 @ SV280 ) @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6900]) ).
thf(7324,plain,
! [SV2637: $i,SV2402: $i,SV1888: $i,SV1137: $i,SV281: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV281 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1137 @ SV1888 @ SV281 ) @ ( c_HOL_Otimes__class_Otimes @ SV2402 @ SV2637 @ SV281 ) @ SV281 )
= ( c_HOL_Otimes__class_Otimes @ SV1137 @ ( c_HOL_Otimes__class_Otimes @ SV1888 @ ( c_HOL_Otimes__class_Otimes @ SV2402 @ SV2637 @ SV281 ) @ SV281 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6901]) ).
thf(7325,plain,
! [SV2638: $i,SV2403: $i,SV1889: $i,SV1138: $i,SV282: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV282 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1138 @ SV1889 @ SV282 ) @ ( c_HOL_Otimes__class_Otimes @ SV2403 @ SV2638 @ SV282 ) @ SV282 )
= ( c_HOL_Otimes__class_Otimes @ SV2403 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV1138 @ SV1889 @ SV282 ) @ SV2638 @ SV282 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6902]) ).
thf(7326,plain,
! [SV288: $i,SV1144: $i,SV1894: $i] :
( ( ( c_lessequals @ SV1894 @ SV1144 @ SV288 )
= $true )
| ( ( ~ ( c_lessequals @ SV1144 @ SV1894 @ SV288 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1144 @ SV1894 @ SV288 )
= $true )
| ( ( class_Orderings_Opreorder @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6903]) ).
thf(7327,plain,
! [SV1151: $i,SV1895: $i,SV297: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1895 @ SV297 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1151 @ SV297 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV297 ) @ SV1151 ) @ SV1895 ) @ SV297 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6904]) ).
thf(7328,plain,
! [SV303: $i,SV1157: $i,SV1897: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1897 @ SV1157 @ SV303 )
= $true )
| ( ( SV1897 = SV1157 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1157 @ SV1897 @ SV303 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6905]) ).
thf(7329,plain,
! [SV304: $i,SV1158: $i,SV1898: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1898 @ SV1158 @ SV304 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1158 @ SV1898 @ SV304 )
= $true )
| ( ( SV1158 = SV1898 )
= $true )
| ( ( class_Orderings_Olinorder @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6906]) ).
thf(7330,plain,
! [SV308: $i,SV1162: $i,SV2639: $i,SV2405: $i,SV1900: $i] :
( ( ( ~ ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2405 ) @ SV2639 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1162 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2405 ) @ SV2639 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV308 ) )
= $true )
| ( ( SV308 = SV1162 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6909]) ).
thf(7331,plain,
! [SV310: $i,SV1164: $i,SV1901: $i] :
( ( ( ~ ( c_lessequals @ SV1901 @ SV1164 @ SV310 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1164 @ SV1901 @ SV310 ) )
= $true )
| ( ( SV1164 = SV1901 )
= $true )
| ( ( class_Orderings_Oorder @ SV310 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6910]) ).
thf(7332,plain,
! [SV311: $i,SV1165: $i,SV1902: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1902 @ SV1165 @ SV311 )
= $true )
| ( ( SV1902 = SV1165 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1165 @ SV1902 @ SV311 )
= $true )
| ( ( class_Orderings_Olinorder @ SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6911]) ).
thf(7333,plain,
! [SV312: $i,SV1166: $i,SV1903: $i] :
( ( ( ~ ( c_lessequals @ SV1903 @ SV1166 @ SV312 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1166 @ SV1903 @ SV312 ) )
= $true )
| ( ( SV1166 = SV1903 )
= $true )
| ( ( class_Orderings_Oorder @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6912]) ).
thf(7334,plain,
! [SV313: $i,SV1904: $i,SV1167: $i] :
( ( ( ~ ( c_lessequals @ SV1167 @ SV1904 @ SV313 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1904 @ SV1167 @ SV313 ) )
= $true )
| ( ( SV1167 = SV1904 )
= $true )
| ( ( class_Orderings_Oorder @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6913]) ).
thf(7335,plain,
! [SV315: $i,SV1169: $i,SV1906: $i] :
( ( ( SV1906 = SV1169 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1906 @ SV1169 @ SV315 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1169 @ SV1906 @ SV315 )
= $true )
| ( ( class_Orderings_Olinorder @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6914]) ).
thf(7336,plain,
! [SV316: $i,SV1907: $i,SV1170: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1170 @ SV1907 @ SV316 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1907 @ SV1170 @ SV316 )
= $true )
| ( ( SV1170 = SV1907 )
= $true )
| ( ( class_Orderings_Olinorder @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6915]) ).
thf(7337,plain,
! [SV317: $i,SV1908: $i,SV1171: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1908 @ SV317 ) @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 )
= $false )
| ( ( c_lessequals @ SV1171 @ SV1908 @ SV317 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6916]) ).
thf(7338,plain,
! [SV318: $i,SV1909: $i,SV1172: $i] :
( ( ( c_lessequals @ SV1172 @ SV1909 @ SV318 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1172 @ SV1909 @ SV318 ) @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV318 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6917]) ).
thf(7339,plain,
! [SV2640: $i,SV2407: $i,SV1910: $i,SV1174: $i,SV320: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV1174 ) @ SV1910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV2407 ) @ SV2640 ) @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SV1910 @ SV2640 @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SV2407 @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6918]) ).
thf(7340,plain,
! [SV1911: $i,SV321: $i,SV2408: $i,SV1175: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1175 @ SV2408 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV321 @ SV1911 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV1175 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1911 ) @ SV2408 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6919]) ).
thf(7341,plain,
! [SV324: $i,SV1912: $i,SV1178: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1178 @ SV1912 @ SV324 )
= $false )
| ( ( c_lessequals @ SV1178 @ SV1912 @ SV324 )
= $true )
| ( ( class_Orderings_Oorder @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6920]) ).
thf(7342,plain,
! [SV325: $i,SV1913: $i,SV1179: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1179 @ SV1913 @ SV325 )
= $false )
| ( ( c_lessequals @ SV1179 @ SV1913 @ SV325 )
= $true )
| ( ( class_Orderings_Opreorder @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6921]) ).
thf(7343,plain,
! [SV2409: $i,SV326: $i,SV1914: $i,SV1180: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1180 @ SV1914 @ SV326 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1180 @ ( c_Orderings_Oord__class_Omin @ SV1914 @ SV2409 @ SV326 ) @ SV326 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6922]) ).
thf(7344,plain,
! [SV2410: $i,SV327: $i,SV1915: $i,SV1181: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1181 @ SV1915 @ SV327 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_Orderings_Oord__class_Omin @ SV2410 @ SV1915 @ SV327 ) @ SV327 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV327 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6923]) ).
thf(7345,plain,
! [SV2411: $i,SV328: $i,SV1916: $i,SV1182: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1182 @ SV1916 @ SV328 ) @ SV2411 @ SV328 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1182 @ SV2411 @ SV328 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6924]) ).
thf(7346,plain,
! [SV2412: $i,SV329: $i,SV1917: $i,SV1183: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1183 @ SV1917 @ SV329 ) @ SV2412 @ SV329 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1917 @ SV2412 @ SV329 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV329 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6925]) ).
thf(7347,plain,
! [SV1918: $i,SV330: $i,SV1184: $i] :
( ( ( c_lessequals @ SV1184 @ SV330 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1184 @ SV1918 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV330 @ SV1184 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1918 @ SV1184 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV330 @ SV1918 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6926]) ).
thf(7348,plain,
! [SV1186: $i,SV1920: $i,SV332: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1920 @ SV332 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1186 @ SV332 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV332 ) @ SV1186 ) @ SV1920 ) @ SV332 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6927]) ).
thf(7349,plain,
! [SV1187: $i,SV1921: $i,SV333: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1921 @ SV333 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1187 @ SV333 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV333 ) @ SV1187 ) @ SV1921 ) @ SV333 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV333 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6928]) ).
thf(7350,plain,
! [SV1188: $i,SV1922: $i,SV334: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV334 @ SV1922 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1188 @ SV334 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV334 @ SV1188 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1922 @ SV1188 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6929]) ).
thf(7351,plain,
! [SV1189: $i,SV335: $i,SV1923: $i] :
( ( ( ~ ( c_lessequals @ SV1923 @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV1189 @ SV335 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1189 @ SV1923 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV335 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6930]) ).
thf(7352,plain,
! [SV1190: $i,SV1924: $i,SV336: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV1924 @ SV336 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1190 @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1190 @ SV1924 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV336 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6931]) ).
thf(7353,plain,
! [SV1191: $i,SV337: $i,SV1925: $i] :
( ( ( ~ ( c_lessequals @ SV1925 @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV1191 @ SV337 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1191 @ SV1925 @ SV337 ) @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV337 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6932]) ).
thf(7354,plain,
! [SV1192: $i,SV1926: $i,SV338: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV1926 @ SV338 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1192 @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1192 @ SV1926 @ SV338 ) @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV338 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6933]) ).
thf(7355,plain,
! [SV1193: $i,SV339: $i,SV1927: $i] :
( ( ( ~ ( c_lessequals @ SV1927 @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV1193 @ SV339 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1193 @ SV1927 @ SV339 ) @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6934]) ).
thf(7356,plain,
! [SV1194: $i,SV1928: $i,SV340: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV1928 @ SV340 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1194 @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1928 @ SV340 ) @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV340 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6935]) ).
thf(7357,plain,
! [SV1929: $i,SV341: $i,SV1195: $i] :
( ( ( ~ ( c_lessequals @ SV1195 @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV1929 @ SV341 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1195 @ SV1929 @ SV341 ) @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV341 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6936]) ).
thf(7358,plain,
! [SV2782: $i,SV2733: $i,SV2641: $i,SV2416: $i,SV1936: $i,SV1206: $i,SV352: $i] :
( ( ! [SY7206: $i,SY7207: $i] :
( ( ( hAPP @ ( hAPP @ SV352 @ ( hAPP @ ( hAPP @ SV1206 @ SV1936 ) @ SV2416 ) ) @ SV2641 )
= ( hAPP @ ( hAPP @ SV1206 @ ( hAPP @ ( hAPP @ SV352 @ SV1936 ) @ SV2641 ) ) @ ( hAPP @ ( hAPP @ SV352 @ SV2416 ) @ SV2641 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2733 @ SV1206 @ SV352 @ SV2782 @ SY7206 @ SY7207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6938]) ).
thf(7359,plain,
! [SV2783: $i,SV2734: $i,SV2642: $i,SV2417: $i,SV1937: $i,SV1207: $i,SV353: $i] :
( ( ! [SY7208: $i,SY7209: $i] :
( ( ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ ( hAPP @ ( hAPP @ SV1937 @ SV2417 ) @ SV2642 ) )
= ( hAPP @ ( hAPP @ SV1937 @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2417 ) ) @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2642 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1937 @ SV353 @ SV2734 @ SV2783 @ SY7208 @ SY7209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6939]) ).
thf(7360,plain,
! [SV2784: $i,SV2735: $i,SV2643: $i,SV2418: $i,SV1938: $i,SV1208: $i,SV354: $i] :
( ( ! [SY7210: $i] :
( ( ( hAPP @ ( hAPP @ SV354 @ SV1208 ) @ SV1938 )
= ( hAPP @ ( hAPP @ SV354 @ SV1938 ) @ SV1208 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2418 @ SV354 @ SV2643 @ SV2735 @ SV2784 @ SY7210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6940]) ).
thf(7361,plain,
! [SV2785: $i,SV2736: $i,SV2644: $i,SV2419: $i,SV1939: $i,SV1209: $i,SV355: $i] :
( ( ! [SY7211: $i,SY7212: $i] :
( ( ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ ( hAPP @ ( hAPP @ SV355 @ SV1939 ) @ SV2419 ) )
= ( hAPP @ ( hAPP @ SV355 @ ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ SV1939 ) ) @ SV2419 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2644 @ SV355 @ SV2736 @ SV2785 @ SY7211 @ SY7212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6941]) ).
thf(7362,plain,
! [SV2786: $i,SV2737: $i,SV2645: $i,SV2420: $i,SV1940: $i,SV1210: $i,SV356: $i] :
( ( ( ( hAPP @ ( hAPP @ SV356 @ SV1210 ) @ SV1940 )
= SV1940 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2420 @ SV356 @ SV2645 @ SV2737 @ SV1210 @ SV2786 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6942]) ).
thf(7363,plain,
! [SV2787: $i,SV2738: $i,SV2646: $i,SV2421: $i,SV1941: $i,SV1211: $i,SV357: $i] :
( ( ( ( hAPP @ ( hAPP @ SV357 @ SV1211 ) @ SV1941 )
= SV1211 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2421 @ SV357 @ SV2646 @ SV1211 @ SV2738 @ SV2787 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6943]) ).
thf(7364,plain,
! [SV2788: $i,SV2739: $i,SV2647: $i,SV2422: $i,SV1942: $i,SV1212: $i,SV358: $i] :
( ( ! [SY7213: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV1212 ) @ SV1942 )
= ( hAPP @ ( hAPP @ SV358 @ SV1942 ) @ SV1212 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV358 @ SV2422 @ SV2647 @ SV2739 @ SV2788 @ SY7213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6944]) ).
thf(7365,plain,
! [SV2789: $i,SV2740: $i,SV2648: $i,SV2423: $i,SV1943: $i,SV1213: $i,SV359: $i] :
( ( ! [SY7214: $i,SY7215: $i] :
( ( ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ ( hAPP @ ( hAPP @ SV359 @ SV1943 ) @ SV2423 ) )
= ( hAPP @ ( hAPP @ SV359 @ ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ SV1943 ) ) @ SV2423 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV359 @ SV2648 @ SV2740 @ SV2789 @ SY7214 @ SY7215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6945]) ).
thf(7366,plain,
! [SV2790: $i,SV2741: $i,SV2649: $i,SV2424: $i,SV1944: $i,SV1214: $i,SV360: $i] :
( ( ( ( hAPP @ ( hAPP @ SV360 @ SV1214 ) @ SV1944 )
= SV1944 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV360 @ SV2424 @ SV2649 @ SV1214 @ SV2741 @ SV2790 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6946]) ).
thf(7367,plain,
! [SV2791: $i,SV2742: $i,SV2650: $i,SV2425: $i,SV1945: $i,SV1215: $i,SV361: $i] :
( ( ! [SY7216: $i,SY7217: $i] :
( ( ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ ( hAPP @ ( hAPP @ SV361 @ SV1945 ) @ SV2425 ) )
= ( hAPP @ ( hAPP @ SV361 @ ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ SV1945 ) ) @ SV2425 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV361 @ SV2650 @ SV2742 @ SV2791 @ SY7216 @ SY7217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6947]) ).
thf(7368,plain,
! [SV2792: $i,SV2743: $i,SV2651: $i,SV2426: $i,SV1946: $i,SV1216: $i,SV362: $i] :
( ( ! [SY7218: $i] :
( ( ( hAPP @ ( hAPP @ SV362 @ SV1216 ) @ SV1946 )
= ( hAPP @ ( hAPP @ SV362 @ SV1946 ) @ SV1216 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV362 @ SV2426 @ SV2651 @ SV2743 @ SV2792 @ SY7218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6948]) ).
thf(7369,plain,
! [SV2793: $i,SV2744: $i,SV2652: $i,SV2427: $i,SV1947: $i,SV1217: $i,SV363: $i] :
( ( ! [SY7219: $i,SY7220: $i] :
( ( ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV1947 ) ) @ SV2427 )
= ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV2427 ) ) @ SV1947 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV363 @ SV2652 @ SV2744 @ SV2793 @ SY7219 @ SY7220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6949]) ).
thf(7370,plain,
! [SV2794: $i,SV2745: $i,SV2653: $i,SV2428: $i,SV1948: $i,SV1218: $i,SV364: $i] :
( ( ! [SY7221: $i,SY7222: $i] :
( ( ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ SV2428 ) )
= ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ SV2428 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV364 @ SV2653 @ SV2745 @ SV2794 @ SY7221 @ SY7222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6950]) ).
thf(7371,plain,
! [SV2795: $i,SV2746: $i,SV2654: $i,SV2429: $i,SV1949: $i,SV1219: $i,SV365: $i] :
( ( ! [SY7223: $i,SY7224: $i] :
( ( ( hAPP @ ( hAPP @ SV365 @ ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ SV1949 ) ) @ SV2429 )
= ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ ( hAPP @ ( hAPP @ SV365 @ SV1949 ) @ SV2429 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV365 @ SV2654 @ SV2746 @ SV2795 @ SY7223 @ SY7224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6951]) ).
thf(7372,plain,
! [SV2796: $i,SV2747: $i,SV2655: $i,SV2430: $i,SV1950: $i,SV1220: $i,SV366: $i] :
( ( ! [SY7225: $i,SY7226: $i,SY7227: $i] :
( ( ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV1950 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV2430 ) @ SV2655 ) )
= ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV2430 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV1950 ) @ SV2655 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV366 @ SV2747 @ SV2796 @ SY7225 @ SY7226 @ SY7227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6952]) ).
thf(7373,plain,
! [SV2797: $i,SV2748: $i,SV2656: $i,SV2431: $i,SV1951: $i,SV1221: $i,SV367: $i] :
( ( ! [SY7228: $i,SY7229: $i] :
( ( ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ SV2431 ) )
= ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ SV2431 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2656 @ SV367 @ SV2748 @ SV2797 @ SY7228 @ SY7229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6953]) ).
thf(7374,plain,
! [SV2798: $i,SV2749: $i,SV2657: $i,SV2432: $i,SV1952: $i,SV1222: $i,SV368: $i] :
( ( ! [SY7230: $i,SY7231: $i] :
( ( ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ ( hAPP @ ( hAPP @ SV368 @ SV1952 ) @ SV2432 ) )
= ( hAPP @ ( hAPP @ SV368 @ ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ SV1952 ) ) @ SV2432 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2657 @ SV368 @ SV2749 @ SV2798 @ SY7230 @ SY7231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6954]) ).
thf(7375,plain,
! [SV2799: $i,SV2750: $i,SV2658: $i,SV2433: $i,SV1953: $i,SV1223: $i,SV369: $i] :
( ( ! [SY7232: $i,SY7233: $i] :
( ( ( hAPP @ ( hAPP @ SV369 @ ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ SV1953 ) ) @ SV2433 )
= ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ ( hAPP @ ( hAPP @ SV369 @ SV1953 ) @ SV2433 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2658 @ SV369 @ SV2750 @ SV2799 @ SY7232 @ SY7233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6955]) ).
thf(7376,plain,
! [SV2800: $i,SV2751: $i,SV2659: $i,SV2434: $i,SV1954: $i,SV1224: $i,SV370: $i] :
( ( ! [SY7234: $i,SY7235: $i] :
( ( ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV1954 ) ) @ SV2434 )
= ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV2434 ) ) @ SV1954 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2659 @ SV370 @ SV2751 @ SV2800 @ SY7234 @ SY7235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6956]) ).
thf(7377,plain,
! [SV2801: $i,SV2752: $i,SV2660: $i,SV2435: $i,SV1955: $i,SV1225: $i,SV371: $i] :
( ( ! [SY7236: $i,SY7237: $i,SY7238: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ SV2660 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ SV2660 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2752 @ SV371 @ SV2801 @ SY7236 @ SY7237 @ SY7238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6957]) ).
thf(7378,plain,
! [SV2802: $i,SV2753: $i,SV2661: $i,SV2436: $i,SV1956: $i,SV1226: $i,SV372: $i] :
( ( ! [SY7239: $i,SY7240: $i,SY7241: $i] :
( ( ( hAPP @ ( hAPP @ SV372 @ ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ SV1956 ) ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) )
= ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ ( hAPP @ ( hAPP @ SV372 @ SV1956 ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2753 @ SV372 @ SV2802 @ SY7239 @ SY7240 @ SY7241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6958]) ).
thf(7379,plain,
! [SV2803: $i,SV2754: $i,SV2662: $i,SV2437: $i,SV1957: $i,SV1227: $i,SV373: $i] :
( ( ! [SY7242: $i,SY7243: $i,SY7244: $i] :
( ( ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV1957 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV2437 ) @ SV2662 ) )
= ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV2437 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV1957 ) @ SV2662 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2754 @ SV373 @ SV2803 @ SY7242 @ SY7243 @ SY7244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6959]) ).
thf(7380,plain,
! [SV2804: $i,SV2755: $i,SV2663: $i,SV2438: $i,SV1958: $i,SV1228: $i,SV374: $i] :
( ( ( ( hAPP @ ( hAPP @ SV374 @ SV1228 ) @ SV1958 )
= SV1228 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2438 @ SV374 @ SV2663 @ SV2755 @ SV1958 @ SV2804 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6960]) ).
thf(7381,plain,
! [SV2805: $i,SV2756: $i,SV2664: $i,SV2439: $i,SV1959: $i,SV1229: $i,SV375: $i] :
( ( ( ( hAPP @ ( hAPP @ SV375 @ SV1229 ) @ SV1959 )
= SV1959 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2439 @ SV375 @ SV2664 @ SV2756 @ SV1229 @ SV2805 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6961]) ).
thf(7382,plain,
! [SV2806: $i,SV2757: $i,SV2665: $i,SV2440: $i,SV1960: $i,SV1230: $i,SV376: $i] :
( ( ( ( hAPP @ ( hAPP @ SV376 @ SV1230 ) @ SV1960 )
= SV1960 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2440 @ SV376 @ SV2665 @ SV1960 @ SV2757 @ SV2806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6962]) ).
thf(7383,plain,
! [SV2807: $i,SV2758: $i,SV2666: $i,SV2441: $i,SV1961: $i,SV1231: $i,SV377: $i] :
( ( ( ( hAPP @ ( hAPP @ SV377 @ SV1231 ) @ SV1961 )
= SV1231 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2441 @ SV377 @ SV2666 @ SV1231 @ SV2758 @ SV2807 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6963]) ).
thf(7384,plain,
! [SV2808: $i,SV2759: $i,SV2667: $i,SV2442: $i,SV1962: $i,SV1232: $i,SV378: $i] :
( ( ! [SY7245: $i,SY7246: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ ( hAPP @ ( hAPP @ SV1232 @ SV1962 ) @ SV2442 ) ) @ SV2667 )
= ( hAPP @ ( hAPP @ SV1232 @ ( hAPP @ ( hAPP @ SV378 @ SV1962 ) @ SV2667 ) ) @ ( hAPP @ ( hAPP @ SV378 @ SV2442 ) @ SV2667 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1232 @ SV378 @ SV2759 @ SV2808 @ SY7245 @ SY7246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6964]) ).
thf(7385,plain,
! [SV2809: $i,SV2760: $i,SV2668: $i,SV2443: $i,SV1963: $i,SV1233: $i,SV379: $i] :
( ( ! [SY7247: $i] :
( ( ( hAPP @ ( hAPP @ SV379 @ SV1233 ) @ SV1963 )
= ( hAPP @ ( hAPP @ SV379 @ SV1963 ) @ SV1233 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2443 @ SV379 @ SV2668 @ SV2760 @ SV2809 @ SY7247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6965]) ).
thf(7386,plain,
! [SV2810: $i,SV2761: $i,SV2669: $i,SV2444: $i,SV1964: $i,SV1234: $i,SV380: $i] :
( ( ( ( hAPP @ ( hAPP @ SV380 @ SV1234 ) @ SV1964 )
= SV1234 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV380 @ SV2444 @ SV2669 @ SV1964 @ SV2761 @ SV2810 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6966]) ).
thf(7387,plain,
! [SV2811: $i,SV2762: $i,SV2670: $i,SV2445: $i,SV1965: $i,SV1235: $i,SV381: $i] :
( ( ( ( hAPP @ ( hAPP @ SV381 @ SV1235 ) @ SV1965 )
= SV1965 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV381 @ SV2445 @ SV2670 @ SV1235 @ SV2762 @ SV2811 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6967]) ).
thf(7388,plain,
! [SV2812: $i,SV2763: $i,SV2671: $i,SV2446: $i,SV1966: $i,SV1236: $i,SV382: $i] :
( ( ( ( hAPP @ ( hAPP @ SV382 @ SV1236 ) @ SV1236 )
= ( hAPP @ ( hAPP @ SV1966 @ ( hAPP @ ( hAPP @ SV382 @ SV2446 ) @ SV2446 ) ) @ SV1236 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV382 @ SV1966 @ SV2671 @ SV2763 @ SV2446 @ SV2812 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6968]) ).
thf(7389,plain,
! [SV2813: $i,SV2764: $i,SV2672: $i,SV2447: $i,SV1967: $i,SV1237: $i,SV383: $i] :
( ( ! [SY7248: $i] :
( ( ( hAPP @ ( hAPP @ SV383 @ SV1237 ) @ ( hAPP @ ( hAPP @ SV1967 @ SV2447 ) @ SV1237 ) )
= ( hAPP @ ( hAPP @ SV1967 @ ( hAPP @ ( hAPP @ SV383 @ SV2447 ) @ SV2672 ) ) @ SV1237 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV383 @ SV1967 @ SV2764 @ SV2813 @ SV2672 @ SY7248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6969]) ).
thf(7390,plain,
! [SV2814: $i,SV2765: $i,SV2673: $i,SV2448: $i,SV1968: $i,SV1238: $i,SV384: $i] :
( ( ! [SY7249: $i] :
( ( ( hAPP @ ( hAPP @ SV384 @ ( hAPP @ ( hAPP @ SV1238 @ SV1968 ) @ SV2448 ) ) @ SV2448 )
= ( hAPP @ ( hAPP @ SV1238 @ ( hAPP @ ( hAPP @ SV384 @ SV1968 ) @ SV2673 ) ) @ SV2448 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV384 @ SV1238 @ SV2765 @ SV2814 @ SV2673 @ SY7249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6970]) ).
thf(7391,plain,
! [SV2815: $i,SV2766: $i,SV2674: $i,SV2449: $i,SV1969: $i,SV1239: $i,SV385: $i] :
( ( ! [SY7250: $i,SY7251: $i] :
( ( ( hAPP @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ SV1239 @ SV1969 ) @ SV2449 ) ) @ ( hAPP @ ( hAPP @ SV1239 @ SV2674 ) @ SV2449 ) )
= ( hAPP @ ( hAPP @ SV1239 @ ( hAPP @ ( hAPP @ SV385 @ SV1969 ) @ SV2674 ) ) @ SV2449 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV385 @ SV1239 @ SV2766 @ SV2815 @ SY7250 @ SY7251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6971]) ).
thf(7392,plain,
! [SV2675: $i,SV2452: $i,SV1977: $i,SV1247: $i,SV394: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV394 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1247 ) @ SV1977 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV2452 ) @ SV2675 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1247 ) @ SV2452 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV394 ) @ SV1977 ) @ SV2675 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6976]) ).
thf(7393,plain,
! [SV2455: $i,SV1984: $i,SV406: $i,SV1256: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1256 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1256 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV1984 @ SV406 ) @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV2455 @ SV406 ) @ SV406 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV406 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6978]) ).
thf(7394,plain,
! [SV2456: $i,SV407: $i,SV1985: $i,SV1257: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1257 @ SV1985 @ SV407 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1985 @ SV1257 @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2456 @ SV1985 @ SV407 ) @ ( c_HOL_Otimes__class_Otimes @ SV2456 @ SV1257 @ SV407 ) @ SV407 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV407 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6979]) ).
thf(7395,plain,
! [SV2457: $i,SV1986: $i,SV408: $i,SV1258: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1258 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV1258 @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1986 @ SV1258 @ SV408 ) @ ( c_HOL_Otimes__class_Otimes @ SV2457 @ SV1258 @ SV408 ) @ SV408 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6980]) ).
thf(7396,plain,
! [SV2458: $i,SV409: $i,SV1987: $i,SV1259: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1259 @ SV1987 @ SV409 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1987 @ SV1259 @ SV409 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1987 @ SV2458 @ SV409 ) @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SV2458 @ SV409 ) @ SV409 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV409 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6981]) ).
thf(7397,plain,
! [SV414: $i,SV1989: $i,SV1264: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1264 @ SV1989 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1264 @ SV1989 @ SV414 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV414 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6982]) ).
thf(7398,plain,
! [SV415: $i,SV1990: $i,SV1265: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1265 @ SV1990 @ SV415 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SV1990 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV415 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6983]) ).
thf(7399,plain,
! [SV416: $i,SV1991: $i,SV1266: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1266 @ SV1991 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1266 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1991 @ SV416 ) @ SV416 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6984]) ).
thf(7400,plain,
! [SV1992: $i,SV417: $i,SV1267: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1267 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1992 @ SV417 ) @ SV417 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1267 @ SV1992 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6985]) ).
thf(7401,plain,
! [SV1268: $i,SV1993: $i,SV420: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV420 @ SV1993 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1993 @ SV1268 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV420 ) @ SV1268 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6986]) ).
thf(7402,plain,
! [SV2459: $i,SV1994: $i,SV1269: $i,SV421: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV1269 ) @ SV1994 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV2459 ) @ SV1994 ) @ SV421 )
= $true )
| ( ( ~ ( c_lessequals @ SV1269 @ SV2459 @ SV421 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6987]) ).
thf(7403,plain,
! [SV2460: $i,SV422: $i,SV1995: $i,SV1270: $i] :
( ( ( c_lessequals @ SV1270 @ SV1995 @ SV422 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1270 ) @ SV2460 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1995 ) @ SV2460 ) @ SV422 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6988]) ).
thf(7404,plain,
! [SV2461: $i,SV1996: $i,SV1271: $i,SV423: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SV1996 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SV2461 ) @ SV423 )
= $true )
| ( ( ~ ( c_lessequals @ SV1996 @ SV2461 @ SV423 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6989]) ).
thf(7405,plain,
! [SV2462: $i,SV424: $i,SV1997: $i,SV1272: $i] :
( ( ( c_lessequals @ SV1272 @ SV1997 @ SV424 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV2462 ) @ SV1272 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV2462 ) @ SV1997 ) @ SV424 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6990]) ).
thf(7406,plain,
! [SV2463: $i,SV1998: $i,SV1273: $i,SV425: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV1273 ) @ SV1998 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV2463 ) @ SV1998 ) @ SV425 )
= $true )
| ( ( ~ ( c_lessequals @ SV1273 @ SV2463 @ SV425 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV425 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6991]) ).
thf(7407,plain,
! [SV2464: $i,SV1999: $i,SV1274: $i,SV426: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SV1999 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SV2464 ) @ SV426 )
= $true )
| ( ( ~ ( c_lessequals @ SV1999 @ SV2464 @ SV426 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV426 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6992]) ).
thf(7408,plain,
! [SV2816: $i,SV2767: $i,SV2676: $i,SV2465: $i,SV2003: $i,SV1281: $i,SV433: $i] :
( ( ! [SY7252: $i] :
( ( ( hAPP @ ( hAPP @ SV433 @ SV1281 ) @ ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ SV2465 ) )
= ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ ( c_Suc @ SV2465 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2676 @ SV433 @ SV2003 @ SV2767 @ SV2816 @ SY7252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6993]) ).
thf(7409,plain,
! [SV2817: $i,SV2768: $i,SV2677: $i,SV2466: $i,SV2004: $i,SV1282: $i,SV434: $i] :
( ( ! [SY7253: $i] :
( ( ( hAPP @ ( hAPP @ SV434 @ ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ SV2466 ) ) @ SV2004 )
= ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ ( c_Suc @ SV2466 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2677 @ SV434 @ SV1282 @ SV2768 @ SV2817 @ SY7253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6994]) ).
thf(7410,plain,
! [SV2818: $i,SV2769: $i,SV2678: $i,SV2467: $i,SV2005: $i,SV1283: $i,SV435: $i] :
( ( ! [SY7254: $i] :
( ( ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ ( c_Suc @ SV2005 ) )
= ( hAPP @ ( hAPP @ SV2467 @ SV1283 ) @ ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ SV2005 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2678 @ SV2467 @ SV435 @ SV2769 @ SV2818 @ SY7254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6995]) ).
thf(7411,plain,
! [SV2819: $i,SV2770: $i,SV2679: $i,SV2468: $i,SV2006: $i,SV1284: $i,SV436: $i] :
( ( ! [SY7255: $i] :
( ( ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ ( c_Suc @ SV2006 ) )
= ( hAPP @ ( hAPP @ SV2468 @ SV1284 ) @ ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ SV2006 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2679 @ SV2468 @ SV436 @ SV2770 @ SV2819 @ SY7255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6996]) ).
thf(7412,plain,
! [SV2470: $i,SV442: $i,SV2012: $i,SV1290: $i] :
( ( ( c_lessequals @ SV1290 @ SV2012 @ SV442 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV442 ) @ SV2012 @ SV442 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1290 @ ( c_Suc @ SV2470 ) @ SV442 ) @ ( c_Power_Opower__class_Opower @ SV2012 @ ( c_Suc @ SV2470 ) @ SV442 ) @ SV442 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV442 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6997]) ).
thf(7413,plain,
! [SV2680: $i,SV2472: $i,SV2015: $i,SV1295: $i,SV447: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SV2472 @ SV2680 @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
| ~ ( c_lessequals @ SV2015 @ SV2680 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SV2472 @ SV447 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7000]) ).
thf(7414,plain,
! [SV2681: $i,SV2473: $i,SV2016: $i,SV1296: $i,SV448: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SV2473 @ SV2681 @ SV448 ) @ SV448 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ SV2016 @ SV2681 @ SV448 )
| ~ ( c_lessequals @ SV1296 @ SV2473 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7001]) ).
thf(7415,plain,
! [SV2019: $i,SV451: $i,SV1299: $i] :
( ( ( c_lessequals @ SV1299 @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1299 @ SV451 ) @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV1299 @ SV451 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV451 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7002]) ).
thf(7416,plain,
! [SV1300: $i,SV452: $i,SV2020: $i] :
( ( ( c_lessequals @ SV2020 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1300 @ SV2020 @ SV452 ) @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 ) )
= $true )
| ( ( c_lessequals @ SV1300 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV452 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7003]) ).
thf(7417,plain,
! [SV1301: $i,SV2021: $i,SV453: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV2021 @ SV453 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1301 @ SV453 ) @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV453 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV1301 @ SV453 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV453 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7004]) ).
thf(7418,plain,
! [SV2022: $i,SV1302: $i,SV454: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV1302 @ SV454 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1302 @ SV2022 @ SV454 ) @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 ) )
= $true )
| ( ( c_lessequals @ SV1302 @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV454 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7005]) ).
thf(7419,plain,
! [SV2023: $i,SV455: $i,SV1303: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1303 @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV2023 @ SV455 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1303 @ SV2023 @ SV455 ) @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV455 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7006]) ).
thf(7420,plain,
! [SV1304: $i,SV456: $i,SV2024: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2024 @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1304 @ SV456 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1304 @ SV2024 @ SV456 ) @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV456 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7007]) ).
thf(7421,plain,
! [SV1305: $i,SV2025: $i,SV457: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV2025 @ SV457 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1305 @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1305 @ SV2025 @ SV457 ) @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV457 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7008]) ).
thf(7422,plain,
! [SV464: $i,SV1311: $i,SV2027: $i] :
( ( ( ~ ( c_lessequals @ SV2027 @ SV1311 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2027 @ SV464 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SV2027 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1311 @ SV2027 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV464 @ SV1311 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7012]) ).
thf(7423,plain,
! [SV465: $i,SV2028: $i,SV1312: $i] :
( ( ( ~ ( c_lessequals @ SV1312 @ SV2028 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1312 @ SV465 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV465 @ SV2028 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV465 @ SV1312 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV2028 @ SV1312 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7013]) ).
thf(7424,plain,
! [SV2475: $i,SV2029: $i,SV466: $i,SV1313: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1313 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ SV2029 ) @ SV2475 ) @ SV466 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1313 @ SV2475 @ SV466 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV2029 @ SV466 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7014]) ).
thf(7425,plain,
! [SV473: $i,SV1320: $i,SV2032: $i] :
( ( ( c_lessequals @ SV2032 @ SV1320 @ tc_nat )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1320 @ SV2032 @ tc_nat ) @ SV473 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1320 @ SV473 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV2032 @ SV473 ) @ SV473 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7017]) ).
thf(7426,plain,
! [SV2476: $i,SV474: $i,SV2033: $i,SV1321: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1321 @ SV2033 @ SV474 ) @ ( c_HOL_Otimes__class_Otimes @ SV2476 @ SV2033 @ SV474 ) @ SV474 )
= $true )
| ( ( ~ ( c_lessequals @ SV2033 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ~ ( c_lessequals @ SV2476 @ SV1321 @ SV474 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7018]) ).
thf(7427,plain,
! [SV2477: $i,SV475: $i,SV2034: $i,SV1322: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2034 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2477 @ SV475 ) @ SV475 )
= $true )
| ( ( ~ ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ~ ( c_lessequals @ SV2477 @ SV2034 @ SV475 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV475 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7019]) ).
thf(7428,plain,
! [SV2478: $i,SV476: $i,SV2035: $i,SV1323: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1323 @ SV2035 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SV2478 @ SV2035 @ SV476 ) @ SV476 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV2035 @ SV476 )
| ~ ( c_lessequals @ SV1323 @ SV2478 @ SV476 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV476 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7020]) ).
thf(7429,plain,
! [SV2479: $i,SV477: $i,SV2036: $i,SV1324: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2036 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2479 @ SV477 ) @ SV477 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV477 ) @ SV1324 @ SV477 )
| ~ ( c_lessequals @ SV2036 @ SV2479 @ SV477 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7021]) ).
thf(7430,plain,
! [SV2480: $i,SV478: $i,SV2037: $i,SV1325: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2037 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2480 @ SV478 ) @ SV478 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV478 ) @ SV1325 @ SV478 )
| ~ ( c_lessequals @ SV2037 @ SV2480 @ SV478 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__mono1 @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7022]) ).
thf(7431,plain,
! [SV2481: $i,SV2041: $i,SV1329: $i,SV482: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SV1329 ) @ SV2041 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SV2481 ) @ SV2041 ) @ SV482 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1329 @ SV2481 @ SV482 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7023]) ).
thf(7432,plain,
! [SV2482: $i,SV2042: $i,SV1330: $i,SV483: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SV1330 ) @ SV2042 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SV2482 ) @ SV2042 ) @ SV483 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SV2482 @ SV483 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV483 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7024]) ).
thf(7433,plain,
! [SV2483: $i,SV484: $i,SV2043: $i,SV1331: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1331 @ SV2043 @ SV484 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV1331 ) @ SV2483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV2043 ) @ SV2483 ) @ SV484 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV484 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7025]) ).
thf(7434,plain,
! [SV2484: $i,SV2044: $i,SV1332: $i,SV485: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SV2044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SV2484 ) @ SV485 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2044 @ SV2484 @ SV485 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV485 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7026]) ).
thf(7435,plain,
! [SV2485: $i,SV2045: $i,SV1333: $i,SV486: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SV2045 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SV2485 ) @ SV486 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2045 @ SV2485 @ SV486 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV486 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7027]) ).
thf(7436,plain,
! [SV2486: $i,SV487: $i,SV2046: $i,SV1334: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1334 @ SV2046 @ SV487 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SV2486 ) @ SV1334 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SV2486 ) @ SV2046 ) @ SV487 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV487 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7028]) ).
thf(7437,plain,
! [SV2487: $i,SV492: $i,SV2050: $i,SV1339: $i] :
( ( ( c_lessequals @ SV1339 @ SV2050 @ SV492 )
= $true )
| ( ( ~ ( c_lessequals @ SV1339 @ SV2487 @ SV492 )
| ~ ( c_lessequals @ SV2487 @ SV2050 @ SV492 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV492 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7030]) ).
thf(7438,plain,
! [SV2488: $i,SV493: $i,SV2051: $i,SV1340: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1340 @ SV2051 @ SV493 )
= $true )
| ( ( ~ ( c_lessequals @ SV1340 @ SV2488 @ SV493 )
| ~ ( c_HOL_Oord__class_Oless @ SV2488 @ SV2051 @ SV493 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7031]) ).
thf(7439,plain,
! [SV2489: $i,SV494: $i,SV2052: $i,SV1341: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1341 @ SV2052 @ SV494 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1341 @ SV2489 @ SV494 )
| ~ ( c_lessequals @ SV2489 @ SV2052 @ SV494 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7032]) ).
thf(7440,plain,
! [SV1342: $i,SV495: $i,SV2053: $i] :
( ( ( ~ ( c_lessequals @ SV2053 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1342 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1342 ) @ SV2053 ) @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV495 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7033]) ).
thf(7441,plain,
! [SV2490: $i,SV496: $i,SV2054: $i,SV1343: $i] :
( ( ( c_lessequals @ SV1343 @ SV2054 @ SV496 )
= $true )
| ( ( ~ ( c_lessequals @ SV2490 @ SV2054 @ SV496 )
| ~ ( c_lessequals @ SV1343 @ SV2490 @ SV496 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7034]) ).
thf(7442,plain,
! [SV1344: $i,SV2055: $i,SV498: $i] :
( ( ( c_lessequals @ SV498 @ SV2055 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV2055 @ SV1344 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV498 @ SV1344 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7035]) ).
thf(7443,plain,
! [SV2056: $i,SV505: $i,SV1349: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1349 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV505 @ SV2056 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV1349 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2056 @ SV1349 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7036]) ).
thf(7444,plain,
! [SV2057: $i,SV1350: $i,SV506: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV506 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1350 @ SV2057 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV1350 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV2057 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7037]) ).
thf(7445,plain,
! [SV507: $i,SV2058: $i,SV1351: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1351 @ SV2058 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV507 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SV1351 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV507 @ SV2058 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7038]) ).
thf(7446,plain,
! [SV1352: $i,SV2059: $i,SV508: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV508 @ SV2059 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1352 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV508 @ SV1352 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2059 @ SV1352 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7039]) ).
thf(7447,plain,
! [SV1353: $i,SV509: $i,SV2060: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2060 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2060 @ SV509 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2060 @ SV1353 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV509 @ SV1353 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7040]) ).
thf(7448,plain,
! [SV2061: $i,SV1354: $i,SV510: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV510 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1354 @ SV2061 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SV1354 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV510 @ SV2061 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7041]) ).
thf(7449,plain,
! [SV2491: $i,SV511: $i,SV2062: $i,SV1355: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1355 @ SV2062 @ SV511 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV2062 @ SV511 ) @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV1355 @ SV511 ) @ SV511 )
| ~ ( c_HOL_Oord__class_Oless @ SV2491 @ ( c_HOL_Ozero__class_Ozero @ SV511 ) @ SV511 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV511 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7042]) ).
thf(7450,plain,
! [SV2492: $i,SV512: $i,SV2063: $i,SV1356: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2063 @ SV512 ) @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2492 @ SV512 ) @ SV512 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2492 @ SV2063 @ SV512 )
| ~ ( c_HOL_Oord__class_Oless @ SV1356 @ ( c_HOL_Ozero__class_Ozero @ SV512 ) @ SV512 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV512 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7043]) ).
thf(7451,plain,
! [SV2493: $i,SV513: $i,SV2064: $i,SV1357: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1357 @ SV2064 @ SV513 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV1357 @ SV513 ) @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV2064 @ SV513 ) @ SV513 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV513 ) @ SV2493 @ SV513 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7044]) ).
thf(7452,plain,
! [SV2494: $i,SV514: $i,SV2065: $i,SV1358: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2065 @ SV514 ) @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2494 @ SV514 ) @ SV514 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2065 @ SV2494 @ SV514 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SV1358 @ SV514 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV514 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7045]) ).
thf(7453,plain,
! [SV2495: $i,SV515: $i,SV2066: $i,SV1359: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2066 @ SV515 ) @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2495 @ SV515 ) @ SV515 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1359 @ ( c_HOL_Ozero__class_Ozero @ SV515 ) @ SV515 )
| ~ ( c_HOL_Oord__class_Oless @ SV2495 @ SV2066 @ SV515 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV515 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7046]) ).
thf(7454,plain,
! [SV2496: $i,SV516: $i,SV2067: $i,SV1360: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2067 @ SV516 ) @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2496 @ SV516 ) @ SV516 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV516 ) @ SV1360 @ SV516 )
| ~ ( c_HOL_Oord__class_Oless @ SV2067 @ SV2496 @ SV516 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV516 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7047]) ).
thf(7455,plain,
! [SV2497: $i,SV517: $i,SV2068: $i,SV1361: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2068 @ SV517 ) @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2497 @ SV517 ) @ SV517 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2068 @ SV2497 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1361 @ SV517 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV517 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7048]) ).
thf(7456,plain,
! [SV2498: $i,SV518: $i,SV2069: $i,SV1362: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2069 @ SV518 ) @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2498 @ SV518 ) @ SV518 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2498 @ SV2069 @ SV518 )
| ~ ( c_HOL_Oord__class_Oless @ SV1362 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7049]) ).
thf(7457,plain,
! [SV2499: $i,SV519: $i,SV2070: $i,SV1363: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1363 @ SV2070 @ SV519 ) @ ( c_HOL_Otimes__class_Otimes @ SV2499 @ SV2070 @ SV519 ) @ SV519 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2070 @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV519 )
| ~ ( c_HOL_Oord__class_Oless @ SV2499 @ SV1363 @ SV519 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV519 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7050]) ).
thf(7458,plain,
! [SV2500: $i,SV520: $i,SV2071: $i,SV1364: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1364 @ SV2071 @ SV520 ) @ ( c_HOL_Otimes__class_Otimes @ SV2500 @ SV2071 @ SV520 ) @ SV520 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV2071 @ SV520 )
| ~ ( c_HOL_Oord__class_Oless @ SV1364 @ SV2500 @ SV520 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV520 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7051]) ).
thf(7459,plain,
! [SV2501: $i,SV521: $i,SV2072: $i,SV1365: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1365 @ SV2072 @ SV521 ) @ ( c_HOL_Otimes__class_Otimes @ SV2501 @ SV2072 @ SV521 ) @ SV521 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1365 @ SV2501 @ SV521 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV521 ) @ SV2072 @ SV521 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV521 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7052]) ).
thf(7460,plain,
! [SV2502: $i,SV522: $i,SV2073: $i,SV1366: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1366 @ SV2073 @ SV522 ) @ ( c_HOL_Otimes__class_Otimes @ SV2502 @ SV2073 @ SV522 ) @ SV522 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2502 @ SV1366 @ SV522 )
| ~ ( c_HOL_Oord__class_Oless @ SV2073 @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV522 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV522 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7053]) ).
thf(7461,plain,
! [SV2503: $i,SV523: $i,SV2074: $i,SV1367: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2074 @ SV523 ) @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2503 @ SV523 ) @ SV523 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV1367 @ SV523 )
| ~ ( c_HOL_Oord__class_Oless @ SV2074 @ SV2503 @ SV523 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7054]) ).
thf(7462,plain,
! [SV2077: $i,SV527: $i,SV2505: $i,SV1371: $i] :
( ( ( c_lessequals @ SV1371 @ SV2505 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV527 @ SV2077 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV527 @ SV1371 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2077 @ SV2505 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7056]) ).
thf(7463,plain,
! [SV2682: $i,SV2506: $i,SV2078: $i,SV1372: $i,SV529: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV529 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SV2506 @ SV2682 @ SV529 ) @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2506 @ SV529 )
| ~ ( c_lessequals @ SV2078 @ SV2682 @ SV529 )
| ~ ( c_lessequals @ SV1372 @ SV2506 @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7057]) ).
thf(7464,plain,
! [SV2683: $i,SV2507: $i,SV2079: $i,SV1373: $i,SV530: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV530 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SV2507 @ SV2683 @ SV530 ) @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
| ~ ( c_lessequals @ SV2079 @ SV2683 @ SV530 )
| ~ ( c_lessequals @ SV1373 @ SV2507 @ SV530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7058]) ).
thf(7465,plain,
! [SV2085: $i,SV1382: $i,SV541: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV1382 @ SV541 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV2085 @ SV541 ) @ SV541 ) )
= $true )
| ( ( c_lessequals @ SV1382 @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV541 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV541 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7062]) ).
thf(7466,plain,
! [SV1383: $i,SV2086: $i,SV542: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV2086 @ SV542 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ ( c_HOL_Otimes__class_Otimes @ SV2086 @ SV1383 @ SV542 ) @ SV542 ) )
= $true )
| ( ( c_lessequals @ SV1383 @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV542 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV542 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7063]) ).
thf(7467,plain,
! [SV1384: $i,SV2087: $i,SV543: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV2087 @ SV543 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ ( c_HOL_Otimes__class_Otimes @ SV1384 @ SV2087 @ SV543 ) @ SV543 ) )
= $true )
| ( ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV543 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV543 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7064]) ).
thf(7468,plain,
! [SV2088: $i,SV1385: $i,SV544: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV1385 @ SV544 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ ( c_HOL_Otimes__class_Otimes @ SV2088 @ SV1385 @ SV544 ) @ SV544 ) )
= $true )
| ( ( c_lessequals @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV544 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV544 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7065]) ).
thf(7469,plain,
! [SV2685: $i,SV2513: $i,SV2092: $i,SV1391: $i,SV550: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV550 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV1391 ) @ SV2092 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV2513 ) @ SV2685 ) @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SV2092 @ SV2685 @ SV550 )
| ~ ( c_lessequals @ SV1391 @ SV2513 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7067]) ).
thf(7470,plain,
! [SV2686: $i,SV2514: $i,SV2093: $i,SV1392: $i,SV551: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV551 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV1392 ) @ SV2093 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV2514 ) @ SV2686 ) @ SV551 )
| ~ ( c_lessequals @ SV2093 @ SV2686 @ SV551 )
| ~ ( c_HOL_Oord__class_Oless @ SV1392 @ SV2514 @ SV551 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7068]) ).
thf(7471,plain,
! [SV2515: $i,SV586: $i,SV2095: $i,SV1425: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1425 @ SV2095 @ SV586 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2515 @ SV2095 @ SV586 )
| ~ ( c_lessequals @ SV1425 @ SV2515 @ SV586 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV586 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7073]) ).
thf(7472,plain,
! [SV2516: $i,SV587: $i,SV2096: $i,SV1426: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1426 @ SV2096 @ SV587 )
= $true )
| ( ( ~ ( c_lessequals @ SV2516 @ SV2096 @ SV587 )
| ~ ( c_HOL_Oord__class_Oless @ SV1426 @ SV2516 @ SV587 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV587 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7074]) ).
thf(7473,plain,
! [SV2687: $i,SV2517: $i,SV2097: $i,SV1427: $i,SV588: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV588 )
= $false )
| ( ( ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2517 ) @ SV588 )
| ~ ( c_lessequals @ SV2687 @ SV2517 @ SV588 )
| ~ ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2687 ) @ SV588 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7075]) ).
thf(7474,plain,
! [SV2099: $i,SV1430: $i,SV591: $i] :
( ( ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ominus__class_Ominus @ SV1430 @ SV2099 @ tc_nat ) ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1430 @ SV2099 @ tc_nat )
= $false )
| ( ( hBOOL @ ( hAPP @ SV591 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7076]) ).
thf(7475,plain,
! [SV2100: $i,SV593: $i,SV1432: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1432 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV593 @ SV2100 ) @ tc_nat )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV593 @ SV2100 ) )
| ( hBOOL @ ( hAPP @ SV593 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV593 @ SV1432 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7077]) ).
thf(7476,plain,
! [SV2688: $i,SV2518: $i,SV2101: $i,SV1433: $i,SV594: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SV2518 @ SV2688 @ SV594 ) @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV2101 @ SV2688 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SV2518 @ SV594 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7078]) ).
thf(7477,plain,
! [SV2520: $i,SV2107: $i,SV606: $i,SV1444: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1444 @ ( c_HOL_Ozero__class_Ozero @ SV606 ) @ SV606 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV2107 @ SV2520 @ SV606 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2107 @ SV1444 @ SV606 ) @ ( c_HOL_Otimes__class_Otimes @ SV2520 @ SV1444 @ SV606 ) @ SV606 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV606 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7080]) ).
thf(7478,plain,
! [SV2521: $i,SV607: $i,SV2108: $i,SV1445: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1445 @ SV2108 @ SV607 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV607 ) @ SV2521 @ SV607 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2108 @ SV2521 @ SV607 ) @ ( c_HOL_Otimes__class_Otimes @ SV1445 @ SV2521 @ SV607 ) @ SV607 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV607 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7081]) ).
thf(7479,plain,
! [SV2522: $i,SV2109: $i,SV608: $i,SV1446: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1446 @ ( c_HOL_Ozero__class_Ozero @ SV608 ) @ SV608 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV2109 @ SV2522 @ SV608 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2109 @ SV608 ) @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2522 @ SV608 ) @ SV608 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV608 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7082]) ).
thf(7480,plain,
! [SV2523: $i,SV609: $i,SV2110: $i,SV1447: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1447 @ SV2110 @ SV609 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV609 ) @ SV2523 @ SV609 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2523 @ SV2110 @ SV609 ) @ ( c_HOL_Otimes__class_Otimes @ SV2523 @ SV1447 @ SV609 ) @ SV609 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV609 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7083]) ).
thf(7481,plain,
! [SV623: $i,SV1460: $i,SV2120: $i] :
( ( ( SV2120 = SV1460 )
= $true )
| ( ( ~ ( c_lessequals @ SV1460 @ SV2120 @ SV623 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1460 @ SV2120 @ SV623 )
= $true )
| ( ( class_Orderings_Oorder @ SV623 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7091]) ).
thf(7482,plain,
! [SV624: $i,SV2121: $i,SV1461: $i] :
( ( ( ~ ( c_lessequals @ SV1461 @ SV2121 @ SV624 ) )
= $true )
| ( ( SV2121 = SV1461 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1461 @ SV2121 @ SV624 )
= $true )
| ( ( class_Orderings_Oorder @ SV624 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7092]) ).
thf(7483,plain,
! [SV628: $i,SV2122: $i,SV1465: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1465 @ SV2122 @ SV628 )
= $true )
| ( ( ~ ( c_lessequals @ SV1465 @ SV2122 @ SV628 ) )
= $true )
| ( ( SV1465 = SV2122 )
= $true )
| ( ( class_Orderings_Oorder @ SV628 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7093]) ).
thf(7484,plain,
! [SV629: $i,SV2123: $i,SV1466: $i] :
( ( ( SV1466 = SV2123 )
= $true )
| ( ( ~ ( c_lessequals @ SV1466 @ SV2123 @ SV629 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1466 @ SV2123 @ SV629 )
= $true )
| ( ( class_Orderings_Oorder @ SV629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7094]) ).
thf(7485,plain,
! [SV630: $i,SV2124: $i,SV1467: $i] :
( ( ( SV1467 = SV2124 )
= $true )
| ( ( ~ ( c_lessequals @ SV1467 @ SV2124 @ SV630 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1467 @ SV2124 @ SV630 )
= $true )
| ( ( class_Orderings_Oorder @ SV630 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7095]) ).
thf(7486,plain,
! [SV631: $i,SV2125: $i,SV1468: $i] :
( ( ( ~ ( c_lessequals @ SV1468 @ SV2125 @ SV631 ) )
= $true )
| ( ( SV1468 = SV2125 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1468 @ SV2125 @ SV631 )
= $true )
| ( ( class_Orderings_Oorder @ SV631 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7096]) ).
thf(7487,plain,
! [SV632: $i,SV2126: $i,SV1469: $i] :
( ( ( ~ ( c_lessequals @ SV1469 @ SV2126 @ SV632 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1469 @ SV2126 @ SV632 )
= $true )
| ( ( SV1469 = SV2126 )
= $true )
| ( ( class_Orderings_Olinorder @ SV632 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7097]) ).
thf(7488,plain,
! [SV633: $i,SV2127: $i,SV1470: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1470 @ SV2127 @ SV633 )
= $true )
| ( ( ~ ( c_lessequals @ SV1470 @ SV2127 @ SV633 ) )
= $true )
| ( ( SV1470 = SV2127 )
= $true )
| ( ( class_Orderings_Olinorder @ SV633 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7098]) ).
thf(7489,plain,
! [SV1471: $i,SV2128: $i,SV634: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV2128 @ SV634 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV1471 @ SV634 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ ( c_HOL_Otimes__class_Otimes @ SV1471 @ SV2128 @ SV634 ) @ SV634 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV634 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7099]) ).
thf(7490,plain,
! [SV1472: $i,SV635: $i,SV2129: $i] :
( ( ( ~ ( c_lessequals @ SV2129 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1472 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ ( c_HOL_Otimes__class_Otimes @ SV1472 @ SV2129 @ SV635 ) @ SV635 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV635 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7100]) ).
thf(7491,plain,
! [SV1473: $i,SV2130: $i,SV636: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV2130 @ SV636 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV1473 @ SV636 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ ( c_HOL_Otimes__class_Otimes @ SV1473 @ SV2130 @ SV636 ) @ SV636 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV636 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7101]) ).
thf(7492,plain,
! [SV1475: $i,SV638: $i,SV2131: $i] :
( ( ( ~ ( c_lessequals @ SV2131 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1475 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ ( c_HOL_Otimes__class_Otimes @ SV1475 @ SV2131 @ SV638 ) @ SV638 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV638 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7102]) ).
thf(7493,plain,
! [SV1476: $i,SV639: $i,SV2132: $i] :
( ( ( ~ ( c_lessequals @ SV2132 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1476 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ ( c_HOL_Otimes__class_Otimes @ SV1476 @ SV2132 @ SV639 ) @ SV639 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV639 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7103]) ).
thf(7494,plain,
! [SV1477: $i,SV2133: $i,SV640: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV2133 @ SV640 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV1477 @ SV640 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ ( c_HOL_Otimes__class_Otimes @ SV1477 @ SV2133 @ SV640 ) @ SV640 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV640 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7104]) ).
thf(7495,plain,
! [SV660: $i,SV2150: $i,SV1496: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1496 @ SV2150 @ SV660 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2150 @ SV1496 @ SV660 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7114]) ).
thf(7496,plain,
! [SV661: $i,SV2151: $i,SV1497: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1497 @ SV2151 @ SV661 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2151 @ SV1497 @ SV661 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV661 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7115]) ).
thf(7497,plain,
! [SV664: $i,SV2153: $i,SV1500: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1500 @ SV2153 @ SV664 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2153 @ SV1500 @ SV664 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7117]) ).
thf(7498,plain,
! [SV665: $i,SV2154: $i,SV1501: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1501 @ SV2154 @ SV665 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2154 @ SV1501 @ SV665 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7118]) ).
thf(7499,plain,
! [SV2820: $i,SV2772: $i,SV2689: $i,SV2544: $i,SV2160: $i,SV1515: $i,SV698: $i] :
( ( ( ( hAPP @ ( hAPP @ SV698 @ SV1515 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV2160 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2544 @ SV2689 @ SV698 @ SV2772 @ SV2160 @ SV2820 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7120]) ).
thf(7500,plain,
! [SV2162: $i,SV702: $i,SV1519: $i,SV2545: $i] :
( ( ( c_Lambda_Obeta @ SV2545 @ SV1519 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV702 @ SV2545 @ SV2162 ) )
= $true )
| ( ( c_Type_Otyping @ SV702 @ SV1519 @ SV2162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7121]) ).
thf(7501,plain,
! [SV2692: $i,SV2549: $i,SV2169: $i,SV1527: $i,SV710: $i] :
( ( ( hBOOL @ ( hAPP @ SV710 @ ( c_Type_Otype_Otype__case @ SV1527 @ SV2169 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2549 ) @ SV2692 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV710 @ ( hAPP @ ( hAPP @ SV2169 @ SV2549 ) @ SV2692 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7123]) ).
thf(7502,plain,
! [SV2693: $i,SV2550: $i,SV2170: $i,SV1528: $i,SV711: $i] :
( ( ( hBOOL @ ( hAPP @ SV711 @ ( c_Type_Otype_Otype__case @ SV1528 @ SV2170 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2550 ) @ SV2693 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV711 @ ( hAPP @ ( hAPP @ SV2170 @ SV2550 ) @ SV2693 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7124]) ).
thf(7503,plain,
! [SV2554: $i,SV2177: $i,SV719: $i,SV1536: $i,SV2696: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2696 @ SV1536 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( c_Type_Oshift @ SV719 @ SV1536 @ SV2177 @ SV2554 ) @ SV2696 )
= ( hAPP @ SV719 @ SV2696 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7127]) ).
thf(7504,plain,
! [SV2556: $i,SV1538: $i,SV2697: $i,SV2179: $i,SV721: $i] :
( ( ( ~ ( c_Type_Otypings @ SV721 @ SV2179 @ SV2697 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV721 @ SV1538 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV2697 @ SV2556 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV721 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1538 @ SV2179 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2556 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7129]) ).
thf(7505,plain,
! [SV1540: $i,SV723: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV723 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV723 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV723 ) @ SV1540 @ SV723 )
= ( c_HOL_Ozero__class_Ozero @ SV723 ) )
| ( SV1540
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV723 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV723 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7131]) ).
thf(7506,plain,
! [SV1541: $i,SV724: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV724 ) @ SV1541 @ SV724 )
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
= $true )
| ( ( SV1541
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV724 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV724 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7132]) ).
thf(7507,plain,
! [SV2559: $i,SV1543: $i,SV2699: $i,SV2182: $i,SV727: $i] :
( ( ( ~ ( c_Type_Otyping @ SV727 @ SV2182 @ SV2699 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV727 @ SV1543 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2699 ) @ SV2559 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV727 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1543 ) @ SV2182 ) @ SV2559 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7133]) ).
thf(7508,plain,
! [SV2775: $i,SV2700: $i,SV2560: $i,SV2183: $i,SV1544: $i,SV728: $i] :
( ( ( ~ ( c_Type_Otyping @ SV728 @ SV1544 @ SV2183 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV728 @ SV2560 @ SV2183 @ tc_Type_Otype ) @ SV2700 @ SV2775 )
| ( c_Type_Otyping @ SV728 @ ( c_Lambda_Osubst @ SV2700 @ SV1544 @ SV2560 ) @ SV2775 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7134]) ).
thf(7509,plain,
! [SV2185: $i,SV1546: $i,SV2701: $i,SV2562: $i,SV730: $i] :
( ( ( c_Type_Otyping @ SV730 @ SV2562 @ SV2701 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV730 @ SV1546 @ SV2185 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV2562 @ SV1546 ) @ SV2701 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7136]) ).
thf(7510,plain,
! [SV2702: $i,SV2564: $i,SV2188: $i,SV1553: $i,SV737: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV737 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1553 @ SV2188 @ SV737 )
!= ( c_HOL_Ominus__class_Ominus @ SV2564 @ SV2702 @ SV737 ) )
| ( c_lessequals @ SV2188 @ SV1553 @ SV737 )
| ~ ( c_lessequals @ SV2702 @ SV2564 @ SV737 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7137]) ).
thf(7511,plain,
! [SV2703: $i,SV2565: $i,SV2189: $i,SV1554: $i,SV738: $i] :
( ( ( ( c_List_Olist_OCons @ SV738 @ SV1554 @ SV2189 )
= ( c_List_Olist_OCons @ SV2565 @ SV2703 @ SV2189 ) )
= $false )
| ( ( SV738 = SV2565 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7138]) ).
thf(7512,plain,
! [SV2704: $i,SV2566: $i,SV2193: $i,SV1558: $i,SV742: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV1558 @ tc_nat ) ) @ SV2193 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2566 @ SV1558 @ tc_nat ) ) @ SV2704 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV2566 @ SV742 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV742 @ SV2566 @ tc_nat ) @ SV1558 @ tc_nat ) ) @ SV2193 )
= SV2704 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7140]) ).
thf(7513,plain,
! [SV2776: $i,SV2705: $i,SV2569: $i,SV2199: $i,SV1566: $i,SV750: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV750 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV1566 @ SV2199 @ SV750 ) ) @ SV2569 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV2705 @ SV2199 @ SV750 ) ) @ SV2776 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ SV2705 @ SV750 ) @ SV2199 @ SV750 ) ) @ SV2569 )
= SV2776 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7144]) ).
thf(7514,plain,
! [SV2571: $i,SV2201: $i,SV1570: $i,SV754: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SV1570 ) @ SV2201 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SV2571 ) @ SV2201 ) )
= $true )
| ( ( SV1570 = SV2571 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV754 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7145]) ).
thf(7515,plain,
! [SV1575: $i,SV2204: $i,SV2573: $i,SV759: $i] :
( ( ( hBOOL @ ( hAPP @ SV759 @ SV2573 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV759 @ SV2204 ) )
= $true )
| ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV759 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1575 ) @ SV2204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7147]) ).
thf(7516,plain,
! [SV2706: $i,SV2574: $i,SV2205: $i,SV1576: $i,SV760: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV760 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV2205 @ SV760 )
!= ( c_HOL_Ominus__class_Ominus @ SV2574 @ SV2706 @ SV760 ) )
| ( c_HOL_Oord__class_Oless @ SV2574 @ SV2706 @ SV760 )
| ~ ( c_HOL_Oord__class_Oless @ SV1576 @ SV2205 @ SV760 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7148]) ).
thf(7517,plain,
! [SV761: $i,SV2206: $i,SV1577: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV1577 @ SV2206 @ SV761 )
= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
= $false )
| ( ( ( SV1577
= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
| ( SV2206
= ( c_HOL_Ozero__class_Ozero @ SV761 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV761 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7149]) ).
thf(7518,plain,
! [SV2575: $i,SV763: $i,SV2208: $i,SV1579: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1579 @ SV2208 @ SV763 )
!= ( c_Power_Opower__class_Opower @ SV2575 @ SV2208 @ SV763 ) )
= $true )
| ( ( ( SV1579 = SV2575 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2208 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV2575 @ SV763 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV763 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7150]) ).
thf(7519,plain,
! [SV2576: $i,SV2209: $i,SV1580: $i,SV764: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SV2209 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SV2576 ) )
= $true )
| ( ( SV2209 = SV2576 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV764 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7151]) ).
thf(7520,plain,
! [SV2214: $i,SV1588: $i,SV773: $i] :
( ( ( class_Int_Onumber__ring @ SV773 )
= $false )
| ( ( ( SV1588
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV773 ) @ SV1588 ) @ SV2214 ) )
| ( SV2214
= ( c_HOL_Ozero__class_Ozero @ SV773 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV773 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7153]) ).
thf(7521,plain,
! [SV2707: $i,SV2578: $i,SV2215: $i,SV1589: $i,SV774: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV774 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV774 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2578 @ SV774 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2707 @ SV774 ) ) )
| ( SV2578 = SV2707 )
| ( SV2215
= ( c_HOL_Ozero__class_Ozero @ SV774 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7154]) ).
thf(7522,plain,
! [SV2708: $i,SV2579: $i,SV2216: $i,SV1590: $i,SV775: $i] :
( ( ( ( c_List_Oreplicate @ SV775 @ SV1590 @ SV2216 )
= ( c_List_Oreplicate @ SV2579 @ SV2708 @ SV2216 ) )
= $false )
| ( ( SV775 = SV2579 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7155]) ).
thf(7523,plain,
! [SV2709: $i,SV2580: $i,SV2217: $i,SV1592: $i,SV778: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV778 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1592 @ SV2217 @ SV778 )
!= ( c_HOL_Ominus__class_Ominus @ SV2580 @ SV2709 @ SV778 ) )
| ( c_HOL_Oord__class_Oless @ SV1592 @ SV2217 @ SV778 )
| ~ ( c_HOL_Oord__class_Oless @ SV2580 @ SV2709 @ SV778 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7156]) ).
thf(7524,plain,
! [SV779: $i,SV2218: $i,SV1593: $i] :
( ( ( ( c_Orderings_Oord__class_Omax @ SV1593 @ SV2218 @ SV779 )
= SV2218 )
= $false )
| ( ( c_lessequals @ SV1593 @ SV2218 @ SV779 )
= $true )
| ( ( class_Orderings_Olinorder @ SV779 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7157]) ).
thf(7525,plain,
! [SV2710: $i,SV2581: $i,SV2219: $i,SV1594: $i,SV780: $i] :
( ( ( ( c_List_Oappend @ SV780 @ ( c_List_Olist_OCons @ SV1594 @ ( c_List_Olist_ONil @ SV2219 ) @ SV2219 ) @ SV2219 )
= ( c_List_Oappend @ SV2581 @ ( c_List_Olist_OCons @ SV2710 @ ( c_List_Olist_ONil @ SV2219 ) @ SV2219 ) @ SV2219 ) )
= $false )
| ( ( SV1594 = SV2710 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7158]) ).
thf(7526,plain,
! [SV2222: $i,SV784: $i,SV2583: $i,SV1598: $i] :
( ( ( SV1598 = SV2583 )
= $true )
| ( ( SV784 = SV2222 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SV1598 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2222 @ SV2583 @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV784 @ SV2583 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2222 @ SV1598 @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7160]) ).
thf(7527,plain,
! [SV2711: $i,SV2584: $i,SV2224: $i,SV1600: $i,SV787: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV787 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV787 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2224 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2711 @ SV787 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2711 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2224 @ SV787 ) ) )
| ( SV2224 = SV2711 )
| ( SV1600 = SV2584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7161]) ).
thf(7528,plain,
! [SV2712: $i,SV2585: $i,SV2225: $i,SV1602: $i,SV789: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV789 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1602 @ SV2225 @ SV789 )
!= ( c_HOL_Ominus__class_Ominus @ SV2585 @ SV2712 @ SV789 ) )
| ( c_lessequals @ SV2712 @ SV2585 @ SV789 )
| ~ ( c_lessequals @ SV2225 @ SV1602 @ SV789 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7162]) ).
thf(7529,plain,
! [SV790: $i,SV2226: $i,SV1603: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV1603 @ SV2226 @ SV790 )
= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
= $false )
| ( ( ( SV2226
= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
| ( SV1603
= ( c_HOL_Ozero__class_Ozero @ SV790 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV790 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7163]) ).
thf(7530,plain,
! [SV1605: $i,SV792: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV792 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV792 )
| ( ( c_Power_Opower__class_Opower @ SV1605 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV792 )
!= ( c_HOL_Ozero__class_Ozero @ SV792 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV792 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV792 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7164]) ).
thf(7531,plain,
! [SV2227: $i,SV1606: $i,SV793: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV793 ) @ SV1606 ) @ SV2227 )
= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV2227 @ SV793 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV1606 @ SV793 )
| ( SV1606
= ( c_HOL_Ozero__class_Ozero @ SV793 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV793 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7165]) ).
thf(7532,plain,
! [SV2228: $i,SV1607: $i,SV2586: $i,SV794: $i] :
( ( ( hBOOL @ ( hAPP @ SV794 @ SV2586 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV794 @ SV1607 ) )
= $true )
| ( ( ( c_Type_Osko__Type__Xtype__induct__1__1 @ SV794 )
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV1607 ) @ SV2228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7166]) ).
thf(7533,plain,
! [SV795: $i,SV2229: $i,SV1608: $i] :
( ( ( c_lessequals @ SV1608 @ SV2229 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1608 @ SV795 @ tc_nat )
| ( SV795 = SV2229 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV795 @ SV1608 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV2229 @ SV1608 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7167]) ).
thf(7534,plain,
! [SV2713: $i,SV2587: $i,SV2230: $i,SV1609: $i,SV796: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV796 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SV2587 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SV2713 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ SV2587 )
= SV2713 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7168]) ).
thf(7535,plain,
! [SV2231: $i,SV1610: $i,SV797: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV797 ) @ ( c_HOL_Otimes__class_Otimes @ SV1610 @ SV1610 @ SV797 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2231 @ SV2231 @ SV797 ) )
= ( c_HOL_Ozero__class_Ozero @ SV797 ) )
= $false )
| ( ( SV2231
= ( c_HOL_Ozero__class_Ozero @ SV797 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV797 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7169]) ).
thf(7536,plain,
! [SV2588: $i,SV2232: $i,SV798: $i,SV1611: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1611 @ SV1611 @ SV798 )
!= ( c_HOL_Ominus__class_Ominus @ SV2232 @ SV2588 @ SV798 ) )
= $true )
| ( ( SV2232 = SV2588 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV798 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7170]) ).
thf(7537,plain,
! [SV2714: $i,SV2589: $i,SV2233: $i,SV1612: $i,SV799: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV799 @ SV1612 @ tc_nat ) ) @ SV2233 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2589 @ SV1612 @ tc_nat ) ) @ SV2714 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV799 @ SV2589 @ tc_nat )
| ( SV2233
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2589 @ SV799 @ tc_nat ) @ SV1612 @ tc_nat ) ) @ SV2714 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7171]) ).
thf(7538,plain,
! [SV2590: $i,SV800: $i,SV1613: $i,SV2234: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2234 @ SV1613 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV800 @ SV2590 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV800 ) @ SV1613 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2234 ) @ SV2590 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7172]) ).
thf(7539,plain,
! [SV2237: $i,SV1616: $i,SV803: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV803 @ tc_nat )
= $false )
| ( ( SV1616 = SV2237 )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1616 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV803 @ SV2237 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7174]) ).
thf(7540,plain,
! [SV2715: $i,SV2592: $i,SV2239: $i,SV1619: $i,SV806: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV806 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV806 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2239 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2715 @ SV806 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2715 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2239 @ SV806 ) ) )
| ( SV2239 = SV2715 )
| ( SV1619 = SV2592 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7175]) ).
thf(7541,plain,
! [SV2777: $i,SV2716: $i,SV2594: $i,SV2241: $i,SV1621: $i,SV808: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV808 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV1621 @ SV2241 @ SV808 ) ) @ SV2594 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV2716 @ SV2241 @ SV808 ) ) @ SV2777 ) )
| ( SV2594
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2716 @ SV1621 @ SV808 ) @ SV2241 @ SV808 ) ) @ SV2777 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7177]) ).
thf(7542,plain,
! [SV2243: $i,SV1623: $i,SV810: $i] :
( ( ( class_Int_Onumber__ring @ SV810 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1623 @ SV2243 @ SV810 )
!= ( c_HOL_Ozero__class_Ozero @ SV810 ) )
| ( SV1623 = SV2243 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV810 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7179]) ).
thf(7543,plain,
! [SV2244: $i,SV812: $i,SV2595: $i,SV1625: $i] :
( ( ( SV1625 = SV2595 )
= $true )
| ( ( SV812 = SV2244 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1625 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2244 @ SV2595 @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV2595 @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2244 @ SV1625 @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7180]) ).
thf(7544,plain,
! [SV816: $i,SV2246: $i,SV1629: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV1629 @ SV2246 @ SV816 )
= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
= $false )
| ( ( ( SV2246
= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
| ( SV1629
= ( c_HOL_Ozero__class_Ozero @ SV816 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV816 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7182]) ).
thf(7545,plain,
! [SV2598: $i,SV2249: $i,SV1633: $i,SV820: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SV2249 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SV2598 ) )
= $true )
| ( ( SV2249 = SV2598 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV820 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7184]) ).
thf(7546,plain,
! [SV2250: $i,SV821: $i,SV1634: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1634 @ SV821 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV2250 @ SV821 ) )
= $false )
| ( ( SV1634 = SV2250 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV821 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7185]) ).
thf(7547,plain,
! [SV2251: $i,SV1635: $i,SV822: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV822 ) @ ( c_HOL_Otimes__class_Otimes @ SV1635 @ SV1635 @ SV822 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2251 @ SV2251 @ SV822 ) )
= ( c_HOL_Ozero__class_Ozero @ SV822 ) )
= $false )
| ( ( SV1635
= ( c_HOL_Ozero__class_Ozero @ SV822 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV822 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7186]) ).
thf(7548,plain,
! [SV2599: $i,SV823: $i,SV2252: $i,SV1636: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1636 @ ( c_Suc @ SV2252 ) @ SV823 )
!= ( c_Power_Opower__class_Opower @ SV2599 @ ( c_Suc @ SV2252 ) @ SV823 ) )
= $true )
| ( ( ( SV1636 = SV2599 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV2599 @ SV823 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV1636 @ SV823 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV823 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7187]) ).
thf(7549,plain,
! [SV2601: $i,SV2259: $i,SV1644: $i,SV832: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV832 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2259 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2601 ) )
| ( SV2259 = SV2601 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV832 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7189]) ).
thf(7550,plain,
! [SV834: $i,SV2261: $i,SV1646: $i] :
( ( ( ( c_Orderings_Oord__class_Omin @ SV1646 @ SV2261 @ SV834 )
= SV1646 )
= $false )
| ( ( c_lessequals @ SV1646 @ SV2261 @ SV834 )
= $true )
| ( ( class_Orderings_Olinorder @ SV834 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7190]) ).
thf(7551,plain,
! [SV2717: $i,SV2602: $i,SV2263: $i,SV1649: $i,SV837: $i] :
( ( ( ( c_List_Oreplicate @ SV837 @ SV1649 @ SV2263 )
= ( c_List_Oreplicate @ SV2602 @ SV2717 @ SV2263 ) )
= $false )
| ( ( ( SV1649 = SV2717 )
| ( SV837
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7191]) ).
thf(7552,plain,
! [SV2821: $i,SV2778: $i,SV2718: $i,SV2603: $i,SV2264: $i,SV1650: $i,SV838: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
| ~ ( c_Type_Otyping @ SV2778 @ SV2603 @ SV1650 )
| ~ ( c_InductTermi_OIT @ SV2603 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2778 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SV2821 )
| ~ ( c_InductTermi_OIT @ SV2264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7192]) ).
thf(7553,plain,
! [SV2265: $i,SV1651: $i,SV839: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV839 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV839 )
| ~ ( class_Power_Opower @ SV839 )
| ( ( c_Power_Opower__class_Opower @ SV1651 @ SV2265 @ SV839 )
!= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
| ( SV1651
= ( c_HOL_Ozero__class_Ozero @ SV839 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV839 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7193]) ).
thf(7554,plain,
! [SV2719: $i,SV2604: $i,SV2267: $i,SV1653: $i,SV841: $i] :
( ( ( ( c_List_Oappend @ SV841 @ ( c_List_Olist_OCons @ SV1653 @ ( c_List_Olist_ONil @ SV2267 ) @ SV2267 ) @ SV2267 )
= ( c_List_Oappend @ SV2604 @ ( c_List_Olist_OCons @ SV2719 @ ( c_List_Olist_ONil @ SV2267 ) @ SV2267 ) @ SV2267 ) )
= $false )
| ( ( SV841 = SV2604 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7194]) ).
thf(7555,plain,
! [SV846: $i,SV2270: $i,SV1657: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1657 @ SV2270 @ SV846 )
= ( c_HOL_Ozero__class_Ozero @ SV846 ) )
= $false )
| ( ( SV1657
= ( c_HOL_Ozero__class_Ozero @ SV846 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV846 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7195]) ).
thf(7556,plain,
! [SV2720: $i,SV2605: $i,SV2272: $i,SV1659: $i,SV848: $i] :
( ( ( ( c_List_Olist_OCons @ SV848 @ SV1659 @ SV2272 )
= ( c_List_Olist_OCons @ SV2605 @ SV2720 @ SV2272 ) )
= $false )
| ( ( SV1659 = SV2720 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7196]) ).
thf(7557,plain,
! [SV2276: $i,SV1666: $i,SV855: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV855 ) @ SV1666 ) @ SV2276 )
= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV2276 @ SV855 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV1666 @ SV855 )
| ( SV2276
= ( c_HOL_Ozero__class_Ozero @ SV855 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV855 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7199]) ).
thf(7558,plain,
! [SV856: $i,SV2277: $i,SV1667: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1667 @ SV2277 @ SV856 )
= ( c_HOL_Ozero__class_Ozero @ SV856 ) )
= $false )
| ( ( SV1667 = SV2277 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV856 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7200]) ).
thf(7559,plain,
! [SV2607: $i,SV858: $i,SV2279: $i,SV1669: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1669 @ SV2279 @ SV858 )
!= ( c_HOL_Ominus__class_Ominus @ SV2607 @ SV2607 @ SV858 ) )
= $true )
| ( ( SV1669 = SV2279 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV858 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7201]) ).
thf(7560,plain,
! [SV861: $i,SV1672: $i,SV2608: $i,SV2281: $i] :
( ( ( SV2281 = SV2608 )
= $true )
| ( ( SV1672
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SV2281 @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV861 ) @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SV2608 @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7202]) ).
thf(7561,plain,
! [SV2822: $i,SV2779: $i,SV2721: $i,SV2609: $i,SV2282: $i,SV1673: $i,SV863: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
| ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
| ~ ( c_Type_Otyping @ SV2779 @ SV2609 @ SV863 )
| ~ ( c_InductTermi_OIT @ SV2609 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2779 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SV2822 )
| ~ ( c_InductTermi_OIT @ SV2282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7203]) ).
thf(7562,plain,
! [SV864: $i,SV2283: $i,SV1674: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1674 @ SV2283 @ SV864 )
= ( c_HOL_Ozero__class_Ozero @ SV864 ) )
= $false )
| ( ( SV1674 = SV2283 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV864 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7204]) ).
thf(7563,plain,
! [SV2610: $i,SV865: $i,SV1: $i,SV2284: $i,SV1675: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1675 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2284 @ SV1 @ tc_nat ) @ SV865 @ tc_nat ) ) @ SV2610 ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1 @ SV2284 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1 @ SV865 @ tc_nat ) ) @ SV1675 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2284 @ SV865 @ tc_nat ) ) @ SV2610 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7205]) ).
thf(7564,plain,
! [SV2611: $i,SV866: $i,SV2: $i,SV2285: $i,SV1676: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV2285 @ tc_nat ) ) @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV866 @ SV2285 @ tc_nat ) ) @ SV2611 ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1676 @ SV866 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV2 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV866 @ SV1676 @ tc_nat ) @ SV2285 @ tc_nat ) ) @ SV2611 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7206]) ).
thf(7565,plain,
! [SV2612: $i,SV1677: $i,SV867: $i,SV2286: $i,SV3: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV3 @ SV2286 @ tc_nat ) @ SV867 @ tc_nat ) ) @ SV1677 ) @ SV2612 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV2286 @ SV3 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV3 @ SV867 @ tc_nat ) ) @ SV1677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2286 @ SV867 @ tc_nat ) ) @ SV2612 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7207]) ).
thf(7566,plain,
! [SV2613: $i,SV868: $i,SV2287: $i,SV1678: $i,SV4: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV4 @ SV1678 @ tc_nat ) ) @ SV2287 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV868 @ SV1678 @ tc_nat ) ) @ SV2613 ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV868 @ SV4 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV868 @ tc_nat ) @ SV1678 @ tc_nat ) ) @ SV2287 ) @ SV2613 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7208]) ).
thf(7567,plain,
! [SV2615: $i,SV2289: $i,SV9: $i,SV1680: $i,SV873: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV2289 @ SV2615 @ SV9 ) @ SV9 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV2289 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1680 @ SV2615 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV873 @ SV2289 @ SV9 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7210]) ).
thf(7568,plain,
! [SV1683: $i,SV13: $i,SV2290: $i,SV877: $i] :
( ( ( ~ ( c_lessequals @ SV877 @ SV2290 @ SV13 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV877 @ SV1683 @ SV13 ) )
= $true )
| ( ( c_lessequals @ SV877 @ ( c_Orderings_Oord__class_Omin @ SV1683 @ SV2290 @ SV13 ) @ SV13 )
= $true )
| ( ( class_Orderings_Olinorder @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7211]) ).
thf(7569,plain,
! [SV1684: $i,SV14: $i,SV2291: $i,SV878: $i] :
( ( ( ~ ( c_lessequals @ SV878 @ SV2291 @ SV14 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV878 @ SV1684 @ SV14 ) )
= $true )
| ( ( c_lessequals @ SV878 @ ( c_Orderings_Oord__class_Omin @ SV1684 @ SV2291 @ SV14 ) @ SV14 )
= $true )
| ( ( class_Orderings_Olinorder @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7212]) ).
thf(7570,plain,
! [SV1685: $i,SV15: $i,SV2292: $i,SV879: $i] :
( ( ( ~ ( c_lessequals @ SV879 @ SV2292 @ SV15 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV879 @ SV1685 @ SV15 ) )
= $true )
| ( ( c_lessequals @ SV879 @ ( c_Orderings_Oord__class_Omin @ SV1685 @ SV2292 @ SV15 ) @ SV15 )
= $true )
| ( ( class_Orderings_Olinorder @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7213]) ).
thf(7571,plain,
! [SV884: $i,SV20: $i,SV2295: $i,SV1689: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1689 @ SV2295 @ SV20 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV884 @ SV2295 @ SV20 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV884 @ SV1689 @ SV20 ) @ SV2295 @ SV20 )
= $true )
| ( ( class_Orderings_Olinorder @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7216]) ).
thf(7572,plain,
! [SV2296: $i,SV1691: $i,SV886: $i,SV22: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV22 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV886 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1691 ) @ SV2296 ) @ SV22 )
| ~ ( c_lessequals @ SV886 @ SV2296 @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV1691 @ SV22 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7217]) ).
thf(7573,plain,
! [SV1696: $i,SV27: $i,SV2298: $i,SV891: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV2298 @ SV27 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV1696 @ SV27 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV891 @ ( c_Orderings_Oord__class_Omin @ SV1696 @ SV2298 @ SV27 ) @ SV27 )
= $true )
| ( ( class_Orderings_Olinorder @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7221]) ).
thf(7574,plain,
! [SV2299: $i,SV1699: $i,SV894: $i,SV30: $i] :
( ( ( class_Int_Onumber__ring @ SV30 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV1699 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV2299 @ SV30 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV2299 @ SV30 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV894 @ SV1699 @ SV30 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7222]) ).
thf(7575,plain,
! [SV2300: $i,SV1700: $i,SV895: $i,SV31: $i] :
( ( ( class_Int_Onumber__ring @ SV31 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1700 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV2300 @ SV31 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV31 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV2300 @ SV31 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1700 @ SV31 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7223]) ).
thf(7576,plain,
! [SV2304: $i,SV914: $i,SV1715: $i,SV51: $i] :
( ( ( c_lessequals @ SV51 @ SV1715 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV914 @ SV2304 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV51 ) @ SV914 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1715 ) @ SV2304 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7226]) ).
thf(7577,plain,
! [SV2619: $i,SV2305: $i,SV1716: $i,SV915: $i,SV52: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV915 ) @ SV1716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV2305 ) @ SV2619 ) @ SV52 )
= $true )
| ( ( ~ ( c_lessequals @ SV1716 @ SV2619 @ SV52 )
| ~ ( c_lessequals @ SV915 @ SV2305 @ SV52 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7227]) ).
thf(7578,plain,
! [SV923: $i,SV1719: $i,SV62: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1719 @ SV62 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV923 @ SV62 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV923 ) @ SV1719 ) @ SV62 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7229]) ).
thf(7579,plain,
! [SV924: $i,SV63: $i,SV1720: $i,SV2306: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2306 @ SV1720 @ SV63 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV924 @ SV2306 @ SV63 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV924 @ SV1720 @ SV63 )
= $true )
| ( ( class_Orderings_Opreorder @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7230]) ).
thf(7580,plain,
! [SV1721: $i,SV64: $i,SV2307: $i,SV925: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV925 @ SV2307 @ SV64 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2307 @ SV1721 @ SV64 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV925 @ SV1721 @ SV64 )
= $true )
| ( ( class_Orderings_Oorder @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7231]) ).
thf(7581,plain,
! [SV933: $i,SV1729: $i,SV72: $i] :
( ( ( hBOOL @ ( hAPP @ SV72 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1729 @ ( c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1 @ SV72 ) @ tc_nat )
= $false )
| ( ( hBOOL @ ( hAPP @ SV72 @ SV1729 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV72 @ SV933 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7234]) ).
thf(7582,plain,
! [SV939: $i,SV78: $i,SV2311: $i,SV1732: $i] :
( ( ( ~ ( c_lessequals @ SV1732 @ SV2311 @ SV78 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV939 @ SV2311 @ SV78 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV939 @ SV1732 @ SV78 ) @ SV2311 @ SV78 )
= $true )
| ( ( class_Orderings_Olinorder @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7237]) ).
thf(7583,plain,
! [SV940: $i,SV79: $i,SV2312: $i,SV1733: $i] :
( ( ( ~ ( c_lessequals @ SV1733 @ SV2312 @ SV79 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV940 @ SV2312 @ SV79 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV940 @ SV1733 @ SV79 ) @ SV2312 @ SV79 )
= $true )
| ( ( class_Orderings_Olinorder @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7238]) ).
thf(7584,plain,
! [SV941: $i,SV80: $i,SV2313: $i,SV1734: $i] :
( ( ( ~ ( c_lessequals @ SV1734 @ SV2313 @ SV80 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV941 @ SV2313 @ SV80 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV941 @ SV1734 @ SV80 ) @ SV2313 @ SV80 )
= $true )
| ( ( class_Orderings_Olinorder @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7239]) ).
thf(7585,plain,
! [SV2823: $i,SV2780: $i,SV2722: $i,SV2620: $i,SV2315: $i,SV1738: $i,SV951: $i,SV90: $i] :
( ( ! [SY7256: $i] :
( ( ( hAPP @ ( hAPP @ SV90 @ ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ SV1738 ) ) @ SV2315 )
= ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ ( c_HOL_Otimes__class_Otimes @ SV1738 @ SV2315 @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2620 @ SV2722 @ SV90 @ SV2780 @ SV2823 @ SY7256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7240]) ).
thf(7586,plain,
! [SV2318: $i,SV1741: $i,SV954: $i,SV93: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV93 )
= $false )
| ( ( ( c_lessequals @ SV954 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV1741 ) @ SV2318 ) @ SV93 )
| ~ ( c_lessequals @ SV954 @ SV2318 @ SV93 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV1741 @ SV93 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7241]) ).
thf(7587,plain,
! [SV2319: $i,SV1742: $i,SV955: $i,SV94: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV94 )
= $false )
| ( ( ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV1742 ) @ SV2319 ) @ SV94 )
| ~ ( c_lessequals @ SV955 @ SV1742 @ SV94 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV2319 @ SV94 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7242]) ).
thf(7588,plain,
! [SV2723: $i,SV2621: $i,SV2320: $i,SV1748: $i,SV967: $i,SV106: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV106 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV967 @ SV1748 @ SV106 ) ) @ SV2320 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV2621 @ SV1748 @ SV106 ) ) @ SV2723 ) @ SV106 )
| ~ ( c_lessequals @ SV2320 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2621 @ SV967 @ SV106 ) @ SV1748 @ SV106 ) ) @ SV2723 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7243]) ).
thf(7589,plain,
! [SV2724: $i,SV2622: $i,SV2321: $i,SV1749: $i,SV968: $i,SV107: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV107 )
= $false )
| ( ( ( c_lessequals @ SV968 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SV2321 @ SV107 ) @ SV2622 @ SV107 ) ) @ SV2724 ) @ SV107 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV2321 @ SV2622 @ SV107 ) ) @ SV968 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV1749 @ SV2622 @ SV107 ) ) @ SV2724 ) @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7244]) ).
thf(7590,plain,
! [SV2725: $i,SV2623: $i,SV2322: $i,SV1750: $i,SV969: $i,SV108: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV108 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV969 @ SV1750 @ SV108 ) ) @ SV2322 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV2623 @ SV1750 @ SV108 ) ) @ SV2725 ) @ SV108 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV969 @ SV2623 @ SV108 ) @ SV1750 @ SV108 ) ) @ SV2322 ) @ SV2725 @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7245]) ).
thf(7591,plain,
! [SV2726: $i,SV2624: $i,SV2323: $i,SV1751: $i,SV970: $i,SV109: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV109 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV970 @ SV1751 @ SV109 ) @ SV2323 @ SV109 ) ) @ SV2624 ) @ SV2726 @ SV109 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV970 @ SV2323 @ SV109 ) ) @ SV2624 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV1751 @ SV2323 @ SV109 ) ) @ SV2726 ) @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7246]) ).
thf(7592,plain,
! [SV1758: $i,SV980: $i,SV2325: $i,SV119: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV2325 @ SV119 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV980 @ SV2325 @ SV119 ) @ ( c_HOL_Otimes__class_Otimes @ SV1758 @ SV2325 @ SV119 ) @ SV119 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV980 @ SV1758 @ SV119 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7248]) ).
thf(7593,plain,
! [SV1759: $i,SV981: $i,SV2326: $i,SV120: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV2326 @ SV120 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV981 @ SV120 ) @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV1759 @ SV120 ) @ SV120 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV981 @ SV1759 @ SV120 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7249]) ).
thf(7594,plain,
! [SV1760: $i,SV982: $i,SV2327: $i,SV121: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV2327 @ SV121 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV982 @ SV2327 @ SV121 ) @ ( c_HOL_Otimes__class_Otimes @ SV1760 @ SV2327 @ SV121 ) @ SV121 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV982 @ SV1760 @ SV121 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7250]) ).
thf(7595,plain,
! [SV1761: $i,SV983: $i,SV2328: $i,SV122: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV2328 @ SV122 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV983 @ SV122 ) @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV1761 @ SV122 ) @ SV122 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV983 @ SV1761 @ SV122 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7251]) ).
thf(7596,plain,
! [SV1763: $i,SV124: $i,SV2329: $i,SV985: $i] :
( ( ( c_lessequals @ SV985 @ SV2329 @ SV124 )
= $true )
| ( ( ~ ( c_lessequals @ SV985 @ ( c_Orderings_Oord__class_Omax @ SV2329 @ SV1763 @ SV124 ) @ SV124 ) )
= $true )
| ( ( c_lessequals @ SV985 @ SV1763 @ SV124 )
= $true )
| ( ( class_Orderings_Olinorder @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7252]) ).
thf(7597,plain,
! [SV2824: $i,SV2781: $i,SV2727: $i,SV2625: $i,SV2331: $i,SV1765: $i,SV989: $i,SV128: $i] :
( ( ! [SY7257: $i] :
( ( ( hAPP @ ( hAPP @ SV128 @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2331 ) ) @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2625 ) )
= ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2331 ) @ SV2625 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2727 @ SV128 @ SV989 @ SV2781 @ SV2824 @ SY7257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7253]) ).
thf(7598,plain,
! [SV131: $i,SV1767: $i,SV2333: $i,SV991: $i] :
( ( ( c_lessequals @ SV991 @ ( c_Orderings_Oord__class_Omin @ SV2333 @ SV1767 @ SV131 ) @ SV131 )
= $false )
| ( ( c_lessequals @ SV991 @ SV1767 @ SV131 )
= $true )
| ( ( class_Orderings_Olinorder @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7254]) ).
thf(7599,plain,
! [SV132: $i,SV2334: $i,SV1768: $i,SV992: $i] :
( ( ( c_lessequals @ SV992 @ ( c_Orderings_Oord__class_Omin @ SV1768 @ SV2334 @ SV132 ) @ SV132 )
= $false )
| ( ( c_lessequals @ SV992 @ SV1768 @ SV132 )
= $true )
| ( ( class_Orderings_Olinorder @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7255]) ).
thf(7600,plain,
! [SV993: $i,SV133: $i,SV2335: $i,SV1769: $i] :
( ( ( c_lessequals @ SV1769 @ SV2335 @ SV133 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV993 @ SV1769 @ SV133 ) @ SV2335 @ SV133 )
= $true )
| ( ( class_Orderings_Olinorder @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7256]) ).
thf(7601,plain,
! [SV1770: $i,SV134: $i,SV2336: $i,SV994: $i] :
( ( ( c_lessequals @ SV994 @ SV2336 @ SV134 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV994 @ SV1770 @ SV134 ) @ SV2336 @ SV134 )
= $true )
| ( ( class_Orderings_Olinorder @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7257]) ).
thf(7602,plain,
! [SV995: $i,SV135: $i,SV2337: $i,SV1771: $i] :
( ( ( c_lessequals @ SV1771 @ SV2337 @ SV135 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV995 @ SV1771 @ SV135 ) @ SV2337 @ SV135 )
= $true )
| ( ( class_Orderings_Olinorder @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7258]) ).
thf(7603,plain,
! [SV1772: $i,SV136: $i,SV2338: $i,SV996: $i] :
( ( ( c_lessequals @ SV996 @ SV2338 @ SV136 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV996 @ SV1772 @ SV136 ) @ SV2338 @ SV136 )
= $true )
| ( ( class_Orderings_Olinorder @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7259]) ).
thf(7604,plain,
! [SV137: $i,SV1773: $i,SV2339: $i,SV997: $i] :
( ( ( c_lessequals @ SV997 @ ( c_Orderings_Oord__class_Omin @ SV2339 @ SV1773 @ SV137 ) @ SV137 )
= $false )
| ( ( c_lessequals @ SV997 @ SV1773 @ SV137 )
= $true )
| ( ( class_Orderings_Olinorder @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7260]) ).
thf(7605,plain,
! [SV138: $i,SV2340: $i,SV1774: $i,SV998: $i] :
( ( ( c_lessequals @ SV998 @ ( c_Orderings_Oord__class_Omin @ SV1774 @ SV2340 @ SV138 ) @ SV138 )
= $false )
| ( ( c_lessequals @ SV998 @ SV1774 @ SV138 )
= $true )
| ( ( class_Orderings_Olinorder @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7261]) ).
thf(7606,plain,
! [SV2728: $i,SV2626: $i,SV2341: $i,SV1776: $i,SV1000: $i,SV140: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV140 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1776 @ SV140 ) ) @ SV2341 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV2626 @ SV1776 @ SV140 ) ) @ SV2728 ) @ SV140 )
| ~ ( c_HOL_Oord__class_Oless @ SV2341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2626 @ SV1000 @ SV140 ) @ SV1776 @ SV140 ) ) @ SV2728 ) @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7262]) ).
thf(7607,plain,
! [SV2729: $i,SV2627: $i,SV2342: $i,SV1777: $i,SV1001: $i,SV141: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV141 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1001 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1777 @ SV2342 @ SV141 ) @ SV2627 @ SV141 ) ) @ SV2729 ) @ SV141 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV2342 @ SV2627 @ SV141 ) ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV1777 @ SV2627 @ SV141 ) ) @ SV2729 ) @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7263]) ).
thf(7608,plain,
! [SV2730: $i,SV2628: $i,SV2343: $i,SV1778: $i,SV1002: $i,SV142: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV142 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1778 @ SV142 ) ) @ SV2343 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV2628 @ SV1778 @ SV142 ) ) @ SV2730 ) @ SV142 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1002 @ SV2628 @ SV142 ) @ SV1778 @ SV142 ) ) @ SV2343 ) @ SV2730 @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7264]) ).
thf(7609,plain,
! [SV2731: $i,SV2629: $i,SV2344: $i,SV1779: $i,SV1003: $i,SV143: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV143 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1003 @ SV1779 @ SV143 ) @ SV2344 @ SV143 ) ) @ SV2629 ) @ SV2731 @ SV143 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1003 @ SV2344 @ SV143 ) ) @ SV2629 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1779 @ SV2344 @ SV143 ) ) @ SV2731 ) @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7265]) ).
thf(7610,plain,
! [SV1004: $i,SV144: $i,SV1780: $i,SV2345: $i] :
( ( ( c_lessequals @ SV2345 @ SV1780 @ SV144 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV2345 @ SV1004 @ SV144 ) @ SV1780 @ SV144 ) )
= $true )
| ( ( c_lessequals @ SV1004 @ SV1780 @ SV144 )
= $true )
| ( ( class_Orderings_Olinorder @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7266]) ).
thf(7611,plain,
! [SV1010: $i,SV1782: $i,SV150: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1782 @ SV150 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ ( c_HOL_Otimes__class_Otimes @ SV1010 @ SV1782 @ SV150 ) @ SV150 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1010 @ SV150 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7267]) ).
thf(7612,plain,
! [SV1011: $i,SV1783: $i,SV151: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1783 @ SV151 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ ( c_HOL_Otimes__class_Otimes @ SV1783 @ SV1011 @ SV151 ) @ SV151 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1011 @ SV151 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7268]) ).
thf(7613,plain,
! [SV1012: $i,SV1784: $i,SV152: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1784 @ SV152 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1012 @ SV152 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SV1784 @ SV152 ) @ SV152 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7269]) ).
thf(7614,plain,
! [SV1013: $i,SV153: $i,SV1785: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1785 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1013 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV1013 @ SV1785 @ SV153 ) @ SV153 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7270]) ).
thf(7615,plain,
! [SV2347: $i,SV1015: $i,SV1786: $i,SV155: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV1786 @ SV155 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1015 @ SV2347 @ SV155 ) @ ( c_Power_Opower__class_Opower @ SV1786 @ SV2347 @ SV155 ) @ SV155 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1786 @ SV155 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7271]) ).
thf(7616,plain,
! [SV182: $i,SV1042: $i,SV1808: $i] :
( ( ( c_lessequals @ SV1808 @ SV1042 @ SV182 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1042 @ SV1808 @ SV182 )
= $false )
| ( ( class_Orderings_Olinorder @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7275]) ).
thf(7617,plain,
! [SV184: $i,SV1044: $i,SV1810: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1810 @ SV1044 @ SV184 )
= $false )
| ( ( c_lessequals @ SV1044 @ SV1810 @ SV184 )
= $false )
| ( ( class_Orderings_Olinorder @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7276]) ).
thf(7618,plain,
! [SV186: $i,SV1046: $i,SV1812: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1812 @ SV1046 @ SV186 )
= $false )
| ( ( c_lessequals @ SV1046 @ SV1812 @ SV186 )
= $false )
| ( ( class_Orderings_Opreorder @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7277]) ).
thf(7619,plain,
! [SV2360: $i,SV1815: $i,SV1052: $i,SV192: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV192 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1052 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV1815 ) @ SV2360 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SV2360 @ SV192 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV1815 @ SV192 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7278]) ).
thf(7620,plain,
! [SV195: $i,SV1818: $i,SV1055: $i] :
( ( ( c_lessequals @ SV1055 @ SV1818 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1055 @ SV195 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV195 @ SV1818 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV195 @ SV1055 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1818 @ SV1055 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7279]) ).
thf(7621,plain,
! [SV196: $i,SV1056: $i,SV1819: $i] :
( ( ( c_lessequals @ SV1819 @ SV1056 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1819 @ SV196 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV196 @ SV1819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1056 @ SV1819 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV196 @ SV1056 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7280]) ).
thf(7622,plain,
! [SV1821: $i,SV2361: $i,SV1059: $i,SV199: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV1059 @ SV199 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1059 @ SV2361 @ SV199 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1821 @ SV199 ) @ ( c_Power_Opower__class_Opower @ SV2361 @ SV1821 @ SV199 ) @ SV199 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7281]) ).
thf(7623,plain,
! [SV1070: $i,SV210: $i,SV1831: $i,SV2364: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1831 @ SV210 ) @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1070 @ SV210 ) @ SV210 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2364 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 ) )
= $true )
| ( ( c_lessequals @ SV1070 @ SV1831 @ SV210 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7286]) ).
thf(7624,plain,
! [SV1071: $i,SV211: $i,SV1832: $i,SV2365: $i] :
( ( ( ~ ( c_lessequals @ SV2365 @ SV1832 @ SV211 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV1832 @ SV211 ) @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV2365 @ SV211 ) @ SV211 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7287]) ).
thf(7625,plain,
! [SV1833: $i,SV212: $i,SV1072: $i,SV2366: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1072 @ SV212 ) @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1833 @ SV212 ) @ SV212 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SV2366 @ SV212 ) )
= $true )
| ( ( c_lessequals @ SV1072 @ SV1833 @ SV212 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7288]) ).
thf(7626,plain,
! [SV1073: $i,SV213: $i,SV2367: $i,SV1834: $i] :
( ( ( ~ ( c_lessequals @ SV1834 @ SV2367 @ SV213 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV1073 @ SV213 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV1834 @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV2367 @ SV213 ) @ SV213 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7289]) ).
thf(7627,plain,
! [SV1835: $i,SV1074: $i,SV2368: $i,SV214: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV2368 @ SV214 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1074 @ SV214 ) @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1835 @ SV214 ) @ SV214 ) )
= $true )
| ( ( c_lessequals @ SV1074 @ SV1835 @ SV214 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7290]) ).
thf(7628,plain,
! [SV1836: $i,SV1075: $i,SV2369: $i,SV215: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV2369 @ SV215 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1075 @ SV2369 @ SV215 ) @ ( c_HOL_Otimes__class_Otimes @ SV1836 @ SV2369 @ SV215 ) @ SV215 ) )
= $true )
| ( ( c_lessequals @ SV1075 @ SV1836 @ SV215 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7291]) ).
thf(7629,plain,
! [SV2370: $i,SV221: $i,SV1839: $i,SV1079: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1079 @ SV1839 @ SV221 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1079 @ ( c_Orderings_Oord__class_Omax @ SV1839 @ SV2370 @ SV221 ) @ SV221 )
= $true )
| ( ( class_Orderings_Olinorder @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7292]) ).
thf(7630,plain,
! [SV1840: $i,SV222: $i,SV2371: $i,SV1080: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1080 @ SV2371 @ SV222 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1080 @ ( c_Orderings_Oord__class_Omax @ SV1840 @ SV2371 @ SV222 ) @ SV222 )
= $true )
| ( ( class_Orderings_Olinorder @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7293]) ).
thf(7631,plain,
! [SV2372: $i,SV223: $i,SV1841: $i,SV1081: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1081 @ SV1841 @ SV223 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1081 @ ( c_Orderings_Oord__class_Omax @ SV1841 @ SV2372 @ SV223 ) @ SV223 )
= $true )
| ( ( class_Orderings_Olinorder @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7294]) ).
thf(7632,plain,
! [SV1842: $i,SV224: $i,SV2373: $i,SV1082: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1082 @ SV2373 @ SV224 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1082 @ ( c_Orderings_Oord__class_Omax @ SV1842 @ SV2373 @ SV224 ) @ SV224 )
= $true )
| ( ( class_Orderings_Olinorder @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7295]) ).
thf(7633,plain,
! [SV1843: $i,SV225: $i,SV2374: $i,SV1083: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SV2374 @ SV225 ) @ SV1843 @ SV225 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1083 @ SV1843 @ SV225 )
= $true )
| ( ( class_Orderings_Olinorder @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7296]) ).
thf(7634,plain,
! [SV1844: $i,SV226: $i,SV1084: $i,SV2375: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV2375 @ SV1084 @ SV226 ) @ SV1844 @ SV226 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1084 @ SV1844 @ SV226 )
= $true )
| ( ( class_Orderings_Olinorder @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7297]) ).
thf(7635,plain,
! [SV1091: $i,SV234: $i,SV1848: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1848 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1091 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV1091 ) @ SV1848 ) @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7299]) ).
thf(7636,plain,
! [SV2378: $i,SV1092: $i,SV235: $i,SV1849: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1849 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV235 ) @ SV1092 @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SV2378 @ SV235 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1092 @ SV1849 @ SV235 ) @ ( c_Power_Opower__class_Opower @ SV2378 @ SV1849 @ SV235 ) @ SV235 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7300]) ).
thf(7637,plain,
! [SV1858: $i,SV244: $i,SV2383: $i,SV1101: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1101 @ SV2383 @ SV244 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1101 @ SV1858 @ SV244 ) @ SV2383 @ SV244 )
= $true )
| ( ( class_Orderings_Olinorder @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7303]) ).
thf(7638,plain,
! [SV1102: $i,SV245: $i,SV2384: $i,SV1859: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1859 @ SV2384 @ SV245 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1102 @ SV1859 @ SV245 ) @ SV2384 @ SV245 )
= $true )
| ( ( class_Orderings_Olinorder @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7304]) ).
thf(7639,plain,
! [SV1861: $i,SV247: $i,SV1104: $i,SV2385: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2385 @ SV1104 @ SV247 ) @ SV1861 @ SV247 )
= $false )
| ( ( c_lessequals @ SV1104 @ SV1861 @ SV247 )
= $true )
| ( ( class_Orderings_Olinorder @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7305]) ).
thf(7640,plain,
! [SV1862: $i,SV248: $i,SV2386: $i,SV1105: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1105 @ SV2386 @ SV248 ) @ SV1862 @ SV248 )
= $false )
| ( ( c_lessequals @ SV1105 @ SV1862 @ SV248 )
= $true )
| ( ( class_Orderings_Olinorder @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7306]) ).
thf(7641,plain,
! [SV1863: $i,SV249: $i,SV2387: $i,SV1106: $i] :
( ( ( c_lessequals @ SV1106 @ SV2387 @ SV249 )
= $false )
| ( ( c_lessequals @ SV1106 @ ( c_Orderings_Oord__class_Omax @ SV1863 @ SV2387 @ SV249 ) @ SV249 )
= $true )
| ( ( class_Orderings_Olinorder @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7307]) ).
thf(7642,plain,
! [SV2388: $i,SV250: $i,SV1864: $i,SV1107: $i] :
( ( ( c_lessequals @ SV1107 @ SV1864 @ SV250 )
= $false )
| ( ( c_lessequals @ SV1107 @ ( c_Orderings_Oord__class_Omax @ SV1864 @ SV2388 @ SV250 ) @ SV250 )
= $true )
| ( ( class_Orderings_Olinorder @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7308]) ).
thf(7643,plain,
! [SV1865: $i,SV251: $i,SV2389: $i,SV1108: $i] :
( ( ( c_lessequals @ SV1108 @ SV2389 @ SV251 )
= $false )
| ( ( c_lessequals @ SV1108 @ ( c_Orderings_Oord__class_Omax @ SV1865 @ SV2389 @ SV251 ) @ SV251 )
= $true )
| ( ( class_Orderings_Olinorder @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7309]) ).
thf(7644,plain,
! [SV2390: $i,SV252: $i,SV1866: $i,SV1109: $i] :
( ( ( c_lessequals @ SV1109 @ SV1866 @ SV252 )
= $false )
| ( ( c_lessequals @ SV1109 @ ( c_Orderings_Oord__class_Omax @ SV1866 @ SV2390 @ SV252 ) @ SV252 )
= $true )
| ( ( class_Orderings_Olinorder @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7310]) ).
thf(7645,plain,
! [SV1867: $i,SV253: $i,SV1110: $i,SV2391: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV2391 @ SV1110 @ SV253 ) @ SV1867 @ SV253 )
= $false )
| ( ( c_lessequals @ SV1110 @ SV1867 @ SV253 )
= $true )
| ( ( class_Orderings_Olinorder @ SV253 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7311]) ).
thf(7646,plain,
! [SV1868: $i,SV254: $i,SV2392: $i,SV1111: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1111 @ SV2392 @ SV254 ) @ SV1868 @ SV254 )
= $false )
| ( ( c_lessequals @ SV1111 @ SV1868 @ SV254 )
= $true )
| ( ( class_Orderings_Olinorder @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7312]) ).
thf(7647,plain,
! [SV1872: $i,SV258: $i,SV2393: $i,SV1115: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1115 @ SV2393 @ SV258 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1115 @ ( c_Orderings_Oord__class_Omax @ SV2393 @ SV1872 @ SV258 ) @ SV258 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1115 @ SV1872 @ SV258 )
= $true )
| ( ( class_Orderings_Olinorder @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7314]) ).
thf(7648,plain,
! [SV2632: $i,SV1122: $i,SV2396: $i,SV1877: $i,SV265: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV265 @ SV1877 @ tc_nat ) ) @ SV2396 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV1877 @ tc_nat ) ) @ SV2632 ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1122 @ SV265 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV265 @ SV1122 @ tc_nat ) @ SV1877 @ tc_nat ) ) @ SV2396 ) @ SV2632 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7316]) ).
thf(7649,plain,
! [SV2633: $i,SV1878: $i,SV1123: $i,SV2397: $i,SV266: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV266 @ SV2397 @ tc_nat ) @ SV1123 @ tc_nat ) ) @ SV1878 ) @ SV2633 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV2397 @ SV266 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV266 @ SV1123 @ tc_nat ) ) @ SV1878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2397 @ SV1123 @ tc_nat ) ) @ SV2633 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7317]) ).
thf(7650,plain,
! [SV2634: $i,SV1124: $i,SV267: $i,SV2398: $i,SV1879: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1879 @ SV2398 @ tc_nat ) ) @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1124 @ SV2398 @ tc_nat ) ) @ SV2634 ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1879 @ SV1124 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV267 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1124 @ SV1879 @ tc_nat ) @ SV2398 @ tc_nat ) ) @ SV2634 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7318]) ).
thf(7651,plain,
! [SV2635: $i,SV1125: $i,SV268: $i,SV2399: $i,SV1880: $i] :
( ( ( c_lessequals @ SV1880 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2399 @ SV268 @ tc_nat ) @ SV1125 @ tc_nat ) ) @ SV2635 ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV268 @ SV2399 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SV1125 @ tc_nat ) ) @ SV1880 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2399 @ SV1125 @ tc_nat ) ) @ SV2635 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7319]) ).
thf(7652,plain,
! [SV1127: $i,SV270: $i,SV1882: $i,SV2400: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2400 @ SV1882 @ SV270 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV2400 @ SV1127 @ SV270 ) @ SV1882 @ SV270 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1127 @ SV1882 @ SV270 )
= $true )
| ( ( class_Orderings_Olinorder @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7320]) ).
thf(7653,plain,
! [SV1129: $i,SV272: $i,SV1883: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1883 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
= $false )
| ( ( ~ ( c_lessequals @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1129 ) @ SV1883 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7321]) ).
thf(7654,plain,
! [SV1130: $i,SV273: $i,SV1884: $i] :
( ( ( c_lessequals @ SV1884 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1130 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV1130 ) @ SV1884 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7322]) ).
thf(7655,plain,
! [SV288: $i,SV1894: $i,SV1144: $i] :
( ( ( c_lessequals @ SV1144 @ SV1894 @ SV288 )
= $false )
| ( ( c_lessequals @ SV1894 @ SV1144 @ SV288 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1144 @ SV1894 @ SV288 )
= $true )
| ( ( class_Orderings_Opreorder @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7326]) ).
thf(7656,plain,
! [SV1151: $i,SV1895: $i,SV297: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1895 @ SV297 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1151 @ SV297 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV297 ) @ SV1151 ) @ SV1895 ) @ SV297 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7327]) ).
thf(7657,plain,
! [SV308: $i,SV1162: $i,SV2639: $i,SV2405: $i,SV1900: $i] :
( ( ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2405 ) @ SV2639 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1162 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2405 ) @ SV2639 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV308 ) )
= $true )
| ( ( SV308 = SV1162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7330]) ).
thf(7658,plain,
! [SV310: $i,SV1164: $i,SV1901: $i] :
( ( ( c_lessequals @ SV1901 @ SV1164 @ SV310 )
= $false )
| ( ( ~ ( c_lessequals @ SV1164 @ SV1901 @ SV310 ) )
= $true )
| ( ( SV1164 = SV1901 )
= $true )
| ( ( class_Orderings_Oorder @ SV310 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7331]) ).
thf(7659,plain,
! [SV312: $i,SV1166: $i,SV1903: $i] :
( ( ( c_lessequals @ SV1903 @ SV1166 @ SV312 )
= $false )
| ( ( ~ ( c_lessequals @ SV1166 @ SV1903 @ SV312 ) )
= $true )
| ( ( SV1166 = SV1903 )
= $true )
| ( ( class_Orderings_Oorder @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7333]) ).
thf(7660,plain,
! [SV313: $i,SV1904: $i,SV1167: $i] :
( ( ( c_lessequals @ SV1167 @ SV1904 @ SV313 )
= $false )
| ( ( ~ ( c_lessequals @ SV1904 @ SV1167 @ SV313 ) )
= $true )
| ( ( SV1167 = SV1904 )
= $true )
| ( ( class_Orderings_Oorder @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7334]) ).
thf(7661,plain,
! [SV2640: $i,SV2407: $i,SV1910: $i,SV1174: $i,SV320: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV1174 ) @ SV1910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV2407 ) @ SV2640 ) @ SV320 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1910 @ SV2640 @ SV320 )
| ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SV2407 @ SV320 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7339]) ).
thf(7662,plain,
! [SV2408: $i,SV1175: $i,SV1911: $i,SV321: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV321 @ SV1911 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1175 @ SV2408 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV321 ) @ SV1175 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1911 ) @ SV2408 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7340]) ).
thf(7663,plain,
! [SV326: $i,SV2409: $i,SV1914: $i,SV1180: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1180 @ ( c_Orderings_Oord__class_Omin @ SV1914 @ SV2409 @ SV326 ) @ SV326 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1180 @ SV1914 @ SV326 )
= $true )
| ( ( class_Orderings_Olinorder @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7343]) ).
thf(7664,plain,
! [SV327: $i,SV1915: $i,SV2410: $i,SV1181: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_Orderings_Oord__class_Omin @ SV2410 @ SV1915 @ SV327 ) @ SV327 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1181 @ SV1915 @ SV327 )
= $true )
| ( ( class_Orderings_Olinorder @ SV327 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7344]) ).
thf(7665,plain,
! [SV1916: $i,SV328: $i,SV2411: $i,SV1182: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1182 @ SV2411 @ SV328 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1182 @ SV1916 @ SV328 ) @ SV2411 @ SV328 )
= $true )
| ( ( class_Orderings_Olinorder @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7345]) ).
thf(7666,plain,
! [SV1183: $i,SV329: $i,SV2412: $i,SV1917: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1917 @ SV2412 @ SV329 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1183 @ SV1917 @ SV329 ) @ SV2412 @ SV329 )
= $true )
| ( ( class_Orderings_Olinorder @ SV329 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7346]) ).
thf(7667,plain,
! [SV1186: $i,SV1920: $i,SV332: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1920 @ SV332 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1186 @ SV332 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV332 ) @ SV1186 ) @ SV1920 ) @ SV332 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7348]) ).
thf(7668,plain,
! [SV1187: $i,SV1921: $i,SV333: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1921 @ SV333 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1187 @ SV333 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV333 ) @ SV1187 ) @ SV1921 ) @ SV333 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV333 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7349]) ).
thf(7669,plain,
! [SV1189: $i,SV335: $i,SV1923: $i] :
( ( ( c_lessequals @ SV1923 @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV1189 @ SV335 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1189 @ SV1923 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV335 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7351]) ).
thf(7670,plain,
! [SV1190: $i,SV1924: $i,SV336: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV1924 @ SV336 )
= $false )
| ( ( ~ ( c_lessequals @ SV1190 @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1190 @ SV1924 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV336 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7352]) ).
thf(7671,plain,
! [SV1191: $i,SV337: $i,SV1925: $i] :
( ( ( c_lessequals @ SV1925 @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV1191 @ SV337 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1191 @ SV1925 @ SV337 ) @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7353]) ).
thf(7672,plain,
! [SV1192: $i,SV1926: $i,SV338: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV1926 @ SV338 )
= $false )
| ( ( ~ ( c_lessequals @ SV1192 @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1192 @ SV1926 @ SV338 ) @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7354]) ).
thf(7673,plain,
! [SV1193: $i,SV339: $i,SV1927: $i] :
( ( ( c_lessequals @ SV1927 @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV1193 @ SV339 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1193 @ SV1927 @ SV339 ) @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7355]) ).
thf(7674,plain,
! [SV1194: $i,SV1928: $i,SV340: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV1928 @ SV340 )
= $false )
| ( ( ~ ( c_lessequals @ SV1194 @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1928 @ SV340 ) @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7356]) ).
thf(7675,plain,
! [SV1929: $i,SV341: $i,SV1195: $i] :
( ( ( c_lessequals @ SV1195 @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV1929 @ SV341 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1195 @ SV1929 @ SV341 ) @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV341 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7357]) ).
thf(7676,plain,
! [SV2825: $i,SV2782: $i,SV2733: $i,SV2641: $i,SV2416: $i,SV1936: $i,SV1206: $i,SV352: $i] :
( ( ! [SY7258: $i] :
( ( ( hAPP @ ( hAPP @ SV352 @ ( hAPP @ ( hAPP @ SV1206 @ SV1936 ) @ SV2416 ) ) @ SV2641 )
= ( hAPP @ ( hAPP @ SV1206 @ ( hAPP @ ( hAPP @ SV352 @ SV1936 ) @ SV2641 ) ) @ ( hAPP @ ( hAPP @ SV352 @ SV2416 ) @ SV2641 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2733 @ SV1206 @ SV352 @ SV2782 @ SV2825 @ SY7258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7358]) ).
thf(7677,plain,
! [SV2826: $i,SV2783: $i,SV2734: $i,SV2642: $i,SV2417: $i,SV1937: $i,SV1207: $i,SV353: $i] :
( ( ! [SY7259: $i] :
( ( ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ ( hAPP @ ( hAPP @ SV1937 @ SV2417 ) @ SV2642 ) )
= ( hAPP @ ( hAPP @ SV1937 @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2417 ) ) @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2642 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1937 @ SV353 @ SV2734 @ SV2783 @ SV2826 @ SY7259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7359]) ).
thf(7678,plain,
! [SV2827: $i,SV2784: $i,SV2735: $i,SV2643: $i,SV2418: $i,SV1938: $i,SV1208: $i,SV354: $i] :
( ( ( ( hAPP @ ( hAPP @ SV354 @ SV1208 ) @ SV1938 )
= ( hAPP @ ( hAPP @ SV354 @ SV1938 ) @ SV1208 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2418 @ SV354 @ SV2643 @ SV2735 @ SV2784 @ SV2827 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7360]) ).
thf(7679,plain,
! [SV2828: $i,SV2785: $i,SV2736: $i,SV2644: $i,SV2419: $i,SV1939: $i,SV1209: $i,SV355: $i] :
( ( ! [SY7260: $i] :
( ( ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ ( hAPP @ ( hAPP @ SV355 @ SV1939 ) @ SV2419 ) )
= ( hAPP @ ( hAPP @ SV355 @ ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ SV1939 ) ) @ SV2419 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2644 @ SV355 @ SV2736 @ SV2785 @ SV2828 @ SY7260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7361]) ).
thf(7680,plain,
! [SV2786: $i,SV2737: $i,SV2645: $i,SV2420: $i,SV1940: $i,SV1210: $i,SV356: $i] :
( ( ( ( hAPP @ ( hAPP @ SV356 @ SV1210 ) @ SV1940 )
= SV1940 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2420 @ SV356 @ SV2645 @ SV2737 @ SV1210 @ SV2786 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7362]) ).
thf(7681,plain,
! [SV2787: $i,SV2738: $i,SV2646: $i,SV2421: $i,SV1941: $i,SV1211: $i,SV357: $i] :
( ( ( ( hAPP @ ( hAPP @ SV357 @ SV1211 ) @ SV1941 )
= SV1211 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2421 @ SV357 @ SV2646 @ SV1211 @ SV2738 @ SV2787 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7363]) ).
thf(7682,plain,
! [SV2829: $i,SV2788: $i,SV2739: $i,SV2647: $i,SV2422: $i,SV1942: $i,SV1212: $i,SV358: $i] :
( ( ( ( hAPP @ ( hAPP @ SV358 @ SV1212 ) @ SV1942 )
= ( hAPP @ ( hAPP @ SV358 @ SV1942 ) @ SV1212 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV358 @ SV2422 @ SV2647 @ SV2739 @ SV2788 @ SV2829 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7364]) ).
thf(7683,plain,
! [SV2830: $i,SV2789: $i,SV2740: $i,SV2648: $i,SV2423: $i,SV1943: $i,SV1213: $i,SV359: $i] :
( ( ! [SY7261: $i] :
( ( ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ ( hAPP @ ( hAPP @ SV359 @ SV1943 ) @ SV2423 ) )
= ( hAPP @ ( hAPP @ SV359 @ ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ SV1943 ) ) @ SV2423 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV359 @ SV2648 @ SV2740 @ SV2789 @ SV2830 @ SY7261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7365]) ).
thf(7684,plain,
! [SV2790: $i,SV2741: $i,SV2649: $i,SV2424: $i,SV1944: $i,SV1214: $i,SV360: $i] :
( ( ( ( hAPP @ ( hAPP @ SV360 @ SV1214 ) @ SV1944 )
= SV1944 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV360 @ SV2424 @ SV2649 @ SV1214 @ SV2741 @ SV2790 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7366]) ).
thf(7685,plain,
! [SV2831: $i,SV2791: $i,SV2742: $i,SV2650: $i,SV2425: $i,SV1945: $i,SV1215: $i,SV361: $i] :
( ( ! [SY7262: $i] :
( ( ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ ( hAPP @ ( hAPP @ SV361 @ SV1945 ) @ SV2425 ) )
= ( hAPP @ ( hAPP @ SV361 @ ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ SV1945 ) ) @ SV2425 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV361 @ SV2650 @ SV2742 @ SV2791 @ SV2831 @ SY7262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7367]) ).
thf(7686,plain,
! [SV2832: $i,SV2792: $i,SV2743: $i,SV2651: $i,SV2426: $i,SV1946: $i,SV1216: $i,SV362: $i] :
( ( ( ( hAPP @ ( hAPP @ SV362 @ SV1216 ) @ SV1946 )
= ( hAPP @ ( hAPP @ SV362 @ SV1946 ) @ SV1216 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV362 @ SV2426 @ SV2651 @ SV2743 @ SV2792 @ SV2832 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7368]) ).
thf(7687,plain,
! [SV2833: $i,SV2793: $i,SV2744: $i,SV2652: $i,SV2427: $i,SV1947: $i,SV1217: $i,SV363: $i] :
( ( ! [SY7263: $i] :
( ( ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV1947 ) ) @ SV2427 )
= ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV2427 ) ) @ SV1947 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV363 @ SV2652 @ SV2744 @ SV2793 @ SV2833 @ SY7263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7369]) ).
thf(7688,plain,
! [SV2834: $i,SV2794: $i,SV2745: $i,SV2653: $i,SV2428: $i,SV1948: $i,SV1218: $i,SV364: $i] :
( ( ! [SY7264: $i] :
( ( ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ SV2428 ) )
= ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ SV2428 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV364 @ SV2653 @ SV2745 @ SV2794 @ SV2834 @ SY7264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7370]) ).
thf(7689,plain,
! [SV2835: $i,SV2795: $i,SV2746: $i,SV2654: $i,SV2429: $i,SV1949: $i,SV1219: $i,SV365: $i] :
( ( ! [SY7265: $i] :
( ( ( hAPP @ ( hAPP @ SV365 @ ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ SV1949 ) ) @ SV2429 )
= ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ ( hAPP @ ( hAPP @ SV365 @ SV1949 ) @ SV2429 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV365 @ SV2654 @ SV2746 @ SV2795 @ SV2835 @ SY7265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7371]) ).
thf(7690,plain,
! [SV2836: $i,SV2796: $i,SV2747: $i,SV2655: $i,SV2430: $i,SV1950: $i,SV1220: $i,SV366: $i] :
( ( ! [SY7266: $i,SY7267: $i] :
( ( ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV1950 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV2430 ) @ SV2655 ) )
= ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV2430 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV1950 ) @ SV2655 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV366 @ SV2747 @ SV2796 @ SV2836 @ SY7266 @ SY7267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7372]) ).
thf(7691,plain,
! [SV2837: $i,SV2797: $i,SV2748: $i,SV2656: $i,SV2431: $i,SV1951: $i,SV1221: $i,SV367: $i] :
( ( ! [SY7268: $i] :
( ( ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ SV2431 ) )
= ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ SV2431 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2656 @ SV367 @ SV2748 @ SV2797 @ SV2837 @ SY7268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7373]) ).
thf(7692,plain,
! [SV2838: $i,SV2798: $i,SV2749: $i,SV2657: $i,SV2432: $i,SV1952: $i,SV1222: $i,SV368: $i] :
( ( ! [SY7269: $i] :
( ( ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ ( hAPP @ ( hAPP @ SV368 @ SV1952 ) @ SV2432 ) )
= ( hAPP @ ( hAPP @ SV368 @ ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ SV1952 ) ) @ SV2432 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2657 @ SV368 @ SV2749 @ SV2798 @ SV2838 @ SY7269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7374]) ).
thf(7693,plain,
! [SV2839: $i,SV2799: $i,SV2750: $i,SV2658: $i,SV2433: $i,SV1953: $i,SV1223: $i,SV369: $i] :
( ( ! [SY7270: $i] :
( ( ( hAPP @ ( hAPP @ SV369 @ ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ SV1953 ) ) @ SV2433 )
= ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ ( hAPP @ ( hAPP @ SV369 @ SV1953 ) @ SV2433 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2658 @ SV369 @ SV2750 @ SV2799 @ SV2839 @ SY7270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7375]) ).
thf(7694,plain,
! [SV2840: $i,SV2800: $i,SV2751: $i,SV2659: $i,SV2434: $i,SV1954: $i,SV1224: $i,SV370: $i] :
( ( ! [SY7271: $i] :
( ( ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV1954 ) ) @ SV2434 )
= ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV2434 ) ) @ SV1954 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2659 @ SV370 @ SV2751 @ SV2800 @ SV2840 @ SY7271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7376]) ).
thf(7695,plain,
! [SV2841: $i,SV2801: $i,SV2752: $i,SV2660: $i,SV2435: $i,SV1955: $i,SV1225: $i,SV371: $i] :
( ( ! [SY7272: $i,SY7273: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ SV2660 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ SV2660 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2752 @ SV371 @ SV2801 @ SV2841 @ SY7272 @ SY7273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7377]) ).
thf(7696,plain,
! [SV2842: $i,SV2802: $i,SV2753: $i,SV2661: $i,SV2436: $i,SV1956: $i,SV1226: $i,SV372: $i] :
( ( ! [SY7274: $i,SY7275: $i] :
( ( ( hAPP @ ( hAPP @ SV372 @ ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ SV1956 ) ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) )
= ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ ( hAPP @ ( hAPP @ SV372 @ SV1956 ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2753 @ SV372 @ SV2802 @ SV2842 @ SY7274 @ SY7275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7378]) ).
thf(7697,plain,
! [SV2843: $i,SV2803: $i,SV2754: $i,SV2662: $i,SV2437: $i,SV1957: $i,SV1227: $i,SV373: $i] :
( ( ! [SY7276: $i,SY7277: $i] :
( ( ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV1957 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV2437 ) @ SV2662 ) )
= ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV2437 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV1957 ) @ SV2662 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2754 @ SV373 @ SV2803 @ SV2843 @ SY7276 @ SY7277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7379]) ).
thf(7698,plain,
! [SV2804: $i,SV2755: $i,SV2663: $i,SV2438: $i,SV1958: $i,SV1228: $i,SV374: $i] :
( ( ( ( hAPP @ ( hAPP @ SV374 @ SV1228 ) @ SV1958 )
= SV1228 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2438 @ SV374 @ SV2663 @ SV2755 @ SV1958 @ SV2804 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7380]) ).
thf(7699,plain,
! [SV2805: $i,SV2756: $i,SV2664: $i,SV2439: $i,SV1959: $i,SV1229: $i,SV375: $i] :
( ( ( ( hAPP @ ( hAPP @ SV375 @ SV1229 ) @ SV1959 )
= SV1959 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2439 @ SV375 @ SV2664 @ SV2756 @ SV1229 @ SV2805 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7381]) ).
thf(7700,plain,
! [SV2806: $i,SV2757: $i,SV2665: $i,SV2440: $i,SV1960: $i,SV1230: $i,SV376: $i] :
( ( ( ( hAPP @ ( hAPP @ SV376 @ SV1230 ) @ SV1960 )
= SV1960 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2440 @ SV376 @ SV2665 @ SV1960 @ SV2757 @ SV2806 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7382]) ).
thf(7701,plain,
! [SV2807: $i,SV2758: $i,SV2666: $i,SV2441: $i,SV1961: $i,SV1231: $i,SV377: $i] :
( ( ( ( hAPP @ ( hAPP @ SV377 @ SV1231 ) @ SV1961 )
= SV1231 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2441 @ SV377 @ SV2666 @ SV1231 @ SV2758 @ SV2807 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7383]) ).
thf(7702,plain,
! [SV2844: $i,SV2808: $i,SV2759: $i,SV2667: $i,SV2442: $i,SV1962: $i,SV1232: $i,SV378: $i] :
( ( ! [SY7278: $i] :
( ( ( hAPP @ ( hAPP @ SV378 @ ( hAPP @ ( hAPP @ SV1232 @ SV1962 ) @ SV2442 ) ) @ SV2667 )
= ( hAPP @ ( hAPP @ SV1232 @ ( hAPP @ ( hAPP @ SV378 @ SV1962 ) @ SV2667 ) ) @ ( hAPP @ ( hAPP @ SV378 @ SV2442 ) @ SV2667 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1232 @ SV378 @ SV2759 @ SV2808 @ SV2844 @ SY7278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7384]) ).
thf(7703,plain,
! [SV2845: $i,SV2809: $i,SV2760: $i,SV2668: $i,SV2443: $i,SV1963: $i,SV1233: $i,SV379: $i] :
( ( ( ( hAPP @ ( hAPP @ SV379 @ SV1233 ) @ SV1963 )
= ( hAPP @ ( hAPP @ SV379 @ SV1963 ) @ SV1233 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2443 @ SV379 @ SV2668 @ SV2760 @ SV2809 @ SV2845 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7385]) ).
thf(7704,plain,
! [SV2810: $i,SV2761: $i,SV2669: $i,SV2444: $i,SV1964: $i,SV1234: $i,SV380: $i] :
( ( ( ( hAPP @ ( hAPP @ SV380 @ SV1234 ) @ SV1964 )
= SV1234 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV380 @ SV2444 @ SV2669 @ SV1964 @ SV2761 @ SV2810 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7386]) ).
thf(7705,plain,
! [SV2811: $i,SV2762: $i,SV2670: $i,SV2445: $i,SV1965: $i,SV1235: $i,SV381: $i] :
( ( ( ( hAPP @ ( hAPP @ SV381 @ SV1235 ) @ SV1965 )
= SV1965 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV381 @ SV2445 @ SV2670 @ SV1235 @ SV2762 @ SV2811 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7387]) ).
thf(7706,plain,
! [SV2812: $i,SV2763: $i,SV2671: $i,SV2446: $i,SV1966: $i,SV1236: $i,SV382: $i] :
( ( ( ( hAPP @ ( hAPP @ SV382 @ SV1236 ) @ SV1236 )
= ( hAPP @ ( hAPP @ SV1966 @ ( hAPP @ ( hAPP @ SV382 @ SV2446 ) @ SV2446 ) ) @ SV1236 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV382 @ SV1966 @ SV2671 @ SV2763 @ SV2446 @ SV2812 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7388]) ).
thf(7707,plain,
! [SV2846: $i,SV2813: $i,SV2764: $i,SV2672: $i,SV2447: $i,SV1967: $i,SV1237: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ SV383 @ SV1237 ) @ ( hAPP @ ( hAPP @ SV1967 @ SV2447 ) @ SV1237 ) )
= ( hAPP @ ( hAPP @ SV1967 @ ( hAPP @ ( hAPP @ SV383 @ SV2447 ) @ SV2672 ) ) @ SV1237 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV383 @ SV1967 @ SV2764 @ SV2813 @ SV2672 @ SV2846 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7389]) ).
thf(7708,plain,
! [SV2847: $i,SV2814: $i,SV2765: $i,SV2673: $i,SV2448: $i,SV1968: $i,SV1238: $i,SV384: $i] :
( ( ( ( hAPP @ ( hAPP @ SV384 @ ( hAPP @ ( hAPP @ SV1238 @ SV1968 ) @ SV2448 ) ) @ SV2448 )
= ( hAPP @ ( hAPP @ SV1238 @ ( hAPP @ ( hAPP @ SV384 @ SV1968 ) @ SV2673 ) ) @ SV2448 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV384 @ SV1238 @ SV2765 @ SV2814 @ SV2673 @ SV2847 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7390]) ).
thf(7709,plain,
! [SV2848: $i,SV2815: $i,SV2766: $i,SV2674: $i,SV2449: $i,SV1969: $i,SV1239: $i,SV385: $i] :
( ( ! [SY7279: $i] :
( ( ( hAPP @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ SV1239 @ SV1969 ) @ SV2449 ) ) @ ( hAPP @ ( hAPP @ SV1239 @ SV2674 ) @ SV2449 ) )
= ( hAPP @ ( hAPP @ SV1239 @ ( hAPP @ ( hAPP @ SV385 @ SV1969 ) @ SV2674 ) ) @ SV2449 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV385 @ SV1239 @ SV2766 @ SV2815 @ SV2848 @ SY7279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7391]) ).
thf(7710,plain,
! [SV2455: $i,SV1984: $i,SV1256: $i,SV406: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1256 @ SV406 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV1984 @ SV406 ) @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV2455 @ SV406 ) @ SV406 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1256 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV406 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7393]) ).
thf(7711,plain,
! [SV2456: $i,SV407: $i,SV1257: $i,SV1985: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1985 @ SV1257 @ SV407 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2456 @ SV1985 @ SV407 ) @ ( c_HOL_Otimes__class_Otimes @ SV2456 @ SV1257 @ SV407 ) @ SV407 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1257 @ SV1985 @ SV407 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV407 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7394]) ).
thf(7712,plain,
! [SV2457: $i,SV1986: $i,SV1258: $i,SV408: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV1258 @ SV408 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1986 @ SV1258 @ SV408 ) @ ( c_HOL_Otimes__class_Otimes @ SV2457 @ SV1258 @ SV408 ) @ SV408 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1258 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7395]) ).
thf(7713,plain,
! [SV2458: $i,SV409: $i,SV1259: $i,SV1987: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1987 @ SV1259 @ SV409 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1987 @ SV2458 @ SV409 ) @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SV2458 @ SV409 ) @ SV409 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1259 @ SV1987 @ SV409 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV409 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7396]) ).
thf(7714,plain,
! [SV1994: $i,SV421: $i,SV2459: $i,SV1269: $i] :
( ( ( c_lessequals @ SV1269 @ SV2459 @ SV421 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV1269 ) @ SV1994 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV2459 ) @ SV1994 ) @ SV421 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7402]) ).
thf(7715,plain,
! [SV1995: $i,SV2460: $i,SV1270: $i,SV422: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1270 ) @ SV2460 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV422 ) @ SV1995 ) @ SV2460 ) @ SV422 )
= $false )
| ( ( c_lessequals @ SV1270 @ SV1995 @ SV422 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7403]) ).
thf(7716,plain,
! [SV1271: $i,SV423: $i,SV2461: $i,SV1996: $i] :
( ( ( c_lessequals @ SV1996 @ SV2461 @ SV423 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SV1996 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV423 ) @ SV1271 ) @ SV2461 ) @ SV423 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7404]) ).
thf(7717,plain,
! [SV1997: $i,SV1272: $i,SV2462: $i,SV424: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV2462 ) @ SV1272 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV2462 ) @ SV1997 ) @ SV424 )
= $false )
| ( ( c_lessequals @ SV1272 @ SV1997 @ SV424 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7405]) ).
thf(7718,plain,
! [SV1998: $i,SV425: $i,SV2463: $i,SV1273: $i] :
( ( ( c_lessequals @ SV1273 @ SV2463 @ SV425 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV1273 ) @ SV1998 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV2463 ) @ SV1998 ) @ SV425 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7406]) ).
thf(7719,plain,
! [SV1274: $i,SV426: $i,SV2464: $i,SV1999: $i] :
( ( ( c_lessequals @ SV1999 @ SV2464 @ SV426 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SV1999 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV426 ) @ SV1274 ) @ SV2464 ) @ SV426 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV426 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7407]) ).
thf(7720,plain,
! [SV2849: $i,SV2816: $i,SV2767: $i,SV2676: $i,SV2465: $i,SV2003: $i,SV1281: $i,SV433: $i] :
( ( ( ( hAPP @ ( hAPP @ SV433 @ SV1281 ) @ ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ SV2465 ) )
= ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ ( c_Suc @ SV2465 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2676 @ SV433 @ SV2003 @ SV2767 @ SV2816 @ SV2849 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7408]) ).
thf(7721,plain,
! [SV2850: $i,SV2817: $i,SV2768: $i,SV2677: $i,SV2466: $i,SV2004: $i,SV1282: $i,SV434: $i] :
( ( ( ( hAPP @ ( hAPP @ SV434 @ ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ SV2466 ) ) @ SV2004 )
= ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ ( c_Suc @ SV2466 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2677 @ SV434 @ SV1282 @ SV2768 @ SV2817 @ SV2850 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7409]) ).
thf(7722,plain,
! [SV2851: $i,SV2818: $i,SV2769: $i,SV2678: $i,SV2467: $i,SV2005: $i,SV1283: $i,SV435: $i] :
( ( ( ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ ( c_Suc @ SV2005 ) )
= ( hAPP @ ( hAPP @ SV2467 @ SV1283 ) @ ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ SV2005 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2678 @ SV2467 @ SV435 @ SV2769 @ SV2818 @ SV2851 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7410]) ).
thf(7723,plain,
! [SV2852: $i,SV2819: $i,SV2770: $i,SV2679: $i,SV2468: $i,SV2006: $i,SV1284: $i,SV436: $i] :
( ( ( ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ ( c_Suc @ SV2006 ) )
= ( hAPP @ ( hAPP @ SV2468 @ SV1284 ) @ ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ SV2006 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2679 @ SV2468 @ SV436 @ SV2770 @ SV2819 @ SV2852 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7411]) ).
thf(7724,plain,
! [SV2470: $i,SV1290: $i,SV2012: $i,SV442: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV442 ) @ SV2012 @ SV442 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1290 @ ( c_Suc @ SV2470 ) @ SV442 ) @ ( c_Power_Opower__class_Opower @ SV2012 @ ( c_Suc @ SV2470 ) @ SV442 ) @ SV442 ) )
= $true )
| ( ( c_lessequals @ SV1290 @ SV2012 @ SV442 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV442 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7412]) ).
thf(7725,plain,
! [SV2680: $i,SV2472: $i,SV447: $i,SV2015: $i,SV1295: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SV2472 @ SV2680 @ SV447 ) @ SV447 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
| ~ ( c_lessequals @ SV2015 @ SV2680 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SV2472 @ SV447 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7413]) ).
thf(7726,plain,
! [SV2681: $i,SV2473: $i,SV448: $i,SV2016: $i,SV1296: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SV2473 @ SV2681 @ SV448 ) @ SV448 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ SV2016 @ SV2681 @ SV448 )
| ~ ( c_lessequals @ SV1296 @ SV2473 @ SV448 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7414]) ).
thf(7727,plain,
! [SV451: $i,SV1299: $i,SV2019: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1299 @ SV451 ) @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 )
= $false )
| ( ( c_lessequals @ SV1299 @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV451 )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV451 ) @ SV1299 @ SV451 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV451 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7415]) ).
thf(7728,plain,
! [SV452: $i,SV2020: $i,SV1300: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1300 @ SV2020 @ SV452 ) @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
= $false )
| ( ( c_lessequals @ SV2020 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
= $true )
| ( ( c_lessequals @ SV1300 @ ( c_HOL_Ozero__class_Ozero @ SV452 ) @ SV452 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV452 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7416]) ).
thf(7729,plain,
! [SV453: $i,SV1301: $i,SV2021: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1301 @ SV453 ) @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV453 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV2021 @ SV453 )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV453 ) @ SV1301 @ SV453 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV453 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7417]) ).
thf(7730,plain,
! [SV454: $i,SV2022: $i,SV1302: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1302 @ SV2022 @ SV454 ) @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV1302 @ SV454 )
= $true )
| ( ( c_lessequals @ SV1302 @ ( c_HOL_Ozero__class_Ozero @ SV454 ) @ SV454 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV454 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7418]) ).
thf(7731,plain,
! [SV2023: $i,SV455: $i,SV1303: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1303 @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV2023 @ SV455 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1303 @ SV2023 @ SV455 ) @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7419]) ).
thf(7732,plain,
! [SV1304: $i,SV456: $i,SV2024: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2024 @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1304 @ SV456 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1304 @ SV2024 @ SV456 ) @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV456 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7420]) ).
thf(7733,plain,
! [SV1305: $i,SV2025: $i,SV457: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV2025 @ SV457 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1305 @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1305 @ SV2025 @ SV457 ) @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7421]) ).
thf(7734,plain,
! [SV464: $i,SV1311: $i,SV2027: $i] :
( ( ( c_lessequals @ SV2027 @ SV1311 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV2027 @ SV464 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SV2027 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1311 @ SV2027 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV464 @ SV1311 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7422]) ).
thf(7735,plain,
! [SV465: $i,SV2028: $i,SV1312: $i] :
( ( ( c_lessequals @ SV1312 @ SV2028 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1312 @ SV465 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV465 @ SV2028 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV465 @ SV1312 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV2028 @ SV1312 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7423]) ).
thf(7736,plain,
! [SV2029: $i,SV466: $i,SV2475: $i,SV1313: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1313 @ SV2475 @ SV466 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV2029 @ SV466 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1313 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ SV2029 ) @ SV2475 ) @ SV466 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7424]) ).
thf(7737,plain,
! [SV1321: $i,SV2476: $i,SV474: $i,SV2033: $i] :
( ( ( ~ ( c_lessequals @ SV2033 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2476 @ SV1321 @ SV474 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1321 @ SV2033 @ SV474 ) @ ( c_HOL_Otimes__class_Otimes @ SV2476 @ SV2033 @ SV474 ) @ SV474 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7426]) ).
thf(7738,plain,
! [SV2034: $i,SV2477: $i,SV475: $i,SV1322: $i] :
( ( ( ~ ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2477 @ SV2034 @ SV475 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2034 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2477 @ SV475 ) @ SV475 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV475 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7427]) ).
thf(7739,plain,
! [SV2478: $i,SV1323: $i,SV2035: $i,SV476: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV2035 @ SV476 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1323 @ SV2478 @ SV476 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1323 @ SV2035 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SV2478 @ SV2035 @ SV476 ) @ SV476 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV476 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7428]) ).
thf(7740,plain,
! [SV2479: $i,SV2036: $i,SV1324: $i,SV477: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV477 ) @ SV1324 @ SV477 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2036 @ SV2479 @ SV477 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2036 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2479 @ SV477 ) @ SV477 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7429]) ).
thf(7741,plain,
! [SV2480: $i,SV2037: $i,SV1325: $i,SV478: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV478 ) @ SV1325 @ SV478 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2037 @ SV2480 @ SV478 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2037 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2480 @ SV478 ) @ SV478 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono1 @ SV478 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7430]) ).
thf(7742,plain,
! [SV2041: $i,SV482: $i,SV2481: $i,SV1329: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1329 @ SV2481 @ SV482 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SV1329 ) @ SV2041 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV482 ) @ SV2481 ) @ SV2041 ) @ SV482 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7431]) ).
thf(7743,plain,
! [SV2042: $i,SV483: $i,SV2482: $i,SV1330: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1330 @ SV2482 @ SV483 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SV1330 ) @ SV2042 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV483 ) @ SV2482 ) @ SV2042 ) @ SV483 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV483 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7432]) ).
thf(7744,plain,
! [SV2043: $i,SV2483: $i,SV1331: $i,SV484: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV1331 ) @ SV2483 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV484 ) @ SV2043 ) @ SV2483 ) @ SV484 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1331 @ SV2043 @ SV484 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7433]) ).
thf(7745,plain,
! [SV1332: $i,SV485: $i,SV2484: $i,SV2044: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2044 @ SV2484 @ SV485 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SV2044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1332 ) @ SV2484 ) @ SV485 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV485 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7434]) ).
thf(7746,plain,
! [SV1333: $i,SV486: $i,SV2485: $i,SV2045: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2045 @ SV2485 @ SV486 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SV2045 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV486 ) @ SV1333 ) @ SV2485 ) @ SV486 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV486 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7435]) ).
thf(7747,plain,
! [SV2046: $i,SV1334: $i,SV2486: $i,SV487: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SV2486 ) @ SV1334 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV487 ) @ SV2486 ) @ SV2046 ) @ SV487 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1334 @ SV2046 @ SV487 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV487 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7436]) ).
thf(7748,plain,
! [SV2050: $i,SV492: $i,SV2487: $i,SV1339: $i] :
( ( ( ~ ( c_lessequals @ SV1339 @ SV2487 @ SV492 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2487 @ SV2050 @ SV492 ) )
= $true )
| ( ( c_lessequals @ SV1339 @ SV2050 @ SV492 )
= $true )
| ( ( class_Orderings_Oorder @ SV492 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7437]) ).
thf(7749,plain,
! [SV2051: $i,SV493: $i,SV2488: $i,SV1340: $i] :
( ( ( ~ ( c_lessequals @ SV1340 @ SV2488 @ SV493 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2488 @ SV2051 @ SV493 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1340 @ SV2051 @ SV493 )
= $true )
| ( ( class_Orderings_Oorder @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7438]) ).
thf(7750,plain,
! [SV2052: $i,SV494: $i,SV2489: $i,SV1341: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1341 @ SV2489 @ SV494 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2489 @ SV2052 @ SV494 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1341 @ SV2052 @ SV494 )
= $true )
| ( ( class_Orderings_Oorder @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7439]) ).
thf(7751,plain,
! [SV1342: $i,SV495: $i,SV2053: $i] :
( ( ( c_lessequals @ SV2053 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
= $false )
| ( ( ~ ( c_lessequals @ SV1342 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1342 ) @ SV2053 ) @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7440]) ).
thf(7752,plain,
! [SV1343: $i,SV496: $i,SV2054: $i,SV2490: $i] :
( ( ( ~ ( c_lessequals @ SV2490 @ SV2054 @ SV496 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1343 @ SV2490 @ SV496 ) )
= $true )
| ( ( c_lessequals @ SV1343 @ SV2054 @ SV496 )
= $true )
| ( ( class_Orderings_Opreorder @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7441]) ).
thf(7753,plain,
! [SV1355: $i,SV511: $i,SV2062: $i,SV2491: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV2062 @ SV511 ) @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV1355 @ SV511 ) @ SV511 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2491 @ ( c_HOL_Ozero__class_Ozero @ SV511 ) @ SV511 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1355 @ SV2062 @ SV511 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV511 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7449]) ).
thf(7754,plain,
! [SV1356: $i,SV512: $i,SV2063: $i,SV2492: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2492 @ SV2063 @ SV512 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1356 @ ( c_HOL_Ozero__class_Ozero @ SV512 ) @ SV512 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2063 @ SV512 ) @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2492 @ SV512 ) @ SV512 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV512 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7450]) ).
thf(7755,plain,
! [SV2064: $i,SV513: $i,SV1357: $i,SV2493: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV1357 @ SV513 ) @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV2064 @ SV513 ) @ SV513 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV513 ) @ SV2493 @ SV513 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1357 @ SV2064 @ SV513 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7451]) ).
thf(7756,plain,
! [SV1358: $i,SV514: $i,SV2494: $i,SV2065: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2065 @ SV2494 @ SV514 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SV1358 @ SV514 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2065 @ SV514 ) @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2494 @ SV514 ) @ SV514 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV514 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7452]) ).
thf(7757,plain,
! [SV2066: $i,SV2495: $i,SV515: $i,SV1359: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1359 @ ( c_HOL_Ozero__class_Ozero @ SV515 ) @ SV515 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2495 @ SV2066 @ SV515 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2066 @ SV515 ) @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2495 @ SV515 ) @ SV515 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV515 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7453]) ).
thf(7758,plain,
! [SV2496: $i,SV2067: $i,SV1360: $i,SV516: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV516 ) @ SV1360 @ SV516 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2067 @ SV2496 @ SV516 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2067 @ SV516 ) @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2496 @ SV516 ) @ SV516 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV516 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7454]) ).
thf(7759,plain,
! [SV1361: $i,SV517: $i,SV2497: $i,SV2068: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2068 @ SV2497 @ SV517 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1361 @ SV517 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2068 @ SV517 ) @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2497 @ SV517 ) @ SV517 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV517 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7455]) ).
thf(7760,plain,
! [SV1362: $i,SV518: $i,SV2069: $i,SV2498: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2498 @ SV2069 @ SV518 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1362 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2069 @ SV518 ) @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2498 @ SV518 ) @ SV518 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7456]) ).
thf(7761,plain,
! [SV1363: $i,SV2499: $i,SV519: $i,SV2070: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2070 @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV519 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2499 @ SV1363 @ SV519 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1363 @ SV2070 @ SV519 ) @ ( c_HOL_Otimes__class_Otimes @ SV2499 @ SV2070 @ SV519 ) @ SV519 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV519 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7457]) ).
thf(7762,plain,
! [SV2500: $i,SV1364: $i,SV2071: $i,SV520: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV2071 @ SV520 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1364 @ SV2500 @ SV520 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1364 @ SV2071 @ SV520 ) @ ( c_HOL_Otimes__class_Otimes @ SV2500 @ SV2071 @ SV520 ) @ SV520 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV520 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7458]) ).
thf(7763,plain,
! [SV2072: $i,SV521: $i,SV2501: $i,SV1365: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1365 @ SV2501 @ SV521 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV521 ) @ SV2072 @ SV521 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1365 @ SV2072 @ SV521 ) @ ( c_HOL_Otimes__class_Otimes @ SV2501 @ SV2072 @ SV521 ) @ SV521 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV521 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7459]) ).
thf(7764,plain,
! [SV2073: $i,SV522: $i,SV1366: $i,SV2502: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2502 @ SV1366 @ SV522 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2073 @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV522 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1366 @ SV2073 @ SV522 ) @ ( c_HOL_Otimes__class_Otimes @ SV2502 @ SV2073 @ SV522 ) @ SV522 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV522 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7460]) ).
thf(7765,plain,
! [SV2503: $i,SV2074: $i,SV1367: $i,SV523: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV1367 @ SV523 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2074 @ SV2503 @ SV523 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2074 @ SV523 ) @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2503 @ SV523 ) @ SV523 )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7461]) ).
thf(7766,plain,
! [SV2505: $i,SV1371: $i,SV2077: $i,SV527: $i] :
( ( ( c_lessequals @ SV527 @ SV2077 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1371 @ SV2505 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV527 @ SV1371 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2077 @ SV2505 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7462]) ).
thf(7767,plain,
! [SV2682: $i,SV2506: $i,SV529: $i,SV2078: $i,SV1372: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SV2506 @ SV2682 @ SV529 ) @ SV529 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2506 @ SV529 )
| ~ ( c_lessequals @ SV2078 @ SV2682 @ SV529 )
| ~ ( c_lessequals @ SV1372 @ SV2506 @ SV529 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7463]) ).
thf(7768,plain,
! [SV2683: $i,SV2507: $i,SV530: $i,SV2079: $i,SV1373: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SV2507 @ SV2683 @ SV530 ) @ SV530 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
| ~ ( c_lessequals @ SV2079 @ SV2683 @ SV530 )
| ~ ( c_lessequals @ SV1373 @ SV2507 @ SV530 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV530 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7464]) ).
thf(7769,plain,
! [SV2085: $i,SV1382: $i,SV541: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV2085 @ SV541 ) @ SV541 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV1382 @ SV541 )
= $true )
| ( ( c_lessequals @ SV1382 @ ( c_HOL_Ozero__class_Ozero @ SV541 ) @ SV541 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV541 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7465]) ).
thf(7770,plain,
! [SV1383: $i,SV2086: $i,SV542: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ ( c_HOL_Otimes__class_Otimes @ SV2086 @ SV1383 @ SV542 ) @ SV542 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV2086 @ SV542 )
= $true )
| ( ( c_lessequals @ SV1383 @ ( c_HOL_Ozero__class_Ozero @ SV542 ) @ SV542 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV542 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7466]) ).
thf(7771,plain,
! [SV2087: $i,SV1384: $i,SV543: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ ( c_HOL_Otimes__class_Otimes @ SV1384 @ SV2087 @ SV543 ) @ SV543 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV2087 @ SV543 )
= $true )
| ( ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV543 ) @ SV543 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV543 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7467]) ).
thf(7772,plain,
! [SV1385: $i,SV2088: $i,SV544: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ ( c_HOL_Otimes__class_Otimes @ SV2088 @ SV1385 @ SV544 ) @ SV544 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV1385 @ SV544 )
= $true )
| ( ( c_lessequals @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV544 ) @ SV544 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV544 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7468]) ).
thf(7773,plain,
! [SV2685: $i,SV2513: $i,SV2092: $i,SV1391: $i,SV550: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV1391 ) @ SV2092 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV2513 ) @ SV2685 ) @ SV550 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2092 @ SV2685 @ SV550 )
| ~ ( c_lessequals @ SV1391 @ SV2513 @ SV550 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV550 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7469]) ).
thf(7774,plain,
! [SV2686: $i,SV2514: $i,SV2093: $i,SV1392: $i,SV551: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV1392 ) @ SV2093 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV2514 ) @ SV2686 ) @ SV551 )
= $true )
| ( ( ~ ( c_lessequals @ SV2093 @ SV2686 @ SV551 )
| ~ ( c_HOL_Oord__class_Oless @ SV1392 @ SV2514 @ SV551 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV551 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7470]) ).
thf(7775,plain,
! [SV1425: $i,SV586: $i,SV2095: $i,SV2515: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2515 @ SV2095 @ SV586 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1425 @ SV2515 @ SV586 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1425 @ SV2095 @ SV586 )
= $true )
| ( ( class_Orderings_Opreorder @ SV586 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7471]) ).
thf(7776,plain,
! [SV1426: $i,SV587: $i,SV2096: $i,SV2516: $i] :
( ( ( ~ ( c_lessequals @ SV2516 @ SV2096 @ SV587 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1426 @ SV2516 @ SV587 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1426 @ SV2096 @ SV587 )
= $true )
| ( ( class_Orderings_Opreorder @ SV587 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7472]) ).
thf(7777,plain,
! [SV2687: $i,SV2517: $i,SV2097: $i,SV588: $i,SV1427: $i] :
( ( ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2517 ) @ SV588 )
= $true )
| ( ( ~ ( c_lessequals @ SV2687 @ SV2517 @ SV588 )
| ~ ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2687 ) @ SV588 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV588 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7473]) ).
thf(7778,plain,
! [SV1432: $i,SV2100: $i,SV593: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV593 @ SV2100 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV593 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1432 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV593 @ SV2100 ) @ tc_nat )
= $false )
| ( ( hBOOL @ ( hAPP @ SV593 @ SV1432 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7475]) ).
thf(7779,plain,
! [SV2688: $i,SV2518: $i,SV594: $i,SV2101: $i,SV1433: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SV2518 @ SV2688 @ SV594 ) @ SV594 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV2101 @ SV2688 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SV2518 @ SV594 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7476]) ).
thf(7780,plain,
! [SV1444: $i,SV606: $i,SV2520: $i,SV2107: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2107 @ SV2520 @ SV606 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2107 @ SV1444 @ SV606 ) @ ( c_HOL_Otimes__class_Otimes @ SV2520 @ SV1444 @ SV606 ) @ SV606 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1444 @ ( c_HOL_Ozero__class_Ozero @ SV606 ) @ SV606 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV606 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7477]) ).
thf(7781,plain,
! [SV1445: $i,SV2108: $i,SV2521: $i,SV607: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV607 ) @ SV2521 @ SV607 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2108 @ SV2521 @ SV607 ) @ ( c_HOL_Otimes__class_Otimes @ SV1445 @ SV2521 @ SV607 ) @ SV607 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1445 @ SV2108 @ SV607 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV607 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7478]) ).
thf(7782,plain,
! [SV1446: $i,SV608: $i,SV2522: $i,SV2109: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2109 @ SV2522 @ SV608 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2109 @ SV608 ) @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2522 @ SV608 ) @ SV608 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1446 @ ( c_HOL_Ozero__class_Ozero @ SV608 ) @ SV608 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV608 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7479]) ).
thf(7783,plain,
! [SV1447: $i,SV2110: $i,SV2523: $i,SV609: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV609 ) @ SV2523 @ SV609 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2523 @ SV2110 @ SV609 ) @ ( c_HOL_Otimes__class_Otimes @ SV2523 @ SV1447 @ SV609 ) @ SV609 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1447 @ SV2110 @ SV609 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV609 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7480]) ).
thf(7784,plain,
! [SV623: $i,SV2120: $i,SV1460: $i] :
( ( ( c_lessequals @ SV1460 @ SV2120 @ SV623 )
= $false )
| ( ( SV2120 = SV1460 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1460 @ SV2120 @ SV623 )
= $true )
| ( ( class_Orderings_Oorder @ SV623 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7481]) ).
thf(7785,plain,
! [SV624: $i,SV2121: $i,SV1461: $i] :
( ( ( c_lessequals @ SV1461 @ SV2121 @ SV624 )
= $false )
| ( ( SV2121 = SV1461 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1461 @ SV2121 @ SV624 )
= $true )
| ( ( class_Orderings_Oorder @ SV624 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7482]) ).
thf(7786,plain,
! [SV628: $i,SV2122: $i,SV1465: $i] :
( ( ( c_lessequals @ SV1465 @ SV2122 @ SV628 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1465 @ SV2122 @ SV628 )
= $true )
| ( ( SV1465 = SV2122 )
= $true )
| ( ( class_Orderings_Oorder @ SV628 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7483]) ).
thf(7787,plain,
! [SV629: $i,SV2123: $i,SV1466: $i] :
( ( ( c_lessequals @ SV1466 @ SV2123 @ SV629 )
= $false )
| ( ( SV1466 = SV2123 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1466 @ SV2123 @ SV629 )
= $true )
| ( ( class_Orderings_Oorder @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7484]) ).
thf(7788,plain,
! [SV630: $i,SV2124: $i,SV1467: $i] :
( ( ( c_lessequals @ SV1467 @ SV2124 @ SV630 )
= $false )
| ( ( SV1467 = SV2124 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1467 @ SV2124 @ SV630 )
= $true )
| ( ( class_Orderings_Oorder @ SV630 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7485]) ).
thf(7789,plain,
! [SV631: $i,SV2125: $i,SV1468: $i] :
( ( ( c_lessequals @ SV1468 @ SV2125 @ SV631 )
= $false )
| ( ( SV1468 = SV2125 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1468 @ SV2125 @ SV631 )
= $true )
| ( ( class_Orderings_Oorder @ SV631 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7486]) ).
thf(7790,plain,
! [SV632: $i,SV2126: $i,SV1469: $i] :
( ( ( c_lessequals @ SV1469 @ SV2126 @ SV632 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1469 @ SV2126 @ SV632 )
= $true )
| ( ( SV1469 = SV2126 )
= $true )
| ( ( class_Orderings_Olinorder @ SV632 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7487]) ).
thf(7791,plain,
! [SV633: $i,SV2127: $i,SV1470: $i] :
( ( ( c_lessequals @ SV1470 @ SV2127 @ SV633 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1470 @ SV2127 @ SV633 )
= $true )
| ( ( SV1470 = SV2127 )
= $true )
| ( ( class_Orderings_Olinorder @ SV633 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7488]) ).
thf(7792,plain,
! [SV1471: $i,SV2128: $i,SV634: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV2128 @ SV634 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV1471 @ SV634 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ ( c_HOL_Otimes__class_Otimes @ SV1471 @ SV2128 @ SV634 ) @ SV634 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV634 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7489]) ).
thf(7793,plain,
! [SV1472: $i,SV635: $i,SV2129: $i] :
( ( ( c_lessequals @ SV2129 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 )
= $false )
| ( ( ~ ( c_lessequals @ SV1472 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ ( c_HOL_Otimes__class_Otimes @ SV1472 @ SV2129 @ SV635 ) @ SV635 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV635 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7490]) ).
thf(7794,plain,
! [SV1473: $i,SV2130: $i,SV636: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV2130 @ SV636 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV1473 @ SV636 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ ( c_HOL_Otimes__class_Otimes @ SV1473 @ SV2130 @ SV636 ) @ SV636 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV636 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7491]) ).
thf(7795,plain,
! [SV1475: $i,SV638: $i,SV2131: $i] :
( ( ( c_lessequals @ SV2131 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 )
= $false )
| ( ( ~ ( c_lessequals @ SV1475 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ ( c_HOL_Otimes__class_Otimes @ SV1475 @ SV2131 @ SV638 ) @ SV638 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV638 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7492]) ).
thf(7796,plain,
! [SV1476: $i,SV639: $i,SV2132: $i] :
( ( ( c_lessequals @ SV2132 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 )
= $false )
| ( ( ~ ( c_lessequals @ SV1476 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ ( c_HOL_Otimes__class_Otimes @ SV1476 @ SV2132 @ SV639 ) @ SV639 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV639 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7493]) ).
thf(7797,plain,
! [SV1477: $i,SV2133: $i,SV640: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV2133 @ SV640 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV1477 @ SV640 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ ( c_HOL_Otimes__class_Otimes @ SV1477 @ SV2133 @ SV640 ) @ SV640 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV640 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7494]) ).
thf(7798,plain,
! [SV660: $i,SV1496: $i,SV2150: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2150 @ SV1496 @ SV660 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1496 @ SV2150 @ SV660 )
= $false )
| ( ( class_Orderings_Oorder @ SV660 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7495]) ).
thf(7799,plain,
! [SV661: $i,SV1497: $i,SV2151: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2151 @ SV1497 @ SV661 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1497 @ SV2151 @ SV661 )
= $false )
| ( ( class_Orderings_Olinorder @ SV661 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7496]) ).
thf(7800,plain,
! [SV664: $i,SV1500: $i,SV2153: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2153 @ SV1500 @ SV664 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1500 @ SV2153 @ SV664 )
= $false )
| ( ( class_Orderings_Opreorder @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7497]) ).
thf(7801,plain,
! [SV665: $i,SV1501: $i,SV2154: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2154 @ SV1501 @ SV665 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1501 @ SV2154 @ SV665 )
= $false )
| ( ( class_Orderings_Opreorder @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7498]) ).
thf(7802,plain,
! [SV2820: $i,SV2772: $i,SV2689: $i,SV2544: $i,SV2160: $i,SV1515: $i,SV698: $i] :
( ( ( ( hAPP @ ( hAPP @ SV698 @ SV1515 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV2160 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2544 @ SV2689 @ SV698 @ SV2772 @ SV2160 @ SV2820 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7499]) ).
thf(7803,plain,
! [SV1519: $i,SV2162: $i,SV2545: $i,SV702: $i] :
( ( ( c_Type_Otyping @ SV702 @ SV2545 @ SV2162 )
= $false )
| ( ( c_Lambda_Obeta @ SV2545 @ SV1519 )
= $false )
| ( ( c_Type_Otyping @ SV702 @ SV1519 @ SV2162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7500]) ).
thf(7804,plain,
! [SV2556: $i,SV1538: $i,SV2697: $i,SV2179: $i,SV721: $i] :
( ( ( c_Type_Otypings @ SV721 @ SV2179 @ SV2697 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV721 @ SV1538 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV2697 @ SV2556 @ tc_Type_Otype @ tc_Type_Otype ) ) )
= $true )
| ( ( c_Type_Otyping @ SV721 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1538 @ SV2179 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2556 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7504]) ).
thf(7805,plain,
! [SV1540: $i,SV723: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV723 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV723 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV723 ) @ SV1540 @ SV723 )
= ( c_HOL_Ozero__class_Ozero @ SV723 ) )
| ( SV1540
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV723 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7505]) ).
thf(7806,plain,
! [SV2559: $i,SV1543: $i,SV2699: $i,SV2182: $i,SV727: $i] :
( ( ( c_Type_Otyping @ SV727 @ SV2182 @ SV2699 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV727 @ SV1543 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2699 ) @ SV2559 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV727 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1543 ) @ SV2182 ) @ SV2559 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7507]) ).
thf(7807,plain,
! [SV2775: $i,SV2700: $i,SV2560: $i,SV2183: $i,SV1544: $i,SV728: $i] :
( ( ( c_Type_Otyping @ SV728 @ SV1544 @ SV2183 )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV728 @ SV2560 @ SV2183 @ tc_Type_Otype ) @ SV2700 @ SV2775 )
| ( c_Type_Otyping @ SV728 @ ( c_Lambda_Osubst @ SV2700 @ SV1544 @ SV2560 ) @ SV2775 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7508]) ).
thf(7808,plain,
! [SV2702: $i,SV2564: $i,SV737: $i,SV2188: $i,SV1553: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1553 @ SV2188 @ SV737 )
!= ( c_HOL_Ominus__class_Ominus @ SV2564 @ SV2702 @ SV737 ) )
= $true )
| ( ( ( c_lessequals @ SV2188 @ SV1553 @ SV737 )
| ~ ( c_lessequals @ SV2702 @ SV2564 @ SV737 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV737 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7510]) ).
thf(7809,plain,
! [SV2704: $i,SV2193: $i,SV1558: $i,SV742: $i,SV2566: $i] :
( ( ( ~ ( c_lessequals @ SV2566 @ SV742 @ tc_nat ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV742 @ SV2566 @ tc_nat ) @ SV1558 @ tc_nat ) ) @ SV2193 )
= SV2704 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV1558 @ tc_nat ) ) @ SV2193 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2566 @ SV1558 @ tc_nat ) ) @ SV2704 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7512]) ).
thf(7810,plain,
! [SV2776: $i,SV2705: $i,SV2569: $i,SV2199: $i,SV1566: $i,SV750: $i] :
( ( ( class_Ring__and__Field_Oring @ SV750 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV1566 @ SV2199 @ SV750 ) ) @ SV2569 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV2705 @ SV2199 @ SV750 ) ) @ SV2776 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ SV2705 @ SV750 ) @ SV2199 @ SV750 ) ) @ SV2569 )
= SV2776 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7513]) ).
thf(7811,plain,
! [SV2571: $i,SV2201: $i,SV1570: $i,SV754: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SV1570 ) @ SV2201 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV754 ) @ SV2571 ) @ SV2201 ) )
= $false )
| ( ( SV1570 = SV2571 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV754 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7514]) ).
thf(7812,plain,
! [SV2706: $i,SV2574: $i,SV760: $i,SV2205: $i,SV1576: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV2205 @ SV760 )
!= ( c_HOL_Ominus__class_Ominus @ SV2574 @ SV2706 @ SV760 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV2574 @ SV2706 @ SV760 )
| ~ ( c_HOL_Oord__class_Oless @ SV1576 @ SV2205 @ SV760 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV760 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7516]) ).
thf(7813,plain,
! [SV2206: $i,SV761: $i,SV1577: $i] :
( ( ( SV1577
= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
= $true )
| ( ( SV2206
= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1577 @ SV2206 @ SV761 )
= ( c_HOL_Ozero__class_Ozero @ SV761 ) )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV761 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7517]) ).
thf(7814,plain,
! [SV2575: $i,SV763: $i,SV2208: $i,SV1579: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1579 @ SV2208 @ SV763 )
= ( c_Power_Opower__class_Opower @ SV2575 @ SV2208 @ SV763 ) )
= $false )
| ( ( ( SV1579 = SV2575 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2208 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV2575 @ SV763 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV763 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7518]) ).
thf(7815,plain,
! [SV2576: $i,SV2209: $i,SV1580: $i,SV764: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SV2209 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV764 ) @ SV1580 ) @ SV2576 ) )
= $false )
| ( ( SV2209 = SV2576 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV764 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7519]) ).
thf(7816,plain,
! [SV2214: $i,SV773: $i,SV1588: $i] :
( ( ( SV1588
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV773 ) @ SV1588 ) @ SV2214 ) )
= $true )
| ( ( SV2214
= ( c_HOL_Ozero__class_Ozero @ SV773 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV773 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV773 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7520]) ).
thf(7817,plain,
! [SV2707: $i,SV2578: $i,SV2215: $i,SV1589: $i,SV774: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV774 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2578 @ SV774 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2707 @ SV774 ) ) )
| ( SV2578 = SV2707 )
| ( SV2215
= ( c_HOL_Ozero__class_Ozero @ SV774 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV774 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7521]) ).
thf(7818,plain,
! [SV2709: $i,SV2580: $i,SV778: $i,SV2217: $i,SV1592: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1592 @ SV2217 @ SV778 )
!= ( c_HOL_Ominus__class_Ominus @ SV2580 @ SV2709 @ SV778 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1592 @ SV2217 @ SV778 )
| ~ ( c_HOL_Oord__class_Oless @ SV2580 @ SV2709 @ SV778 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV778 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7523]) ).
thf(7819,plain,
! [SV2711: $i,SV2584: $i,SV2224: $i,SV1600: $i,SV787: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV787 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2224 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2711 @ SV787 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2711 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2224 @ SV787 ) ) )
| ( SV2224 = SV2711 )
| ( SV1600 = SV2584 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV787 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7527]) ).
thf(7820,plain,
! [SV2712: $i,SV2585: $i,SV789: $i,SV2225: $i,SV1602: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1602 @ SV2225 @ SV789 )
!= ( c_HOL_Ominus__class_Ominus @ SV2585 @ SV2712 @ SV789 ) )
= $true )
| ( ( ( c_lessequals @ SV2712 @ SV2585 @ SV789 )
| ~ ( c_lessequals @ SV2225 @ SV1602 @ SV789 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV789 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7528]) ).
thf(7821,plain,
! [SV1603: $i,SV790: $i,SV2226: $i] :
( ( ( SV2226
= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
= $true )
| ( ( SV1603
= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1603 @ SV2226 @ SV790 )
= ( c_HOL_Ozero__class_Ozero @ SV790 ) )
= $false )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV790 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7529]) ).
thf(7822,plain,
! [SV1605: $i,SV792: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV792 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV792 )
| ( ( c_Power_Opower__class_Opower @ SV1605 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV792 )
!= ( c_HOL_Ozero__class_Ozero @ SV792 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV792 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV792 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7530]) ).
thf(7823,plain,
! [SV1606: $i,SV2227: $i,SV793: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV2227 @ SV793 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV1606 @ SV793 )
| ( SV1606
= ( c_HOL_Ozero__class_Ozero @ SV793 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV793 ) @ SV1606 ) @ SV2227 )
= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV793 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7531]) ).
thf(7824,plain,
! [SV2229: $i,SV795: $i,SV1608: $i] :
( ( ( ~ ( c_lessequals @ SV1608 @ SV795 @ tc_nat ) )
= $true )
| ( ( SV795 = SV2229 )
= $true )
| ( ( c_lessequals @ SV1608 @ SV2229 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV795 @ SV1608 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV2229 @ SV1608 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7533]) ).
thf(7825,plain,
! [SV2713: $i,SV2587: $i,SV2230: $i,SV1609: $i,SV796: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SV2587 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SV2713 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ SV2587 )
= SV2713 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV796 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7534]) ).
thf(7826,plain,
! [SV2588: $i,SV2232: $i,SV798: $i,SV1611: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1611 @ SV1611 @ SV798 )
= ( c_HOL_Ominus__class_Ominus @ SV2232 @ SV2588 @ SV798 ) )
= $false )
| ( ( SV2232 = SV2588 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV798 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7536]) ).
thf(7827,plain,
! [SV2714: $i,SV1612: $i,SV2233: $i,SV2589: $i,SV799: $i] :
( ( ( ~ ( c_lessequals @ SV799 @ SV2589 @ tc_nat ) )
= $true )
| ( ( SV2233
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2589 @ SV799 @ tc_nat ) @ SV1612 @ tc_nat ) ) @ SV2714 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV799 @ SV1612 @ tc_nat ) ) @ SV2233 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2589 @ SV1612 @ tc_nat ) ) @ SV2714 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7537]) ).
thf(7828,plain,
! [SV2590: $i,SV800: $i,SV1613: $i,SV2234: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2234 @ SV1613 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV800 @ SV2590 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV800 ) @ SV1613 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2234 ) @ SV2590 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7538]) ).
thf(7829,plain,
! [SV2715: $i,SV2592: $i,SV2239: $i,SV1619: $i,SV806: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV806 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2239 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2715 @ SV806 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2715 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2239 @ SV806 ) ) )
| ( SV2239 = SV2715 )
| ( SV1619 = SV2592 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV806 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7540]) ).
thf(7830,plain,
! [SV2777: $i,SV2716: $i,SV2594: $i,SV2241: $i,SV1621: $i,SV808: $i] :
( ( ( class_Ring__and__Field_Oring @ SV808 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV1621 @ SV2241 @ SV808 ) ) @ SV2594 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV2716 @ SV2241 @ SV808 ) ) @ SV2777 ) )
| ( SV2594
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2716 @ SV1621 @ SV808 ) @ SV2241 @ SV808 ) ) @ SV2777 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7541]) ).
thf(7831,plain,
! [SV810: $i,SV2243: $i,SV1623: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1623 @ SV2243 @ SV810 )
!= ( c_HOL_Ozero__class_Ozero @ SV810 ) )
= $true )
| ( ( SV1623 = SV2243 )
= $true )
| ( ( class_Int_Onumber__ring @ SV810 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV810 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7542]) ).
thf(7832,plain,
! [SV1629: $i,SV816: $i,SV2246: $i] :
( ( ( SV2246
= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
= $true )
| ( ( SV1629
= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1629 @ SV2246 @ SV816 )
= ( c_HOL_Ozero__class_Ozero @ SV816 ) )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV816 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7544]) ).
thf(7833,plain,
! [SV2598: $i,SV2249: $i,SV1633: $i,SV820: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SV2249 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV820 ) @ SV1633 ) @ SV2598 ) )
= $false )
| ( ( SV2249 = SV2598 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV820 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7545]) ).
thf(7834,plain,
! [SV2599: $i,SV823: $i,SV2252: $i,SV1636: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1636 @ ( c_Suc @ SV2252 ) @ SV823 )
= ( c_Power_Opower__class_Opower @ SV2599 @ ( c_Suc @ SV2252 ) @ SV823 ) )
= $false )
| ( ( ( SV1636 = SV2599 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV2599 @ SV823 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV1636 @ SV823 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV823 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7548]) ).
thf(7835,plain,
! [SV2601: $i,SV2259: $i,SV1644: $i,SV832: $i] :
( ( ( class_Int_Onumber__ring @ SV832 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2259 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2601 ) )
| ( SV2259 = SV2601 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV832 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7549]) ).
thf(7836,plain,
! [SV2602: $i,SV2263: $i,SV837: $i,SV2717: $i,SV1649: $i] :
( ( ( SV1649 = SV2717 )
= $true )
| ( ( SV837
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Oreplicate @ SV837 @ SV1649 @ SV2263 )
= ( c_List_Oreplicate @ SV2602 @ SV2717 @ SV2263 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7551]) ).
thf(7837,plain,
! [SV2821: $i,SV2778: $i,SV2718: $i,SV2603: $i,SV2264: $i,SV1650: $i,SV838: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
= $true )
| ( ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
| ~ ( c_Type_Otyping @ SV2778 @ SV2603 @ SV1650 )
| ~ ( c_InductTermi_OIT @ SV2603 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2778 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SV2821 )
| ~ ( c_InductTermi_OIT @ SV2264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7552]) ).
thf(7838,plain,
! [SV2265: $i,SV1651: $i,SV839: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV839 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV839 )
| ( ( c_Power_Opower__class_Opower @ SV1651 @ SV2265 @ SV839 )
!= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
| ( SV1651
= ( c_HOL_Ozero__class_Ozero @ SV839 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV839 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV839 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7553]) ).
thf(7839,plain,
! [SV1666: $i,SV2276: $i,SV855: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV2276 @ SV855 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV1666 @ SV855 )
| ( SV2276
= ( c_HOL_Ozero__class_Ozero @ SV855 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV855 ) @ SV1666 ) @ SV2276 )
= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV855 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7557]) ).
thf(7840,plain,
! [SV2607: $i,SV858: $i,SV2279: $i,SV1669: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1669 @ SV2279 @ SV858 )
= ( c_HOL_Ominus__class_Ominus @ SV2607 @ SV2607 @ SV858 ) )
= $false )
| ( ( SV1669 = SV2279 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV858 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7559]) ).
thf(7841,plain,
! [SV2822: $i,SV2779: $i,SV2721: $i,SV2609: $i,SV2282: $i,SV1673: $i,SV863: $i] :
( ( ( v_T____
!= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
= $true )
| ( ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
| ~ ( c_Type_Otyping @ SV2779 @ SV2609 @ SV863 )
| ~ ( c_InductTermi_OIT @ SV2609 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2779 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SV2822 )
| ~ ( c_InductTermi_OIT @ SV2282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7561]) ).
thf(7842,plain,
! [SV2610: $i,SV865: $i,SV1675: $i,SV2284: $i,SV1: $i] :
( ( ( c_lessequals @ SV1 @ SV2284 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1675 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2284 @ SV1 @ tc_nat ) @ SV865 @ tc_nat ) ) @ SV2610 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1 @ SV865 @ tc_nat ) ) @ SV1675 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2284 @ SV865 @ tc_nat ) ) @ SV2610 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7563]) ).
thf(7843,plain,
! [SV2611: $i,SV2: $i,SV2285: $i,SV866: $i,SV1676: $i] :
( ( ( c_lessequals @ SV1676 @ SV866 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV2285 @ tc_nat ) ) @ SV2 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV866 @ SV2285 @ tc_nat ) ) @ SV2611 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV866 @ SV1676 @ tc_nat ) @ SV2285 @ tc_nat ) ) @ SV2611 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7564]) ).
thf(7844,plain,
! [SV2612: $i,SV1677: $i,SV867: $i,SV3: $i,SV2286: $i] :
( ( ( c_lessequals @ SV2286 @ SV3 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV3 @ SV2286 @ tc_nat ) @ SV867 @ tc_nat ) ) @ SV1677 ) @ SV2612 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV3 @ SV867 @ tc_nat ) ) @ SV1677 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2286 @ SV867 @ tc_nat ) ) @ SV2612 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7565]) ).
thf(7845,plain,
! [SV2613: $i,SV2287: $i,SV1678: $i,SV4: $i,SV868: $i] :
( ( ( c_lessequals @ SV868 @ SV4 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV4 @ SV1678 @ tc_nat ) ) @ SV2287 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV868 @ SV1678 @ tc_nat ) ) @ SV2613 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV868 @ tc_nat ) @ SV1678 @ tc_nat ) ) @ SV2287 ) @ SV2613 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7566]) ).
thf(7846,plain,
! [SV873: $i,SV2615: $i,SV2289: $i,SV1680: $i,SV9: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV2289 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1680 @ SV2615 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV873 @ SV2289 @ SV9 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV2289 @ SV2615 @ SV9 ) @ SV9 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7567]) ).
thf(7847,plain,
! [SV1683: $i,SV13: $i,SV2290: $i,SV877: $i] :
( ( ( c_lessequals @ SV877 @ SV2290 @ SV13 )
= $false )
| ( ( ~ ( c_lessequals @ SV877 @ SV1683 @ SV13 ) )
= $true )
| ( ( c_lessequals @ SV877 @ ( c_Orderings_Oord__class_Omin @ SV1683 @ SV2290 @ SV13 ) @ SV13 )
= $true )
| ( ( class_Orderings_Olinorder @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7568]) ).
thf(7848,plain,
! [SV1684: $i,SV14: $i,SV2291: $i,SV878: $i] :
( ( ( c_lessequals @ SV878 @ SV2291 @ SV14 )
= $false )
| ( ( ~ ( c_lessequals @ SV878 @ SV1684 @ SV14 ) )
= $true )
| ( ( c_lessequals @ SV878 @ ( c_Orderings_Oord__class_Omin @ SV1684 @ SV2291 @ SV14 ) @ SV14 )
= $true )
| ( ( class_Orderings_Olinorder @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7569]) ).
thf(7849,plain,
! [SV1685: $i,SV15: $i,SV2292: $i,SV879: $i] :
( ( ( c_lessequals @ SV879 @ SV2292 @ SV15 )
= $false )
| ( ( ~ ( c_lessequals @ SV879 @ SV1685 @ SV15 ) )
= $true )
| ( ( c_lessequals @ SV879 @ ( c_Orderings_Oord__class_Omin @ SV1685 @ SV2292 @ SV15 ) @ SV15 )
= $true )
| ( ( class_Orderings_Olinorder @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7570]) ).
thf(7850,plain,
! [SV884: $i,SV20: $i,SV2295: $i,SV1689: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1689 @ SV2295 @ SV20 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV884 @ SV2295 @ SV20 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV884 @ SV1689 @ SV20 ) @ SV2295 @ SV20 )
= $true )
| ( ( class_Orderings_Olinorder @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7571]) ).
thf(7851,plain,
! [SV2296: $i,SV1691: $i,SV22: $i,SV886: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV886 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1691 ) @ SV2296 ) @ SV22 )
= $true )
| ( ( ~ ( c_lessequals @ SV886 @ SV2296 @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV1691 @ SV22 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV22 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7572]) ).
thf(7852,plain,
! [SV1696: $i,SV27: $i,SV2298: $i,SV891: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV891 @ SV2298 @ SV27 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV1696 @ SV27 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV891 @ ( c_Orderings_Oord__class_Omin @ SV1696 @ SV2298 @ SV27 ) @ SV27 )
= $true )
| ( ( class_Orderings_Olinorder @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7573]) ).
thf(7853,plain,
! [SV2305: $i,SV915: $i,SV52: $i,SV2619: $i,SV1716: $i] :
( ( ( ~ ( c_lessequals @ SV1716 @ SV2619 @ SV52 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV915 @ SV2305 @ SV52 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV915 ) @ SV1716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV2305 ) @ SV2619 ) @ SV52 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7577]) ).
thf(7854,plain,
! [SV1719: $i,SV923: $i,SV62: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV923 @ SV62 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1719 @ SV62 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV62 ) @ SV923 ) @ SV1719 ) @ SV62 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7578]) ).
thf(7855,plain,
! [SV924: $i,SV63: $i,SV1720: $i,SV2306: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2306 @ SV1720 @ SV63 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV924 @ SV2306 @ SV63 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV924 @ SV1720 @ SV63 )
= $true )
| ( ( class_Orderings_Opreorder @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7579]) ).
thf(7856,plain,
! [SV1721: $i,SV64: $i,SV2307: $i,SV925: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV925 @ SV2307 @ SV64 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2307 @ SV1721 @ SV64 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV925 @ SV1721 @ SV64 )
= $true )
| ( ( class_Orderings_Oorder @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7580]) ).
thf(7857,plain,
! [SV939: $i,SV78: $i,SV2311: $i,SV1732: $i] :
( ( ( c_lessequals @ SV1732 @ SV2311 @ SV78 )
= $false )
| ( ( ~ ( c_lessequals @ SV939 @ SV2311 @ SV78 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV939 @ SV1732 @ SV78 ) @ SV2311 @ SV78 )
= $true )
| ( ( class_Orderings_Olinorder @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7582]) ).
thf(7858,plain,
! [SV940: $i,SV79: $i,SV2312: $i,SV1733: $i] :
( ( ( c_lessequals @ SV1733 @ SV2312 @ SV79 )
= $false )
| ( ( ~ ( c_lessequals @ SV940 @ SV2312 @ SV79 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV940 @ SV1733 @ SV79 ) @ SV2312 @ SV79 )
= $true )
| ( ( class_Orderings_Olinorder @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7583]) ).
thf(7859,plain,
! [SV941: $i,SV80: $i,SV2313: $i,SV1734: $i] :
( ( ( c_lessequals @ SV1734 @ SV2313 @ SV80 )
= $false )
| ( ( ~ ( c_lessequals @ SV941 @ SV2313 @ SV80 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV941 @ SV1734 @ SV80 ) @ SV2313 @ SV80 )
= $true )
| ( ( class_Orderings_Olinorder @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7584]) ).
thf(7860,plain,
! [SV2853: $i,SV2823: $i,SV2780: $i,SV2722: $i,SV2620: $i,SV2315: $i,SV1738: $i,SV951: $i,SV90: $i] :
( ( ( ( hAPP @ ( hAPP @ SV90 @ ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ SV1738 ) ) @ SV2315 )
= ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ ( c_HOL_Otimes__class_Otimes @ SV1738 @ SV2315 @ tc_nat ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2620 @ SV2722 @ SV90 @ SV2780 @ SV2823 @ SV2853 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7585]) ).
thf(7861,plain,
! [SV2318: $i,SV1741: $i,SV93: $i,SV954: $i] :
( ( ( c_lessequals @ SV954 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV1741 ) @ SV2318 ) @ SV93 )
= $true )
| ( ( ~ ( c_lessequals @ SV954 @ SV2318 @ SV93 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV1741 @ SV93 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV93 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7586]) ).
thf(7862,plain,
! [SV2319: $i,SV1742: $i,SV94: $i,SV955: $i] :
( ( ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV1742 ) @ SV2319 ) @ SV94 )
= $true )
| ( ( ~ ( c_lessequals @ SV955 @ SV1742 @ SV94 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV2319 @ SV94 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV94 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7587]) ).
thf(7863,plain,
! [SV2723: $i,SV2621: $i,SV2320: $i,SV1748: $i,SV967: $i,SV106: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV967 @ SV1748 @ SV106 ) ) @ SV2320 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV2621 @ SV1748 @ SV106 ) ) @ SV2723 ) @ SV106 )
= $true )
| ( ( ~ ( c_lessequals @ SV2320 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2621 @ SV967 @ SV106 ) @ SV1748 @ SV106 ) ) @ SV2723 ) @ SV106 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7588]) ).
thf(7864,plain,
! [SV2724: $i,SV2622: $i,SV2321: $i,SV1749: $i,SV107: $i,SV968: $i] :
( ( ( c_lessequals @ SV968 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SV2321 @ SV107 ) @ SV2622 @ SV107 ) ) @ SV2724 ) @ SV107 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV2321 @ SV2622 @ SV107 ) ) @ SV968 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV1749 @ SV2622 @ SV107 ) ) @ SV2724 ) @ SV107 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7589]) ).
thf(7865,plain,
! [SV2725: $i,SV2623: $i,SV2322: $i,SV1750: $i,SV969: $i,SV108: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV969 @ SV1750 @ SV108 ) ) @ SV2322 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV2623 @ SV1750 @ SV108 ) ) @ SV2725 ) @ SV108 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV969 @ SV2623 @ SV108 ) @ SV1750 @ SV108 ) ) @ SV2322 ) @ SV2725 @ SV108 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7590]) ).
thf(7866,plain,
! [SV2726: $i,SV2624: $i,SV2323: $i,SV1751: $i,SV970: $i,SV109: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV970 @ SV1751 @ SV109 ) @ SV2323 @ SV109 ) ) @ SV2624 ) @ SV2726 @ SV109 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV970 @ SV2323 @ SV109 ) ) @ SV2624 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV1751 @ SV2323 @ SV109 ) ) @ SV2726 ) @ SV109 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7591]) ).
thf(7867,plain,
! [SV1758: $i,SV980: $i,SV2325: $i,SV119: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV2325 @ SV119 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV980 @ SV2325 @ SV119 ) @ ( c_HOL_Otimes__class_Otimes @ SV1758 @ SV2325 @ SV119 ) @ SV119 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV980 @ SV1758 @ SV119 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7592]) ).
thf(7868,plain,
! [SV1759: $i,SV981: $i,SV2326: $i,SV120: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV2326 @ SV120 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV981 @ SV120 ) @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV1759 @ SV120 ) @ SV120 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV981 @ SV1759 @ SV120 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7593]) ).
thf(7869,plain,
! [SV1760: $i,SV982: $i,SV2327: $i,SV121: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV2327 @ SV121 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV982 @ SV2327 @ SV121 ) @ ( c_HOL_Otimes__class_Otimes @ SV1760 @ SV2327 @ SV121 ) @ SV121 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV982 @ SV1760 @ SV121 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7594]) ).
thf(7870,plain,
! [SV1761: $i,SV983: $i,SV2328: $i,SV122: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV2328 @ SV122 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV983 @ SV122 ) @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV1761 @ SV122 ) @ SV122 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV983 @ SV1761 @ SV122 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7595]) ).
thf(7871,plain,
! [SV124: $i,SV1763: $i,SV2329: $i,SV985: $i] :
( ( ( c_lessequals @ SV985 @ ( c_Orderings_Oord__class_Omax @ SV2329 @ SV1763 @ SV124 ) @ SV124 )
= $false )
| ( ( c_lessequals @ SV985 @ SV2329 @ SV124 )
= $true )
| ( ( c_lessequals @ SV985 @ SV1763 @ SV124 )
= $true )
| ( ( class_Orderings_Olinorder @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7596]) ).
thf(7872,plain,
! [SV2854: $i,SV2824: $i,SV2781: $i,SV2727: $i,SV2625: $i,SV2331: $i,SV1765: $i,SV989: $i,SV128: $i] :
( ( ( ( hAPP @ ( hAPP @ SV128 @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2331 ) ) @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2625 ) )
= ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2331 ) @ SV2625 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2727 @ SV128 @ SV989 @ SV2781 @ SV2824 @ SV2854 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7597]) ).
thf(7873,plain,
! [SV2728: $i,SV2626: $i,SV2341: $i,SV1776: $i,SV1000: $i,SV140: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1776 @ SV140 ) ) @ SV2341 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV2626 @ SV1776 @ SV140 ) ) @ SV2728 ) @ SV140 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2626 @ SV1000 @ SV140 ) @ SV1776 @ SV140 ) ) @ SV2728 ) @ SV140 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7606]) ).
thf(7874,plain,
! [SV2729: $i,SV2627: $i,SV2342: $i,SV1777: $i,SV141: $i,SV1001: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1001 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1777 @ SV2342 @ SV141 ) @ SV2627 @ SV141 ) ) @ SV2729 ) @ SV141 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV2342 @ SV2627 @ SV141 ) ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV1777 @ SV2627 @ SV141 ) ) @ SV2729 ) @ SV141 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7607]) ).
thf(7875,plain,
! [SV2730: $i,SV2628: $i,SV2343: $i,SV1778: $i,SV1002: $i,SV142: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1778 @ SV142 ) ) @ SV2343 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV2628 @ SV1778 @ SV142 ) ) @ SV2730 ) @ SV142 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1002 @ SV2628 @ SV142 ) @ SV1778 @ SV142 ) ) @ SV2343 ) @ SV2730 @ SV142 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7608]) ).
thf(7876,plain,
! [SV2731: $i,SV2629: $i,SV2344: $i,SV1779: $i,SV1003: $i,SV143: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1003 @ SV1779 @ SV143 ) @ SV2344 @ SV143 ) ) @ SV2629 ) @ SV2731 @ SV143 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1003 @ SV2344 @ SV143 ) ) @ SV2629 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1779 @ SV2344 @ SV143 ) ) @ SV2731 ) @ SV143 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7609]) ).
thf(7877,plain,
! [SV1780: $i,SV144: $i,SV1004: $i,SV2345: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV2345 @ SV1004 @ SV144 ) @ SV1780 @ SV144 )
= $false )
| ( ( c_lessequals @ SV2345 @ SV1780 @ SV144 )
= $true )
| ( ( c_lessequals @ SV1004 @ SV1780 @ SV144 )
= $true )
| ( ( class_Orderings_Olinorder @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7610]) ).
thf(7878,plain,
! [SV1782: $i,SV1010: $i,SV150: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ ( c_HOL_Otimes__class_Otimes @ SV1010 @ SV1782 @ SV150 ) @ SV150 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1782 @ SV150 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV150 ) @ SV1010 @ SV150 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7611]) ).
thf(7879,plain,
! [SV1011: $i,SV1783: $i,SV151: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ ( c_HOL_Otimes__class_Otimes @ SV1783 @ SV1011 @ SV151 ) @ SV151 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1783 @ SV151 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV151 ) @ SV1011 @ SV151 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7612]) ).
thf(7880,plain,
! [SV1784: $i,SV1012: $i,SV152: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1012 @ SV152 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV1784 @ SV152 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV1012 @ SV1784 @ SV152 ) @ SV152 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7613]) ).
thf(7881,plain,
! [SV1785: $i,SV153: $i,SV1013: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1013 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1785 @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV153 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV1013 @ SV1785 @ SV153 ) @ SV153 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7614]) ).
thf(7882,plain,
! [SV2347: $i,SV1015: $i,SV1786: $i,SV155: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV1786 @ SV155 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1015 @ SV2347 @ SV155 ) @ ( c_Power_Opower__class_Opower @ SV1786 @ SV2347 @ SV155 ) @ SV155 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1786 @ SV155 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7615]) ).
thf(7883,plain,
! [SV2360: $i,SV1815: $i,SV192: $i,SV1052: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1052 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV1815 ) @ SV2360 ) @ SV192 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SV2360 @ SV192 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV1815 @ SV192 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV192 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7619]) ).
thf(7884,plain,
! [SV1818: $i,SV195: $i,SV1055: $i] :
( ( ( c_lessequals @ SV1055 @ SV195 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1055 @ SV1818 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV195 @ SV1818 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV195 @ SV1055 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1818 @ SV1055 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7620]) ).
thf(7885,plain,
! [SV1056: $i,SV196: $i,SV1819: $i] :
( ( ( c_lessequals @ SV1819 @ SV196 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1819 @ SV1056 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV196 @ SV1819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1056 @ SV1819 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV196 @ SV1056 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7621]) ).
thf(7886,plain,
! [SV1821: $i,SV2361: $i,SV1059: $i,SV199: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV1059 @ SV199 )
= $false )
| ( ( ~ ( c_lessequals @ SV1059 @ SV2361 @ SV199 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1821 @ SV199 ) @ ( c_Power_Opower__class_Opower @ SV2361 @ SV1821 @ SV199 ) @ SV199 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7622]) ).
thf(7887,plain,
! [SV1070: $i,SV210: $i,SV1831: $i,SV2364: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1831 @ SV210 ) @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1070 @ SV210 ) @ SV210 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2364 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 ) )
= $true )
| ( ( c_lessequals @ SV1070 @ SV1831 @ SV210 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7623]) ).
thf(7888,plain,
! [SV1071: $i,SV211: $i,SV1832: $i,SV2365: $i] :
( ( ( c_lessequals @ SV2365 @ SV1832 @ SV211 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV1832 @ SV211 ) @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV2365 @ SV211 ) @ SV211 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7624]) ).
thf(7889,plain,
! [SV1833: $i,SV212: $i,SV1072: $i,SV2366: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1072 @ SV212 ) @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1833 @ SV212 ) @ SV212 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SV2366 @ SV212 ) )
= $true )
| ( ( c_lessequals @ SV1072 @ SV1833 @ SV212 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7625]) ).
thf(7890,plain,
! [SV1073: $i,SV213: $i,SV2367: $i,SV1834: $i] :
( ( ( c_lessequals @ SV1834 @ SV2367 @ SV213 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV1073 @ SV213 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV1834 @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV2367 @ SV213 ) @ SV213 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7626]) ).
thf(7891,plain,
! [SV1835: $i,SV1074: $i,SV2368: $i,SV214: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV2368 @ SV214 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1074 @ SV214 ) @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1835 @ SV214 ) @ SV214 ) )
= $true )
| ( ( c_lessequals @ SV1074 @ SV1835 @ SV214 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7627]) ).
thf(7892,plain,
! [SV1836: $i,SV1075: $i,SV2369: $i,SV215: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV2369 @ SV215 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1075 @ SV2369 @ SV215 ) @ ( c_HOL_Otimes__class_Otimes @ SV1836 @ SV2369 @ SV215 ) @ SV215 ) )
= $true )
| ( ( c_lessequals @ SV1075 @ SV1836 @ SV215 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7628]) ).
thf(7893,plain,
! [SV1848: $i,SV234: $i,SV1091: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1091 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1848 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV234 ) @ SV1091 ) @ SV1848 ) @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7635]) ).
thf(7894,plain,
! [SV2378: $i,SV1092: $i,SV235: $i,SV1849: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1849 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV235 ) @ SV1092 @ SV235 )
| ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SV2378 @ SV235 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1092 @ SV1849 @ SV235 ) @ ( c_Power_Opower__class_Opower @ SV2378 @ SV1849 @ SV235 ) @ SV235 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7636]) ).
thf(7895,plain,
! [SV258: $i,SV1872: $i,SV2393: $i,SV1115: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1115 @ ( c_Orderings_Oord__class_Omax @ SV2393 @ SV1872 @ SV258 ) @ SV258 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1115 @ SV2393 @ SV258 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1115 @ SV1872 @ SV258 )
= $true )
| ( ( class_Orderings_Olinorder @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7647]) ).
thf(7896,plain,
! [SV2632: $i,SV2396: $i,SV1877: $i,SV265: $i,SV1122: $i] :
( ( ( c_lessequals @ SV1122 @ SV265 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV265 @ SV1877 @ tc_nat ) ) @ SV2396 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1122 @ SV1877 @ tc_nat ) ) @ SV2632 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV265 @ SV1122 @ tc_nat ) @ SV1877 @ tc_nat ) ) @ SV2396 ) @ SV2632 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7648]) ).
thf(7897,plain,
! [SV2633: $i,SV1878: $i,SV1123: $i,SV266: $i,SV2397: $i] :
( ( ( c_lessequals @ SV2397 @ SV266 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV266 @ SV2397 @ tc_nat ) @ SV1123 @ tc_nat ) ) @ SV1878 ) @ SV2633 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV266 @ SV1123 @ tc_nat ) ) @ SV1878 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2397 @ SV1123 @ tc_nat ) ) @ SV2633 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7649]) ).
thf(7898,plain,
! [SV2634: $i,SV267: $i,SV2398: $i,SV1124: $i,SV1879: $i] :
( ( ( c_lessequals @ SV1879 @ SV1124 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1879 @ SV2398 @ tc_nat ) ) @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1124 @ SV2398 @ tc_nat ) ) @ SV2634 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV267 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1124 @ SV1879 @ tc_nat ) @ SV2398 @ tc_nat ) ) @ SV2634 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7650]) ).
thf(7899,plain,
! [SV2635: $i,SV1125: $i,SV1880: $i,SV2399: $i,SV268: $i] :
( ( ( c_lessequals @ SV268 @ SV2399 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1880 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2399 @ SV268 @ tc_nat ) @ SV1125 @ tc_nat ) ) @ SV2635 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SV1125 @ tc_nat ) ) @ SV1880 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2399 @ SV1125 @ tc_nat ) ) @ SV2635 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7651]) ).
thf(7900,plain,
! [SV1882: $i,SV270: $i,SV1127: $i,SV2400: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV2400 @ SV1127 @ SV270 ) @ SV1882 @ SV270 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2400 @ SV1882 @ SV270 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1127 @ SV1882 @ SV270 )
= $true )
| ( ( class_Orderings_Olinorder @ SV270 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7652]) ).
thf(7901,plain,
! [SV1883: $i,SV272: $i,SV1129: $i] :
( ( ( c_lessequals @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1883 @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1129 ) @ SV1883 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7653]) ).
thf(7902,plain,
! [SV1884: $i,SV273: $i,SV1130: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1130 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
= $false )
| ( ( c_lessequals @ SV1884 @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV1130 ) @ SV1884 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7654]) ).
thf(7903,plain,
! [SV1895: $i,SV1151: $i,SV297: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1151 @ SV297 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV1895 @ SV297 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV297 ) @ SV1151 ) @ SV1895 ) @ SV297 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7656]) ).
thf(7904,plain,
! [SV1162: $i,SV308: $i,SV2639: $i,SV2405: $i,SV1900: $i] :
( ( ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2405 ) @ SV2639 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV308 )
= $false )
| ( ( c_Type_Otyping @ SV1900 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV2405 ) @ SV2639 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1162 )
= $false )
| ( ( SV308 = SV1162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7657]) ).
thf(7905,plain,
! [SV310: $i,SV1901: $i,SV1164: $i] :
( ( ( c_lessequals @ SV1164 @ SV1901 @ SV310 )
= $false )
| ( ( c_lessequals @ SV1901 @ SV1164 @ SV310 )
= $false )
| ( ( SV1164 = SV1901 )
= $true )
| ( ( class_Orderings_Oorder @ SV310 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7658]) ).
thf(7906,plain,
! [SV312: $i,SV1903: $i,SV1166: $i] :
( ( ( c_lessequals @ SV1166 @ SV1903 @ SV312 )
= $false )
| ( ( c_lessequals @ SV1903 @ SV1166 @ SV312 )
= $false )
| ( ( SV1166 = SV1903 )
= $true )
| ( ( class_Orderings_Oorder @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7659]) ).
thf(7907,plain,
! [SV313: $i,SV1167: $i,SV1904: $i] :
( ( ( c_lessequals @ SV1904 @ SV1167 @ SV313 )
= $false )
| ( ( c_lessequals @ SV1167 @ SV1904 @ SV313 )
= $false )
| ( ( SV1167 = SV1904 )
= $true )
| ( ( class_Orderings_Oorder @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7660]) ).
thf(7908,plain,
! [SV2407: $i,SV1174: $i,SV320: $i,SV2640: $i,SV1910: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1910 @ SV2640 @ SV320 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SV2407 @ SV320 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV1174 ) @ SV1910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV2407 ) @ SV2640 ) @ SV320 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7661]) ).
thf(7909,plain,
! [SV1920: $i,SV1186: $i,SV332: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1186 @ SV332 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1920 @ SV332 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV332 ) @ SV1186 ) @ SV1920 ) @ SV332 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7667]) ).
thf(7910,plain,
! [SV1921: $i,SV1187: $i,SV333: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1187 @ SV333 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ SV1921 @ SV333 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV333 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV333 ) @ SV1187 ) @ SV1921 ) @ SV333 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV333 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7668]) ).
thf(7911,plain,
! [SV1923: $i,SV1189: $i,SV335: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV1189 @ SV335 )
= $false )
| ( ( c_lessequals @ SV1923 @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1189 @ SV1923 @ SV335 ) @ ( c_HOL_Ozero__class_Ozero @ SV335 ) @ SV335 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV335 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7669]) ).
thf(7912,plain,
! [SV1924: $i,SV336: $i,SV1190: $i] :
( ( ( c_lessequals @ SV1190 @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV1924 @ SV336 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1190 @ SV1924 @ SV336 ) @ ( c_HOL_Ozero__class_Ozero @ SV336 ) @ SV336 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV336 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7670]) ).
thf(7913,plain,
! [SV1925: $i,SV1191: $i,SV337: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV1191 @ SV337 )
= $false )
| ( ( c_lessequals @ SV1925 @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1191 @ SV1925 @ SV337 ) @ ( c_HOL_Ozero__class_Ozero @ SV337 ) @ SV337 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7671]) ).
thf(7914,plain,
! [SV1926: $i,SV338: $i,SV1192: $i] :
( ( ( c_lessequals @ SV1192 @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV1926 @ SV338 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1192 @ SV1926 @ SV338 ) @ ( c_HOL_Ozero__class_Ozero @ SV338 ) @ SV338 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7672]) ).
thf(7915,plain,
! [SV1927: $i,SV1193: $i,SV339: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV1193 @ SV339 )
= $false )
| ( ( c_lessequals @ SV1927 @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1193 @ SV1927 @ SV339 ) @ ( c_HOL_Ozero__class_Ozero @ SV339 ) @ SV339 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7673]) ).
thf(7916,plain,
! [SV1928: $i,SV340: $i,SV1194: $i] :
( ( ( c_lessequals @ SV1194 @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV1928 @ SV340 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1194 @ SV1928 @ SV340 ) @ ( c_HOL_Ozero__class_Ozero @ SV340 ) @ SV340 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7674]) ).
thf(7917,plain,
! [SV1195: $i,SV1929: $i,SV341: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV1929 @ SV341 )
= $false )
| ( ( c_lessequals @ SV1195 @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1195 @ SV1929 @ SV341 ) @ ( c_HOL_Ozero__class_Ozero @ SV341 ) @ SV341 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV341 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7675]) ).
thf(7918,plain,
! [SV2855: $i,SV2825: $i,SV2782: $i,SV2733: $i,SV2641: $i,SV2416: $i,SV1936: $i,SV1206: $i,SV352: $i] :
( ( ( ( hAPP @ ( hAPP @ SV352 @ ( hAPP @ ( hAPP @ SV1206 @ SV1936 ) @ SV2416 ) ) @ SV2641 )
= ( hAPP @ ( hAPP @ SV1206 @ ( hAPP @ ( hAPP @ SV352 @ SV1936 ) @ SV2641 ) ) @ ( hAPP @ ( hAPP @ SV352 @ SV2416 ) @ SV2641 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2733 @ SV1206 @ SV352 @ SV2782 @ SV2825 @ SV2855 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7676]) ).
thf(7919,plain,
! [SV2856: $i,SV2826: $i,SV2783: $i,SV2734: $i,SV2642: $i,SV2417: $i,SV1937: $i,SV1207: $i,SV353: $i] :
( ( ( ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ ( hAPP @ ( hAPP @ SV1937 @ SV2417 ) @ SV2642 ) )
= ( hAPP @ ( hAPP @ SV1937 @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2417 ) ) @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2642 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1937 @ SV353 @ SV2734 @ SV2783 @ SV2826 @ SV2856 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7677]) ).
thf(7920,plain,
! [SV2827: $i,SV2784: $i,SV2735: $i,SV2643: $i,SV2418: $i,SV1938: $i,SV1208: $i,SV354: $i] :
( ( ( ( hAPP @ ( hAPP @ SV354 @ SV1208 ) @ SV1938 )
= ( hAPP @ ( hAPP @ SV354 @ SV1938 ) @ SV1208 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2418 @ SV354 @ SV2643 @ SV2735 @ SV2784 @ SV2827 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7678]) ).
thf(7921,plain,
! [SV2857: $i,SV2828: $i,SV2785: $i,SV2736: $i,SV2644: $i,SV2419: $i,SV1939: $i,SV1209: $i,SV355: $i] :
( ( ( ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ ( hAPP @ ( hAPP @ SV355 @ SV1939 ) @ SV2419 ) )
= ( hAPP @ ( hAPP @ SV355 @ ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ SV1939 ) ) @ SV2419 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2644 @ SV355 @ SV2736 @ SV2785 @ SV2828 @ SV2857 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7679]) ).
thf(7922,plain,
! [SV1940: $i,SV2786: $i,SV1210: $i,SV2737: $i,SV2645: $i,SV356: $i,SV2420: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2420 @ SV356 @ SV2645 @ SV2737 @ SV1210 @ SV2786 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV356 @ SV1210 ) @ SV1940 )
= SV1940 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7680]) ).
thf(7923,plain,
! [SV1941: $i,SV2787: $i,SV2738: $i,SV1211: $i,SV2646: $i,SV357: $i,SV2421: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2421 @ SV357 @ SV2646 @ SV1211 @ SV2738 @ SV2787 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV357 @ SV1211 ) @ SV1941 )
= SV1211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7681]) ).
thf(7924,plain,
! [SV2829: $i,SV2788: $i,SV2739: $i,SV2647: $i,SV2422: $i,SV1942: $i,SV1212: $i,SV358: $i] :
( ( ( ( hAPP @ ( hAPP @ SV358 @ SV1212 ) @ SV1942 )
= ( hAPP @ ( hAPP @ SV358 @ SV1942 ) @ SV1212 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV358 @ SV2422 @ SV2647 @ SV2739 @ SV2788 @ SV2829 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7682]) ).
thf(7925,plain,
! [SV2858: $i,SV2830: $i,SV2789: $i,SV2740: $i,SV2648: $i,SV2423: $i,SV1943: $i,SV1213: $i,SV359: $i] :
( ( ( ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ ( hAPP @ ( hAPP @ SV359 @ SV1943 ) @ SV2423 ) )
= ( hAPP @ ( hAPP @ SV359 @ ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ SV1943 ) ) @ SV2423 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV359 @ SV2648 @ SV2740 @ SV2789 @ SV2830 @ SV2858 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7683]) ).
thf(7926,plain,
! [SV1944: $i,SV2790: $i,SV2741: $i,SV1214: $i,SV2649: $i,SV2424: $i,SV360: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV360 @ SV2424 @ SV2649 @ SV1214 @ SV2741 @ SV2790 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV360 @ SV1214 ) @ SV1944 )
= SV1944 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7684]) ).
thf(7927,plain,
! [SV2859: $i,SV2831: $i,SV2791: $i,SV2742: $i,SV2650: $i,SV2425: $i,SV1945: $i,SV1215: $i,SV361: $i] :
( ( ( ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ ( hAPP @ ( hAPP @ SV361 @ SV1945 ) @ SV2425 ) )
= ( hAPP @ ( hAPP @ SV361 @ ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ SV1945 ) ) @ SV2425 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV361 @ SV2650 @ SV2742 @ SV2791 @ SV2831 @ SV2859 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7685]) ).
thf(7928,plain,
! [SV2832: $i,SV2792: $i,SV2743: $i,SV2651: $i,SV2426: $i,SV1946: $i,SV1216: $i,SV362: $i] :
( ( ( ( hAPP @ ( hAPP @ SV362 @ SV1216 ) @ SV1946 )
= ( hAPP @ ( hAPP @ SV362 @ SV1946 ) @ SV1216 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV362 @ SV2426 @ SV2651 @ SV2743 @ SV2792 @ SV2832 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7686]) ).
thf(7929,plain,
! [SV2860: $i,SV2833: $i,SV2793: $i,SV2744: $i,SV2652: $i,SV2427: $i,SV1947: $i,SV1217: $i,SV363: $i] :
( ( ( ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV1947 ) ) @ SV2427 )
= ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV2427 ) ) @ SV1947 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV363 @ SV2652 @ SV2744 @ SV2793 @ SV2833 @ SV2860 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7687]) ).
thf(7930,plain,
! [SV2861: $i,SV2834: $i,SV2794: $i,SV2745: $i,SV2653: $i,SV2428: $i,SV1948: $i,SV1218: $i,SV364: $i] :
( ( ( ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ SV2428 ) )
= ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ SV2428 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV364 @ SV2653 @ SV2745 @ SV2794 @ SV2834 @ SV2861 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7688]) ).
thf(7931,plain,
! [SV2862: $i,SV2835: $i,SV2795: $i,SV2746: $i,SV2654: $i,SV2429: $i,SV1949: $i,SV1219: $i,SV365: $i] :
( ( ( ( hAPP @ ( hAPP @ SV365 @ ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ SV1949 ) ) @ SV2429 )
= ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ ( hAPP @ ( hAPP @ SV365 @ SV1949 ) @ SV2429 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV365 @ SV2654 @ SV2746 @ SV2795 @ SV2835 @ SV2862 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7689]) ).
thf(7932,plain,
! [SV2863: $i,SV2836: $i,SV2796: $i,SV2747: $i,SV2655: $i,SV2430: $i,SV1950: $i,SV1220: $i,SV366: $i] :
( ( ! [SY7280: $i] :
( ( ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV1950 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV2430 ) @ SV2655 ) )
= ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV2430 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV1950 ) @ SV2655 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV366 @ SV2747 @ SV2796 @ SV2836 @ SV2863 @ SY7280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7690]) ).
thf(7933,plain,
! [SV2864: $i,SV2837: $i,SV2797: $i,SV2748: $i,SV2656: $i,SV2431: $i,SV1951: $i,SV1221: $i,SV367: $i] :
( ( ( ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ SV2431 ) )
= ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ SV2431 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2656 @ SV367 @ SV2748 @ SV2797 @ SV2837 @ SV2864 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7691]) ).
thf(7934,plain,
! [SV2865: $i,SV2838: $i,SV2798: $i,SV2749: $i,SV2657: $i,SV2432: $i,SV1952: $i,SV1222: $i,SV368: $i] :
( ( ( ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ ( hAPP @ ( hAPP @ SV368 @ SV1952 ) @ SV2432 ) )
= ( hAPP @ ( hAPP @ SV368 @ ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ SV1952 ) ) @ SV2432 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2657 @ SV368 @ SV2749 @ SV2798 @ SV2838 @ SV2865 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7692]) ).
thf(7935,plain,
! [SV2866: $i,SV2839: $i,SV2799: $i,SV2750: $i,SV2658: $i,SV2433: $i,SV1953: $i,SV1223: $i,SV369: $i] :
( ( ( ( hAPP @ ( hAPP @ SV369 @ ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ SV1953 ) ) @ SV2433 )
= ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ ( hAPP @ ( hAPP @ SV369 @ SV1953 ) @ SV2433 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2658 @ SV369 @ SV2750 @ SV2799 @ SV2839 @ SV2866 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7693]) ).
thf(7936,plain,
! [SV2867: $i,SV2840: $i,SV2800: $i,SV2751: $i,SV2659: $i,SV2434: $i,SV1954: $i,SV1224: $i,SV370: $i] :
( ( ( ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV1954 ) ) @ SV2434 )
= ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV2434 ) ) @ SV1954 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2659 @ SV370 @ SV2751 @ SV2800 @ SV2840 @ SV2867 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7694]) ).
thf(7937,plain,
! [SV2868: $i,SV2841: $i,SV2801: $i,SV2752: $i,SV2660: $i,SV2435: $i,SV1955: $i,SV1225: $i,SV371: $i] :
( ( ! [SY7281: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ SV2660 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ SV2660 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2752 @ SV371 @ SV2801 @ SV2841 @ SV2868 @ SY7281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7695]) ).
thf(7938,plain,
! [SV2869: $i,SV2842: $i,SV2802: $i,SV2753: $i,SV2661: $i,SV2436: $i,SV1956: $i,SV1226: $i,SV372: $i] :
( ( ! [SY7282: $i] :
( ( ( hAPP @ ( hAPP @ SV372 @ ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ SV1956 ) ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) )
= ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ ( hAPP @ ( hAPP @ SV372 @ SV1956 ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2753 @ SV372 @ SV2802 @ SV2842 @ SV2869 @ SY7282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7696]) ).
thf(7939,plain,
! [SV2870: $i,SV2843: $i,SV2803: $i,SV2754: $i,SV2662: $i,SV2437: $i,SV1957: $i,SV1227: $i,SV373: $i] :
( ( ! [SY7283: $i] :
( ( ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV1957 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV2437 ) @ SV2662 ) )
= ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV2437 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV1957 ) @ SV2662 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2754 @ SV373 @ SV2803 @ SV2843 @ SV2870 @ SY7283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7697]) ).
thf(7940,plain,
! [SV1228: $i,SV2804: $i,SV1958: $i,SV2755: $i,SV2663: $i,SV374: $i,SV2438: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2438 @ SV374 @ SV2663 @ SV2755 @ SV1958 @ SV2804 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV374 @ SV1228 ) @ SV1958 )
= SV1228 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7698]) ).
thf(7941,plain,
! [SV1959: $i,SV2805: $i,SV1229: $i,SV2756: $i,SV2664: $i,SV375: $i,SV2439: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2439 @ SV375 @ SV2664 @ SV2756 @ SV1229 @ SV2805 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV375 @ SV1229 ) @ SV1959 )
= SV1959 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7699]) ).
thf(7942,plain,
! [SV1230: $i,SV2806: $i,SV2757: $i,SV1960: $i,SV2665: $i,SV376: $i,SV2440: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2440 @ SV376 @ SV2665 @ SV1960 @ SV2757 @ SV2806 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV376 @ SV1230 ) @ SV1960 )
= SV1960 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7700]) ).
thf(7943,plain,
! [SV1961: $i,SV2807: $i,SV2758: $i,SV1231: $i,SV2666: $i,SV377: $i,SV2441: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2441 @ SV377 @ SV2666 @ SV1231 @ SV2758 @ SV2807 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV377 @ SV1231 ) @ SV1961 )
= SV1231 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7701]) ).
thf(7944,plain,
! [SV2871: $i,SV2844: $i,SV2808: $i,SV2759: $i,SV2667: $i,SV2442: $i,SV1962: $i,SV1232: $i,SV378: $i] :
( ( ( ( hAPP @ ( hAPP @ SV378 @ ( hAPP @ ( hAPP @ SV1232 @ SV1962 ) @ SV2442 ) ) @ SV2667 )
= ( hAPP @ ( hAPP @ SV1232 @ ( hAPP @ ( hAPP @ SV378 @ SV1962 ) @ SV2667 ) ) @ ( hAPP @ ( hAPP @ SV378 @ SV2442 ) @ SV2667 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1232 @ SV378 @ SV2759 @ SV2808 @ SV2844 @ SV2871 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7702]) ).
thf(7945,plain,
! [SV2845: $i,SV2809: $i,SV2760: $i,SV2668: $i,SV2443: $i,SV1963: $i,SV1233: $i,SV379: $i] :
( ( ( ( hAPP @ ( hAPP @ SV379 @ SV1233 ) @ SV1963 )
= ( hAPP @ ( hAPP @ SV379 @ SV1963 ) @ SV1233 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2443 @ SV379 @ SV2668 @ SV2760 @ SV2809 @ SV2845 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7703]) ).
thf(7946,plain,
! [SV1234: $i,SV2810: $i,SV2761: $i,SV1964: $i,SV2669: $i,SV2444: $i,SV380: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV380 @ SV2444 @ SV2669 @ SV1964 @ SV2761 @ SV2810 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV380 @ SV1234 ) @ SV1964 )
= SV1234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7704]) ).
thf(7947,plain,
! [SV1965: $i,SV2811: $i,SV2762: $i,SV1235: $i,SV2670: $i,SV2445: $i,SV381: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV381 @ SV2445 @ SV2670 @ SV1235 @ SV2762 @ SV2811 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV381 @ SV1235 ) @ SV1965 )
= SV1965 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7705]) ).
thf(7948,plain,
! [SV1236: $i,SV2812: $i,SV2446: $i,SV2763: $i,SV2671: $i,SV1966: $i,SV382: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV382 @ SV1966 @ SV2671 @ SV2763 @ SV2446 @ SV2812 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV382 @ SV1236 ) @ SV1236 )
= ( hAPP @ ( hAPP @ SV1966 @ ( hAPP @ ( hAPP @ SV382 @ SV2446 ) @ SV2446 ) ) @ SV1236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7706]) ).
thf(7949,plain,
! [SV2846: $i,SV2813: $i,SV2764: $i,SV2672: $i,SV2447: $i,SV1967: $i,SV1237: $i,SV383: $i] :
( ( ( ( hAPP @ ( hAPP @ SV383 @ SV1237 ) @ ( hAPP @ ( hAPP @ SV1967 @ SV2447 ) @ SV1237 ) )
= ( hAPP @ ( hAPP @ SV1967 @ ( hAPP @ ( hAPP @ SV383 @ SV2447 ) @ SV2672 ) ) @ SV1237 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV383 @ SV1967 @ SV2764 @ SV2813 @ SV2672 @ SV2846 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7707]) ).
thf(7950,plain,
! [SV2847: $i,SV2814: $i,SV2765: $i,SV2673: $i,SV2448: $i,SV1968: $i,SV1238: $i,SV384: $i] :
( ( ( ( hAPP @ ( hAPP @ SV384 @ ( hAPP @ ( hAPP @ SV1238 @ SV1968 ) @ SV2448 ) ) @ SV2448 )
= ( hAPP @ ( hAPP @ SV1238 @ ( hAPP @ ( hAPP @ SV384 @ SV1968 ) @ SV2673 ) ) @ SV2448 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV384 @ SV1238 @ SV2765 @ SV2814 @ SV2673 @ SV2847 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7708]) ).
thf(7951,plain,
! [SV2872: $i,SV2848: $i,SV2815: $i,SV2766: $i,SV2674: $i,SV2449: $i,SV1969: $i,SV1239: $i,SV385: $i] :
( ( ( ( hAPP @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ SV1239 @ SV1969 ) @ SV2449 ) ) @ ( hAPP @ ( hAPP @ SV1239 @ SV2674 ) @ SV2449 ) )
= ( hAPP @ ( hAPP @ SV1239 @ ( hAPP @ ( hAPP @ SV385 @ SV1969 ) @ SV2674 ) ) @ SV2449 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV385 @ SV1239 @ SV2766 @ SV2815 @ SV2848 @ SV2872 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7709]) ).
thf(7952,plain,
! [SV2455: $i,SV406: $i,SV1984: $i,SV1256: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV1984 @ SV406 ) @ ( c_HOL_Otimes__class_Otimes @ SV1256 @ SV2455 @ SV406 ) @ SV406 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1256 @ SV406 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1256 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7710]) ).
thf(7953,plain,
! [SV1257: $i,SV407: $i,SV1985: $i,SV2456: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2456 @ SV1985 @ SV407 ) @ ( c_HOL_Otimes__class_Otimes @ SV2456 @ SV1257 @ SV407 ) @ SV407 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1985 @ SV1257 @ SV407 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1257 @ SV1985 @ SV407 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7711]) ).
thf(7954,plain,
! [SV2457: $i,SV408: $i,SV1258: $i,SV1986: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1986 @ SV1258 @ SV408 ) @ ( c_HOL_Otimes__class_Otimes @ SV2457 @ SV1258 @ SV408 ) @ SV408 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV1258 @ SV408 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1258 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7712]) ).
thf(7955,plain,
! [SV1259: $i,SV409: $i,SV2458: $i,SV1987: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1987 @ SV2458 @ SV409 ) @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SV2458 @ SV409 ) @ SV409 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1987 @ SV1259 @ SV409 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1259 @ SV1987 @ SV409 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV409 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7713]) ).
thf(7956,plain,
! [SV2849: $i,SV2816: $i,SV2767: $i,SV2676: $i,SV2465: $i,SV2003: $i,SV1281: $i,SV433: $i] :
( ( ( ( hAPP @ ( hAPP @ SV433 @ SV1281 ) @ ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ SV2465 ) )
= ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ ( c_Suc @ SV2465 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2676 @ SV433 @ SV2003 @ SV2767 @ SV2816 @ SV2849 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7720]) ).
thf(7957,plain,
! [SV2850: $i,SV2817: $i,SV2768: $i,SV2677: $i,SV2466: $i,SV2004: $i,SV1282: $i,SV434: $i] :
( ( ( ( hAPP @ ( hAPP @ SV434 @ ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ SV2466 ) ) @ SV2004 )
= ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ ( c_Suc @ SV2466 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2677 @ SV434 @ SV1282 @ SV2768 @ SV2817 @ SV2850 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7721]) ).
thf(7958,plain,
! [SV2851: $i,SV2818: $i,SV2769: $i,SV2678: $i,SV2467: $i,SV2005: $i,SV1283: $i,SV435: $i] :
( ( ( ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ ( c_Suc @ SV2005 ) )
= ( hAPP @ ( hAPP @ SV2467 @ SV1283 ) @ ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ SV2005 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2678 @ SV2467 @ SV435 @ SV2769 @ SV2818 @ SV2851 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7722]) ).
thf(7959,plain,
! [SV2852: $i,SV2819: $i,SV2770: $i,SV2679: $i,SV2468: $i,SV2006: $i,SV1284: $i,SV436: $i] :
( ( ( ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ ( c_Suc @ SV2006 ) )
= ( hAPP @ ( hAPP @ SV2468 @ SV1284 ) @ ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ SV2006 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2679 @ SV2468 @ SV436 @ SV2770 @ SV2819 @ SV2852 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7723]) ).
thf(7960,plain,
! [SV2470: $i,SV1290: $i,SV2012: $i,SV442: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV442 ) @ SV2012 @ SV442 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1290 @ ( c_Suc @ SV2470 ) @ SV442 ) @ ( c_Power_Opower__class_Opower @ SV2012 @ ( c_Suc @ SV2470 ) @ SV442 ) @ SV442 ) )
= $true )
| ( ( c_lessequals @ SV1290 @ SV2012 @ SV442 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV442 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7724]) ).
thf(7961,plain,
! [SV2472: $i,SV2680: $i,SV1295: $i,SV2015: $i,SV447: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
| ~ ( c_lessequals @ SV2015 @ SV2680 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SV2472 @ SV447 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SV2472 @ SV2680 @ SV447 ) @ SV447 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7725]) ).
thf(7962,plain,
! [SV2473: $i,SV2681: $i,SV1296: $i,SV2016: $i,SV448: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ SV2016 @ SV2681 @ SV448 )
| ~ ( c_lessequals @ SV1296 @ SV2473 @ SV448 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SV2473 @ SV2681 @ SV448 ) @ SV448 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7726]) ).
thf(7963,plain,
! [SV1303: $i,SV2023: $i,SV455: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV2023 @ SV455 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1303 @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1303 @ SV2023 @ SV455 ) @ ( c_HOL_Ozero__class_Ozero @ SV455 ) @ SV455 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7731]) ).
thf(7964,plain,
! [SV2024: $i,SV1304: $i,SV456: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1304 @ SV456 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2024 @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1304 @ SV2024 @ SV456 ) @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV456 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV456 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7732]) ).
thf(7965,plain,
! [SV2025: $i,SV457: $i,SV1305: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1305 @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV2025 @ SV457 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1305 @ SV2025 @ SV457 ) @ ( c_HOL_Ozero__class_Ozero @ SV457 ) @ SV457 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7733]) ).
thf(7966,plain,
! [SV1311: $i,SV464: $i,SV2027: $i] :
( ( ( c_lessequals @ SV2027 @ SV464 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV2027 @ SV1311 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SV2027 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1311 @ SV2027 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV464 @ SV1311 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7734]) ).
thf(7967,plain,
! [SV2028: $i,SV465: $i,SV1312: $i] :
( ( ( c_lessequals @ SV1312 @ SV465 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1312 @ SV2028 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV465 @ SV2028 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV465 @ SV1312 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV2028 @ SV1312 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7735]) ).
thf(7968,plain,
! [SV2029: $i,SV466: $i,SV2475: $i,SV1313: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1313 @ SV2475 @ SV466 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV2029 @ SV466 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1313 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ SV2029 ) @ SV2475 ) @ SV466 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7736]) ).
thf(7969,plain,
! [SV1321: $i,SV2476: $i,SV474: $i,SV2033: $i] :
( ( ( c_lessequals @ SV2033 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
= $false )
| ( ( ~ ( c_lessequals @ SV2476 @ SV1321 @ SV474 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1321 @ SV2033 @ SV474 ) @ ( c_HOL_Otimes__class_Otimes @ SV2476 @ SV2033 @ SV474 ) @ SV474 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7737]) ).
thf(7970,plain,
! [SV2034: $i,SV2477: $i,SV475: $i,SV1322: $i] :
( ( ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
= $false )
| ( ( ~ ( c_lessequals @ SV2477 @ SV2034 @ SV475 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2034 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2477 @ SV475 ) @ SV475 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV475 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7738]) ).
thf(7971,plain,
! [SV2478: $i,SV1323: $i,SV2035: $i,SV476: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV2035 @ SV476 )
= $false )
| ( ( ~ ( c_lessequals @ SV1323 @ SV2478 @ SV476 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1323 @ SV2035 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SV2478 @ SV2035 @ SV476 ) @ SV476 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7739]) ).
thf(7972,plain,
! [SV2479: $i,SV2036: $i,SV1324: $i,SV477: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV477 ) @ SV1324 @ SV477 )
= $false )
| ( ( ~ ( c_lessequals @ SV2036 @ SV2479 @ SV477 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2036 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2479 @ SV477 ) @ SV477 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7740]) ).
thf(7973,plain,
! [SV2480: $i,SV2037: $i,SV1325: $i,SV478: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV478 ) @ SV1325 @ SV478 )
= $false )
| ( ( ~ ( c_lessequals @ SV2037 @ SV2480 @ SV478 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2037 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2480 @ SV478 ) @ SV478 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono1 @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7741]) ).
thf(7974,plain,
! [SV2050: $i,SV492: $i,SV2487: $i,SV1339: $i] :
( ( ( c_lessequals @ SV1339 @ SV2487 @ SV492 )
= $false )
| ( ( ~ ( c_lessequals @ SV2487 @ SV2050 @ SV492 ) )
= $true )
| ( ( c_lessequals @ SV1339 @ SV2050 @ SV492 )
= $true )
| ( ( class_Orderings_Oorder @ SV492 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7748]) ).
thf(7975,plain,
! [SV2051: $i,SV493: $i,SV2488: $i,SV1340: $i] :
( ( ( c_lessequals @ SV1340 @ SV2488 @ SV493 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2488 @ SV2051 @ SV493 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1340 @ SV2051 @ SV493 )
= $true )
| ( ( class_Orderings_Oorder @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7749]) ).
thf(7976,plain,
! [SV2052: $i,SV494: $i,SV2489: $i,SV1341: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1341 @ SV2489 @ SV494 )
= $false )
| ( ( ~ ( c_lessequals @ SV2489 @ SV2052 @ SV494 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1341 @ SV2052 @ SV494 )
= $true )
| ( ( class_Orderings_Oorder @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7750]) ).
thf(7977,plain,
! [SV2053: $i,SV495: $i,SV1342: $i] :
( ( ( c_lessequals @ SV1342 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
= $false )
| ( ( c_lessequals @ SV2053 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV495 ) @ SV1342 ) @ SV2053 ) @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7751]) ).
thf(7978,plain,
! [SV1343: $i,SV496: $i,SV2054: $i,SV2490: $i] :
( ( ( c_lessequals @ SV2490 @ SV2054 @ SV496 )
= $false )
| ( ( ~ ( c_lessequals @ SV1343 @ SV2490 @ SV496 ) )
= $true )
| ( ( c_lessequals @ SV1343 @ SV2054 @ SV496 )
= $true )
| ( ( class_Orderings_Opreorder @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7752]) ).
thf(7979,plain,
! [SV1355: $i,SV511: $i,SV2062: $i,SV2491: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV2062 @ SV511 ) @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV1355 @ SV511 ) @ SV511 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2491 @ ( c_HOL_Ozero__class_Ozero @ SV511 ) @ SV511 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1355 @ SV2062 @ SV511 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV511 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7753]) ).
thf(7980,plain,
! [SV1356: $i,SV512: $i,SV2063: $i,SV2492: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2492 @ SV2063 @ SV512 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1356 @ ( c_HOL_Ozero__class_Ozero @ SV512 ) @ SV512 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2063 @ SV512 ) @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2492 @ SV512 ) @ SV512 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV512 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7754]) ).
thf(7981,plain,
! [SV2064: $i,SV513: $i,SV1357: $i,SV2493: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV1357 @ SV513 ) @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV2064 @ SV513 ) @ SV513 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV513 ) @ SV2493 @ SV513 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1357 @ SV2064 @ SV513 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7755]) ).
thf(7982,plain,
! [SV1358: $i,SV514: $i,SV2494: $i,SV2065: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2065 @ SV2494 @ SV514 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SV1358 @ SV514 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2065 @ SV514 ) @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2494 @ SV514 ) @ SV514 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7756]) ).
thf(7983,plain,
! [SV2066: $i,SV2495: $i,SV515: $i,SV1359: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1359 @ ( c_HOL_Ozero__class_Ozero @ SV515 ) @ SV515 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2495 @ SV2066 @ SV515 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2066 @ SV515 ) @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2495 @ SV515 ) @ SV515 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV515 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7757]) ).
thf(7984,plain,
! [SV2496: $i,SV2067: $i,SV1360: $i,SV516: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV516 ) @ SV1360 @ SV516 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2067 @ SV2496 @ SV516 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2067 @ SV516 ) @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2496 @ SV516 ) @ SV516 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV516 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7758]) ).
thf(7985,plain,
! [SV1361: $i,SV517: $i,SV2497: $i,SV2068: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2068 @ SV2497 @ SV517 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1361 @ SV517 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2068 @ SV517 ) @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2497 @ SV517 ) @ SV517 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV517 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7759]) ).
thf(7986,plain,
! [SV1362: $i,SV518: $i,SV2069: $i,SV2498: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2498 @ SV2069 @ SV518 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1362 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2069 @ SV518 ) @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2498 @ SV518 ) @ SV518 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV518 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7760]) ).
thf(7987,plain,
! [SV1363: $i,SV2499: $i,SV519: $i,SV2070: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2070 @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV519 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2499 @ SV1363 @ SV519 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1363 @ SV2070 @ SV519 ) @ ( c_HOL_Otimes__class_Otimes @ SV2499 @ SV2070 @ SV519 ) @ SV519 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV519 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7761]) ).
thf(7988,plain,
! [SV2500: $i,SV1364: $i,SV2071: $i,SV520: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV2071 @ SV520 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1364 @ SV2500 @ SV520 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1364 @ SV2071 @ SV520 ) @ ( c_HOL_Otimes__class_Otimes @ SV2500 @ SV2071 @ SV520 ) @ SV520 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV520 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7762]) ).
thf(7989,plain,
! [SV2072: $i,SV521: $i,SV2501: $i,SV1365: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1365 @ SV2501 @ SV521 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV521 ) @ SV2072 @ SV521 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1365 @ SV2072 @ SV521 ) @ ( c_HOL_Otimes__class_Otimes @ SV2501 @ SV2072 @ SV521 ) @ SV521 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV521 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7763]) ).
thf(7990,plain,
! [SV2073: $i,SV522: $i,SV1366: $i,SV2502: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2502 @ SV1366 @ SV522 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2073 @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV522 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1366 @ SV2073 @ SV522 ) @ ( c_HOL_Otimes__class_Otimes @ SV2502 @ SV2073 @ SV522 ) @ SV522 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV522 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7764]) ).
thf(7991,plain,
! [SV2503: $i,SV2074: $i,SV1367: $i,SV523: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV1367 @ SV523 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2074 @ SV2503 @ SV523 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2074 @ SV523 ) @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2503 @ SV523 ) @ SV523 )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7765]) ).
thf(7992,plain,
! [SV1372: $i,SV2682: $i,SV2506: $i,SV2078: $i,SV529: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2506 @ SV529 )
| ~ ( c_lessequals @ SV2078 @ SV2682 @ SV529 )
| ~ ( c_lessequals @ SV1372 @ SV2506 @ SV529 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SV2506 @ SV2682 @ SV529 ) @ SV529 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7767]) ).
thf(7993,plain,
! [SV2507: $i,SV2683: $i,SV1373: $i,SV2079: $i,SV530: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
| ~ ( c_lessequals @ SV2079 @ SV2683 @ SV530 )
| ~ ( c_lessequals @ SV1373 @ SV2507 @ SV530 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SV2507 @ SV2683 @ SV530 ) @ SV530 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV530 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7768]) ).
thf(7994,plain,
! [SV2513: $i,SV1391: $i,SV550: $i,SV2685: $i,SV2092: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2092 @ SV2685 @ SV550 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1391 @ SV2513 @ SV550 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV1391 ) @ SV2092 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV2513 ) @ SV2685 ) @ SV550 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV550 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7773]) ).
thf(7995,plain,
! [SV2514: $i,SV1392: $i,SV551: $i,SV2686: $i,SV2093: $i] :
( ( ( ~ ( c_lessequals @ SV2093 @ SV2686 @ SV551 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1392 @ SV2514 @ SV551 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV1392 ) @ SV2093 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV2514 ) @ SV2686 ) @ SV551 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV551 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7774]) ).
thf(7996,plain,
! [SV1425: $i,SV586: $i,SV2095: $i,SV2515: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2515 @ SV2095 @ SV586 )
= $false )
| ( ( ~ ( c_lessequals @ SV1425 @ SV2515 @ SV586 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1425 @ SV2095 @ SV586 )
= $true )
| ( ( class_Orderings_Opreorder @ SV586 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7775]) ).
thf(7997,plain,
! [SV1426: $i,SV587: $i,SV2096: $i,SV2516: $i] :
( ( ( c_lessequals @ SV2516 @ SV2096 @ SV587 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1426 @ SV2516 @ SV587 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1426 @ SV2096 @ SV587 )
= $true )
| ( ( class_Orderings_Opreorder @ SV587 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7776]) ).
thf(7998,plain,
! [SV2097: $i,SV1427: $i,SV588: $i,SV2517: $i,SV2687: $i] :
( ( ( ~ ( c_lessequals @ SV2687 @ SV2517 @ SV588 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2687 ) @ SV588 ) )
= $true )
| ( ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2517 ) @ SV588 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV588 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7777]) ).
thf(7999,plain,
! [SV1432: $i,SV2100: $i,SV593: $i] :
( ( ( hBOOL @ ( hAPP @ SV593 @ SV2100 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV593 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1432 @ ( c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1 @ SV593 @ SV2100 ) @ tc_nat )
= $false )
| ( ( hBOOL @ ( hAPP @ SV593 @ SV1432 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7778]) ).
thf(8000,plain,
! [SV2518: $i,SV2688: $i,SV1433: $i,SV2101: $i,SV594: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV2101 @ SV2688 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SV2518 @ SV594 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SV2518 @ SV2688 @ SV594 ) @ SV594 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7779]) ).
thf(8001,plain,
! [SV2520: $i,SV606: $i,SV1444: $i,SV2107: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2107 @ SV1444 @ SV606 ) @ ( c_HOL_Otimes__class_Otimes @ SV2520 @ SV1444 @ SV606 ) @ SV606 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2107 @ SV2520 @ SV606 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1444 @ ( c_HOL_Ozero__class_Ozero @ SV606 ) @ SV606 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV606 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7780]) ).
thf(8002,plain,
! [SV1445: $i,SV607: $i,SV2521: $i,SV2108: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2108 @ SV2521 @ SV607 ) @ ( c_HOL_Otimes__class_Otimes @ SV1445 @ SV2521 @ SV607 ) @ SV607 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV607 ) @ SV2521 @ SV607 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1445 @ SV2108 @ SV607 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV607 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7781]) ).
thf(8003,plain,
! [SV2522: $i,SV608: $i,SV2109: $i,SV1446: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2109 @ SV608 ) @ ( c_HOL_Otimes__class_Otimes @ SV1446 @ SV2522 @ SV608 ) @ SV608 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2109 @ SV2522 @ SV608 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1446 @ ( c_HOL_Ozero__class_Ozero @ SV608 ) @ SV608 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV608 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7782]) ).
thf(8004,plain,
! [SV1447: $i,SV609: $i,SV2110: $i,SV2523: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2523 @ SV2110 @ SV609 ) @ ( c_HOL_Otimes__class_Otimes @ SV2523 @ SV1447 @ SV609 ) @ SV609 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV609 ) @ SV2523 @ SV609 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1447 @ SV2110 @ SV609 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV609 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7783]) ).
thf(8005,plain,
! [SV2128: $i,SV1471: $i,SV634: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV1471 @ SV634 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ SV2128 @ SV634 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV634 ) @ ( c_HOL_Otimes__class_Otimes @ SV1471 @ SV2128 @ SV634 ) @ SV634 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV634 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7792]) ).
thf(8006,plain,
! [SV2129: $i,SV635: $i,SV1472: $i] :
( ( ( c_lessequals @ SV1472 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 )
= $false )
| ( ( c_lessequals @ SV2129 @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ ( c_HOL_Otimes__class_Otimes @ SV1472 @ SV2129 @ SV635 ) @ SV635 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV635 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7793]) ).
thf(8007,plain,
! [SV2130: $i,SV1473: $i,SV636: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV1473 @ SV636 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV2130 @ SV636 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ ( c_HOL_Otimes__class_Otimes @ SV1473 @ SV2130 @ SV636 ) @ SV636 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV636 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7794]) ).
thf(8008,plain,
! [SV2131: $i,SV638: $i,SV1475: $i] :
( ( ( c_lessequals @ SV1475 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 )
= $false )
| ( ( c_lessequals @ SV2131 @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV638 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ ( c_HOL_Otimes__class_Otimes @ SV1475 @ SV2131 @ SV638 ) @ SV638 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV638 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7795]) ).
thf(8009,plain,
! [SV2132: $i,SV639: $i,SV1476: $i] :
( ( ( c_lessequals @ SV1476 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 )
= $false )
| ( ( c_lessequals @ SV2132 @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV639 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ ( c_HOL_Otimes__class_Otimes @ SV1476 @ SV2132 @ SV639 ) @ SV639 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV639 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7796]) ).
thf(8010,plain,
! [SV2133: $i,SV1477: $i,SV640: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV1477 @ SV640 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ SV2133 @ SV640 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV640 ) @ ( c_HOL_Otimes__class_Otimes @ SV1477 @ SV2133 @ SV640 ) @ SV640 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV640 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7797]) ).
thf(8011,plain,
! [SV1515: $i,SV2820: $i,SV2160: $i,SV2772: $i,SV698: $i,SV2689: $i,SV2544: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2544 @ SV2689 @ SV698 @ SV2772 @ SV2160 @ SV2820 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV698 @ SV1515 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV2160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7802]) ).
thf(8012,plain,
! [SV2179: $i,SV2556: $i,SV2697: $i,SV1538: $i,SV721: $i] :
( ( ( c_Type_Otyping @ SV721 @ SV1538 @ ( c_List_Ofoldr @ c_Type_Otype_OFun @ SV2697 @ SV2556 @ tc_Type_Otype @ tc_Type_Otype ) )
= $false )
| ( ( c_Type_Otypings @ SV721 @ SV2179 @ SV2697 )
= $false )
| ( ( c_Type_Otyping @ SV721 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1538 @ SV2179 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV2556 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7804]) ).
thf(8013,plain,
! [SV1540: $i,SV723: $i] :
( ( ( ~ ( class_Power_Opower @ SV723 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV723 ) @ SV1540 @ SV723 )
= ( c_HOL_Ozero__class_Ozero @ SV723 ) )
| ( SV1540
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV723 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV723 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV723 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7805]) ).
thf(8014,plain,
! [SV2182: $i,SV2559: $i,SV2699: $i,SV1543: $i,SV727: $i] :
( ( ( c_Type_Otyping @ SV727 @ SV1543 @ ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV2699 ) @ SV2559 ) )
= $false )
| ( ( c_Type_Otyping @ SV727 @ SV2182 @ SV2699 )
= $false )
| ( ( c_Type_Otyping @ SV727 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1543 ) @ SV2182 ) @ SV2559 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7806]) ).
thf(8015,plain,
! [SV1544: $i,SV2775: $i,SV2700: $i,SV2183: $i,SV2560: $i,SV728: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV728 @ SV2560 @ SV2183 @ tc_Type_Otype ) @ SV2700 @ SV2775 ) )
= $true )
| ( ( c_Type_Otyping @ SV728 @ ( c_Lambda_Osubst @ SV2700 @ SV1544 @ SV2560 ) @ SV2775 )
= $true )
| ( ( c_Type_Otyping @ SV728 @ SV1544 @ SV2183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7807]) ).
thf(8016,plain,
! [SV2702: $i,SV2564: $i,SV737: $i,SV2188: $i,SV1553: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1553 @ SV2188 @ SV737 )
= ( c_HOL_Ominus__class_Ominus @ SV2564 @ SV2702 @ SV737 ) )
= $false )
| ( ( ( c_lessequals @ SV2188 @ SV1553 @ SV737 )
| ~ ( c_lessequals @ SV2702 @ SV2564 @ SV737 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV737 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7808]) ).
thf(8017,plain,
! [SV2704: $i,SV2193: $i,SV1558: $i,SV742: $i,SV2566: $i] :
( ( ( c_lessequals @ SV2566 @ SV742 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV742 @ SV2566 @ tc_nat ) @ SV1558 @ tc_nat ) ) @ SV2193 )
= SV2704 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV742 @ SV1558 @ tc_nat ) ) @ SV2193 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2566 @ SV1558 @ tc_nat ) ) @ SV2704 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7809]) ).
thf(8018,plain,
! [SV2776: $i,SV2705: $i,SV2569: $i,SV2199: $i,SV1566: $i,SV750: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV1566 @ SV2199 @ SV750 ) ) @ SV2569 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV2705 @ SV2199 @ SV750 ) ) @ SV2776 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ SV2705 @ SV750 ) @ SV2199 @ SV750 ) ) @ SV2569 )
= SV2776 )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV750 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7810]) ).
thf(8019,plain,
! [SV2706: $i,SV2574: $i,SV760: $i,SV2205: $i,SV1576: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV2205 @ SV760 )
= ( c_HOL_Ominus__class_Ominus @ SV2574 @ SV2706 @ SV760 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV2574 @ SV2706 @ SV760 )
| ~ ( c_HOL_Oord__class_Oless @ SV1576 @ SV2205 @ SV760 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV760 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7812]) ).
thf(8020,plain,
! [SV763: $i,SV2208: $i,SV2575: $i,SV1579: $i] :
( ( ( SV1579 = SV2575 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2208 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV2575 @ SV763 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1579 @ SV2208 @ SV763 )
= ( c_Power_Opower__class_Opower @ SV2575 @ SV2208 @ SV763 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV763 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7814]) ).
thf(8021,plain,
! [SV2214: $i,SV773: $i,SV1588: $i] :
( ( ( SV1588
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV773 ) @ SV1588 ) @ SV2214 ) )
= $false )
| ( ( SV2214
= ( c_HOL_Ozero__class_Ozero @ SV773 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV773 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV773 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7816]) ).
thf(8022,plain,
! [SV2707: $i,SV2578: $i,SV2215: $i,SV1589: $i,SV774: $i] :
( ( ( class_Int_Onumber__ring @ SV774 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2578 @ SV774 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2707 @ SV774 ) ) )
| ( SV2578 = SV2707 )
| ( SV2215
= ( c_HOL_Ozero__class_Ozero @ SV774 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV774 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7817]) ).
thf(8023,plain,
! [SV2709: $i,SV2580: $i,SV778: $i,SV2217: $i,SV1592: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1592 @ SV2217 @ SV778 )
= ( c_HOL_Ominus__class_Ominus @ SV2580 @ SV2709 @ SV778 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1592 @ SV2217 @ SV778 )
| ~ ( c_HOL_Oord__class_Oless @ SV2580 @ SV2709 @ SV778 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV778 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7818]) ).
thf(8024,plain,
! [SV2711: $i,SV2584: $i,SV2224: $i,SV1600: $i,SV787: $i] :
( ( ( class_Int_Onumber__ring @ SV787 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2224 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2711 @ SV787 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2711 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2224 @ SV787 ) ) )
| ( SV2224 = SV2711 )
| ( SV1600 = SV2584 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV787 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7819]) ).
thf(8025,plain,
! [SV2712: $i,SV2585: $i,SV789: $i,SV2225: $i,SV1602: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1602 @ SV2225 @ SV789 )
= ( c_HOL_Ominus__class_Ominus @ SV2585 @ SV2712 @ SV789 ) )
= $false )
| ( ( ( c_lessequals @ SV2712 @ SV2585 @ SV789 )
| ~ ( c_lessequals @ SV2225 @ SV1602 @ SV789 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV789 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7820]) ).
thf(8026,plain,
! [SV1605: $i,SV792: $i] :
( ( ( ~ ( class_Power_Opower @ SV792 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1605 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV792 )
!= ( c_HOL_Ozero__class_Ozero @ SV792 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV792 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV792 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV792 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7822]) ).
thf(8027,plain,
! [SV1606: $i,SV2227: $i,SV793: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV2227 @ SV793 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV1606 @ SV793 )
| ( SV1606
= ( c_HOL_Ozero__class_Ozero @ SV793 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV793 ) @ SV1606 ) @ SV2227 )
= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV793 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7823]) ).
thf(8028,plain,
! [SV2229: $i,SV795: $i,SV1608: $i] :
( ( ( c_lessequals @ SV1608 @ SV795 @ tc_nat )
= $false )
| ( ( SV795 = SV2229 )
= $true )
| ( ( c_lessequals @ SV1608 @ SV2229 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV795 @ SV1608 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV2229 @ SV1608 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7824]) ).
thf(8029,plain,
! [SV2713: $i,SV2587: $i,SV2230: $i,SV1609: $i,SV796: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SV2587 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV2230 ) @ SV2713 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV796 ) @ SV1609 ) @ SV2587 )
= SV2713 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV796 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7825]) ).
thf(8030,plain,
! [SV2714: $i,SV1612: $i,SV2233: $i,SV2589: $i,SV799: $i] :
( ( ( c_lessequals @ SV799 @ SV2589 @ tc_nat )
= $false )
| ( ( SV2233
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2589 @ SV799 @ tc_nat ) @ SV1612 @ tc_nat ) ) @ SV2714 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV799 @ SV1612 @ tc_nat ) ) @ SV2233 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV2589 @ SV1612 @ tc_nat ) ) @ SV2714 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7827]) ).
thf(8031,plain,
! [SV2715: $i,SV2592: $i,SV2239: $i,SV1619: $i,SV806: $i] :
( ( ( class_Int_Onumber__ring @ SV806 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2239 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2715 @ SV806 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2715 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2239 @ SV806 ) ) )
| ( SV2239 = SV2715 )
| ( SV1619 = SV2592 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV806 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7829]) ).
thf(8032,plain,
! [SV2777: $i,SV2716: $i,SV2594: $i,SV2241: $i,SV1621: $i,SV808: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV1621 @ SV2241 @ SV808 ) ) @ SV2594 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV2716 @ SV2241 @ SV808 ) ) @ SV2777 ) )
= $true )
| ( ( SV2594
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2716 @ SV1621 @ SV808 ) @ SV2241 @ SV808 ) ) @ SV2777 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV808 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7830]) ).
thf(8033,plain,
! [SV810: $i,SV2243: $i,SV1623: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1623 @ SV2243 @ SV810 )
= ( c_HOL_Ozero__class_Ozero @ SV810 ) )
= $false )
| ( ( SV1623 = SV2243 )
= $true )
| ( ( class_Int_Onumber__ring @ SV810 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV810 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7831]) ).
thf(8034,plain,
! [SV2252: $i,SV823: $i,SV2599: $i,SV1636: $i] :
( ( ( SV1636 = SV2599 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV2599 @ SV823 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV1636 @ SV823 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1636 @ ( c_Suc @ SV2252 ) @ SV823 )
= ( c_Power_Opower__class_Opower @ SV2599 @ ( c_Suc @ SV2252 ) @ SV823 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV823 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7834]) ).
thf(8035,plain,
! [SV2601: $i,SV2259: $i,SV1644: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2259 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2601 ) )
= $true )
| ( ( SV2259 = SV2601 )
= $true )
| ( ( class_Int_Onumber__ring @ SV832 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV832 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7835]) ).
thf(8036,plain,
! [SV2821: $i,SV2778: $i,SV2718: $i,SV2603: $i,SV2264: $i,SV1650: $i,SV838: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
= $false )
| ( ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
| ~ ( c_Type_Otyping @ SV2778 @ SV2603 @ SV1650 )
| ~ ( c_InductTermi_OIT @ SV2603 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2778 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SV2821 )
| ~ ( c_InductTermi_OIT @ SV2264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7837]) ).
thf(8037,plain,
! [SV2265: $i,SV1651: $i,SV839: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV839 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV839 )
| ( ( c_Power_Opower__class_Opower @ SV1651 @ SV2265 @ SV839 )
!= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
| ( SV1651
= ( c_HOL_Ozero__class_Ozero @ SV839 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV839 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV839 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7838]) ).
thf(8038,plain,
! [SV1666: $i,SV2276: $i,SV855: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV2276 @ SV855 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV1666 @ SV855 )
| ( SV2276
= ( c_HOL_Ozero__class_Ozero @ SV855 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV855 ) @ SV1666 ) @ SV2276 )
= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV855 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7839]) ).
thf(8039,plain,
! [SV2822: $i,SV2779: $i,SV2721: $i,SV2609: $i,SV2282: $i,SV1673: $i,SV863: $i] :
( ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
= $false )
| ( ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
| ~ ( c_Type_Otyping @ SV2779 @ SV2609 @ SV863 )
| ~ ( c_InductTermi_OIT @ SV2609 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2779 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SV2822 )
| ~ ( c_InductTermi_OIT @ SV2282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7841]) ).
thf(8040,plain,
! [SV873: $i,SV2615: $i,SV2289: $i,SV1680: $i,SV9: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV2289 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1680 @ SV2615 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV873 @ SV2289 @ SV9 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV2289 @ SV2615 @ SV9 ) @ SV9 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7846]) ).
thf(8041,plain,
! [SV2290: $i,SV13: $i,SV1683: $i,SV877: $i] :
( ( ( c_lessequals @ SV877 @ SV1683 @ SV13 )
= $false )
| ( ( c_lessequals @ SV877 @ SV2290 @ SV13 )
= $false )
| ( ( c_lessequals @ SV877 @ ( c_Orderings_Oord__class_Omin @ SV1683 @ SV2290 @ SV13 ) @ SV13 )
= $true )
| ( ( class_Orderings_Olinorder @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7847]) ).
thf(8042,plain,
! [SV2291: $i,SV14: $i,SV1684: $i,SV878: $i] :
( ( ( c_lessequals @ SV878 @ SV1684 @ SV14 )
= $false )
| ( ( c_lessequals @ SV878 @ SV2291 @ SV14 )
= $false )
| ( ( c_lessequals @ SV878 @ ( c_Orderings_Oord__class_Omin @ SV1684 @ SV2291 @ SV14 ) @ SV14 )
= $true )
| ( ( class_Orderings_Olinorder @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7848]) ).
thf(8043,plain,
! [SV2292: $i,SV15: $i,SV1685: $i,SV879: $i] :
( ( ( c_lessequals @ SV879 @ SV1685 @ SV15 )
= $false )
| ( ( c_lessequals @ SV879 @ SV2292 @ SV15 )
= $false )
| ( ( c_lessequals @ SV879 @ ( c_Orderings_Oord__class_Omin @ SV1685 @ SV2292 @ SV15 ) @ SV15 )
= $true )
| ( ( class_Orderings_Olinorder @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7849]) ).
thf(8044,plain,
! [SV1689: $i,SV20: $i,SV2295: $i,SV884: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV884 @ SV2295 @ SV20 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1689 @ SV2295 @ SV20 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV884 @ SV1689 @ SV20 ) @ SV2295 @ SV20 )
= $true )
| ( ( class_Orderings_Olinorder @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7850]) ).
thf(8045,plain,
! [SV1691: $i,SV22: $i,SV2296: $i,SV886: $i] :
( ( ( ~ ( c_lessequals @ SV886 @ SV2296 @ SV22 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV1691 @ SV22 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV886 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1691 ) @ SV2296 ) @ SV22 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV22 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7851]) ).
thf(8046,plain,
! [SV2298: $i,SV27: $i,SV1696: $i,SV891: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV891 @ SV1696 @ SV27 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV891 @ SV2298 @ SV27 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV891 @ ( c_Orderings_Oord__class_Omin @ SV1696 @ SV2298 @ SV27 ) @ SV27 )
= $true )
| ( ( class_Orderings_Olinorder @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7852]) ).
thf(8047,plain,
! [SV2305: $i,SV915: $i,SV52: $i,SV2619: $i,SV1716: $i] :
( ( ( c_lessequals @ SV1716 @ SV2619 @ SV52 )
= $false )
| ( ( ~ ( c_lessequals @ SV915 @ SV2305 @ SV52 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV915 ) @ SV1716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV2305 ) @ SV2619 ) @ SV52 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7853]) ).
thf(8048,plain,
! [SV1720: $i,SV63: $i,SV2306: $i,SV924: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV924 @ SV2306 @ SV63 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2306 @ SV1720 @ SV63 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV924 @ SV1720 @ SV63 )
= $true )
| ( ( class_Orderings_Opreorder @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7855]) ).
thf(8049,plain,
! [SV925: $i,SV64: $i,SV1721: $i,SV2307: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2307 @ SV1721 @ SV64 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV925 @ SV2307 @ SV64 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV925 @ SV1721 @ SV64 )
= $true )
| ( ( class_Orderings_Oorder @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7856]) ).
thf(8050,plain,
! [SV1732: $i,SV78: $i,SV2311: $i,SV939: $i] :
( ( ( c_lessequals @ SV939 @ SV2311 @ SV78 )
= $false )
| ( ( c_lessequals @ SV1732 @ SV2311 @ SV78 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV939 @ SV1732 @ SV78 ) @ SV2311 @ SV78 )
= $true )
| ( ( class_Orderings_Olinorder @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7857]) ).
thf(8051,plain,
! [SV1733: $i,SV79: $i,SV2312: $i,SV940: $i] :
( ( ( c_lessequals @ SV940 @ SV2312 @ SV79 )
= $false )
| ( ( c_lessequals @ SV1733 @ SV2312 @ SV79 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV940 @ SV1733 @ SV79 ) @ SV2312 @ SV79 )
= $true )
| ( ( class_Orderings_Olinorder @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7858]) ).
thf(8052,plain,
! [SV1734: $i,SV80: $i,SV2313: $i,SV941: $i] :
( ( ( c_lessequals @ SV941 @ SV2313 @ SV80 )
= $false )
| ( ( c_lessequals @ SV1734 @ SV2313 @ SV80 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV941 @ SV1734 @ SV80 ) @ SV2313 @ SV80 )
= $true )
| ( ( class_Orderings_Olinorder @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7859]) ).
thf(8053,plain,
! [SV2853: $i,SV2823: $i,SV2780: $i,SV2722: $i,SV2620: $i,SV2315: $i,SV1738: $i,SV951: $i,SV90: $i] :
( ( ( ( hAPP @ ( hAPP @ SV90 @ ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ SV1738 ) ) @ SV2315 )
= ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ ( c_HOL_Otimes__class_Otimes @ SV1738 @ SV2315 @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2620 @ SV2722 @ SV90 @ SV2780 @ SV2823 @ SV2853 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7860]) ).
thf(8054,plain,
! [SV1741: $i,SV93: $i,SV2318: $i,SV954: $i] :
( ( ( ~ ( c_lessequals @ SV954 @ SV2318 @ SV93 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV1741 @ SV93 ) )
= $true )
| ( ( c_lessequals @ SV954 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV1741 ) @ SV2318 ) @ SV93 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV93 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7861]) ).
thf(8055,plain,
! [SV2319: $i,SV94: $i,SV1742: $i,SV955: $i] :
( ( ( ~ ( c_lessequals @ SV955 @ SV1742 @ SV94 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV2319 @ SV94 ) )
= $true )
| ( ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV1742 ) @ SV2319 ) @ SV94 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV94 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7862]) ).
thf(8056,plain,
! [SV2723: $i,SV1748: $i,SV967: $i,SV2621: $i,SV106: $i,SV2320: $i] :
( ( ( c_lessequals @ SV2320 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2621 @ SV967 @ SV106 ) @ SV1748 @ SV106 ) ) @ SV2723 ) @ SV106 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV967 @ SV1748 @ SV106 ) ) @ SV2320 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV106 ) @ ( c_HOL_Otimes__class_Otimes @ SV2621 @ SV1748 @ SV106 ) ) @ SV2723 ) @ SV106 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7863]) ).
thf(8057,plain,
! [SV2724: $i,SV1749: $i,SV968: $i,SV2622: $i,SV2321: $i,SV107: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV2321 @ SV2622 @ SV107 ) ) @ SV968 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ SV1749 @ SV2622 @ SV107 ) ) @ SV2724 ) @ SV107 )
= $false )
| ( ( c_lessequals @ SV968 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV107 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SV2321 @ SV107 ) @ SV2622 @ SV107 ) ) @ SV2724 ) @ SV107 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7864]) ).
thf(8058,plain,
! [SV2725: $i,SV2322: $i,SV1750: $i,SV2623: $i,SV969: $i,SV108: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV969 @ SV2623 @ SV108 ) @ SV1750 @ SV108 ) ) @ SV2322 ) @ SV2725 @ SV108 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV969 @ SV1750 @ SV108 ) ) @ SV2322 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ SV2623 @ SV1750 @ SV108 ) ) @ SV2725 ) @ SV108 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7865]) ).
thf(8059,plain,
! [SV2726: $i,SV1751: $i,SV2624: $i,SV2323: $i,SV970: $i,SV109: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV970 @ SV2323 @ SV109 ) ) @ SV2624 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ SV1751 @ SV2323 @ SV109 ) ) @ SV2726 ) @ SV109 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV970 @ SV1751 @ SV109 ) @ SV2323 @ SV109 ) ) @ SV2624 ) @ SV2726 @ SV109 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7866]) ).
thf(8060,plain,
! [SV1758: $i,SV119: $i,SV2325: $i,SV980: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV980 @ SV2325 @ SV119 ) @ ( c_HOL_Otimes__class_Otimes @ SV1758 @ SV2325 @ SV119 ) @ SV119 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV2325 @ SV119 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV980 @ SV1758 @ SV119 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7867]) ).
thf(8061,plain,
! [SV1759: $i,SV120: $i,SV981: $i,SV2326: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV981 @ SV120 ) @ ( c_HOL_Otimes__class_Otimes @ SV2326 @ SV1759 @ SV120 ) @ SV120 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV2326 @ SV120 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV981 @ SV1759 @ SV120 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7868]) ).
thf(8062,plain,
! [SV1760: $i,SV121: $i,SV2327: $i,SV982: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV982 @ SV2327 @ SV121 ) @ ( c_HOL_Otimes__class_Otimes @ SV1760 @ SV2327 @ SV121 ) @ SV121 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV2327 @ SV121 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV982 @ SV1760 @ SV121 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7869]) ).
thf(8063,plain,
! [SV1761: $i,SV122: $i,SV983: $i,SV2328: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV983 @ SV122 ) @ ( c_HOL_Otimes__class_Otimes @ SV2328 @ SV1761 @ SV122 ) @ SV122 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV2328 @ SV122 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV983 @ SV1761 @ SV122 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7870]) ).
thf(8064,plain,
! [SV2854: $i,SV2824: $i,SV2781: $i,SV2727: $i,SV2625: $i,SV2331: $i,SV1765: $i,SV989: $i,SV128: $i] :
( ( ( ( hAPP @ ( hAPP @ SV128 @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2331 ) ) @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2625 ) )
= ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2331 ) @ SV2625 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2727 @ SV128 @ SV989 @ SV2781 @ SV2824 @ SV2854 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7872]) ).
thf(8065,plain,
! [SV2728: $i,SV1776: $i,SV1000: $i,SV2626: $i,SV140: $i,SV2341: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2341 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2626 @ SV1000 @ SV140 ) @ SV1776 @ SV140 ) ) @ SV2728 ) @ SV140 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1776 @ SV140 ) ) @ SV2341 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV140 ) @ ( c_HOL_Otimes__class_Otimes @ SV2626 @ SV1776 @ SV140 ) ) @ SV2728 ) @ SV140 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7873]) ).
thf(8066,plain,
! [SV2729: $i,SV1777: $i,SV1001: $i,SV2627: $i,SV2342: $i,SV141: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV2342 @ SV2627 @ SV141 ) ) @ SV1001 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ SV1777 @ SV2627 @ SV141 ) ) @ SV2729 ) @ SV141 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1001 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV141 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1777 @ SV2342 @ SV141 ) @ SV2627 @ SV141 ) ) @ SV2729 ) @ SV141 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7874]) ).
thf(8067,plain,
! [SV2730: $i,SV2343: $i,SV1778: $i,SV2628: $i,SV1002: $i,SV142: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1002 @ SV2628 @ SV142 ) @ SV1778 @ SV142 ) ) @ SV2343 ) @ SV2730 @ SV142 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1778 @ SV142 ) ) @ SV2343 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( c_HOL_Otimes__class_Otimes @ SV2628 @ SV1778 @ SV142 ) ) @ SV2730 ) @ SV142 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7875]) ).
thf(8068,plain,
! [SV2731: $i,SV1779: $i,SV2629: $i,SV2344: $i,SV1003: $i,SV143: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1003 @ SV2344 @ SV143 ) ) @ SV2629 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ SV1779 @ SV2344 @ SV143 ) ) @ SV2731 ) @ SV143 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1003 @ SV1779 @ SV143 ) @ SV2344 @ SV143 ) ) @ SV2629 ) @ SV2731 @ SV143 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7876]) ).
thf(8069,plain,
! [SV1786: $i,SV155: $i,SV2347: $i,SV1015: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1015 @ SV2347 @ SV155 ) @ ( c_Power_Opower__class_Opower @ SV1786 @ SV2347 @ SV155 ) @ SV155 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV1786 @ SV155 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1786 @ SV155 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7882]) ).
thf(8070,plain,
! [SV1815: $i,SV192: $i,SV2360: $i,SV1052: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SV2360 @ SV192 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV1815 @ SV192 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1052 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV1815 ) @ SV2360 ) @ SV192 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV192 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7883]) ).
thf(8071,plain,
! [SV1821: $i,SV199: $i,SV2361: $i,SV1059: $i] :
( ( ( c_lessequals @ SV1059 @ SV2361 @ SV199 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV1059 @ SV199 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1821 @ SV199 ) @ ( c_Power_Opower__class_Opower @ SV2361 @ SV1821 @ SV199 ) @ SV199 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7886]) ).
thf(8072,plain,
! [SV1070: $i,SV1831: $i,SV210: $i,SV2364: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2364 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1831 @ SV210 ) @ ( c_HOL_Otimes__class_Otimes @ SV2364 @ SV1070 @ SV210 ) @ SV210 )
= $false )
| ( ( c_lessequals @ SV1070 @ SV1831 @ SV210 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7887]) ).
thf(8073,plain,
! [SV1832: $i,SV2365: $i,SV211: $i,SV1071: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 )
= $false )
| ( ( c_lessequals @ SV2365 @ SV1832 @ SV211 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV1832 @ SV211 ) @ ( c_HOL_Otimes__class_Otimes @ SV1071 @ SV2365 @ SV211 ) @ SV211 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7888]) ).
thf(8074,plain,
! [SV1833: $i,SV1072: $i,SV2366: $i,SV212: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SV2366 @ SV212 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1072 @ SV212 ) @ ( c_HOL_Otimes__class_Otimes @ SV2366 @ SV1833 @ SV212 ) @ SV212 )
= $false )
| ( ( c_lessequals @ SV1072 @ SV1833 @ SV212 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7889]) ).
thf(8075,plain,
! [SV2367: $i,SV1834: $i,SV1073: $i,SV213: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV1073 @ SV213 )
= $false )
| ( ( c_lessequals @ SV1834 @ SV2367 @ SV213 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV1834 @ SV213 ) @ ( c_HOL_Otimes__class_Otimes @ SV1073 @ SV2367 @ SV213 ) @ SV213 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7890]) ).
thf(8076,plain,
! [SV1835: $i,SV214: $i,SV1074: $i,SV2368: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1074 @ SV214 ) @ ( c_HOL_Otimes__class_Otimes @ SV2368 @ SV1835 @ SV214 ) @ SV214 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV2368 @ SV214 )
= $false )
| ( ( c_lessequals @ SV1074 @ SV1835 @ SV214 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7891]) ).
thf(8077,plain,
! [SV1836: $i,SV215: $i,SV2369: $i,SV1075: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1075 @ SV2369 @ SV215 ) @ ( c_HOL_Otimes__class_Otimes @ SV1836 @ SV2369 @ SV215 ) @ SV215 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV2369 @ SV215 )
= $false )
| ( ( c_lessequals @ SV1075 @ SV1836 @ SV215 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7892]) ).
thf(8078,plain,
! [SV1849: $i,SV2378: $i,SV1092: $i,SV235: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV235 ) @ SV1092 @ SV235 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SV2378 @ SV235 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1849 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1092 @ SV1849 @ SV235 ) @ ( c_Power_Opower__class_Opower @ SV2378 @ SV1849 @ SV235 ) @ SV235 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7894]) ).
thf(8079,plain,
! [SV2407: $i,SV1174: $i,SV320: $i,SV2640: $i,SV1910: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1910 @ SV2640 @ SV320 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SV2407 @ SV320 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV1174 ) @ SV1910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV2407 ) @ SV2640 ) @ SV320 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7908]) ).
thf(8080,plain,
! [SV2855: $i,SV2825: $i,SV2782: $i,SV2733: $i,SV2641: $i,SV2416: $i,SV1936: $i,SV1206: $i,SV352: $i] :
( ( ( ( hAPP @ ( hAPP @ SV352 @ ( hAPP @ ( hAPP @ SV1206 @ SV1936 ) @ SV2416 ) ) @ SV2641 )
= ( hAPP @ ( hAPP @ SV1206 @ ( hAPP @ ( hAPP @ SV352 @ SV1936 ) @ SV2641 ) ) @ ( hAPP @ ( hAPP @ SV352 @ SV2416 ) @ SV2641 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2733 @ SV1206 @ SV352 @ SV2782 @ SV2825 @ SV2855 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7918]) ).
thf(8081,plain,
! [SV2856: $i,SV2826: $i,SV2783: $i,SV2734: $i,SV2642: $i,SV2417: $i,SV1937: $i,SV1207: $i,SV353: $i] :
( ( ( ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ ( hAPP @ ( hAPP @ SV1937 @ SV2417 ) @ SV2642 ) )
= ( hAPP @ ( hAPP @ SV1937 @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2417 ) ) @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2642 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1937 @ SV353 @ SV2734 @ SV2783 @ SV2826 @ SV2856 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7919]) ).
thf(8082,plain,
! [SV1938: $i,SV1208: $i,SV2827: $i,SV2784: $i,SV2735: $i,SV2643: $i,SV354: $i,SV2418: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2418 @ SV354 @ SV2643 @ SV2735 @ SV2784 @ SV2827 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV354 @ SV1208 ) @ SV1938 )
= ( hAPP @ ( hAPP @ SV354 @ SV1938 ) @ SV1208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7920]) ).
thf(8083,plain,
! [SV2857: $i,SV2828: $i,SV2785: $i,SV2736: $i,SV2644: $i,SV2419: $i,SV1939: $i,SV1209: $i,SV355: $i] :
( ( ( ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ ( hAPP @ ( hAPP @ SV355 @ SV1939 ) @ SV2419 ) )
= ( hAPP @ ( hAPP @ SV355 @ ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ SV1939 ) ) @ SV2419 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2644 @ SV355 @ SV2736 @ SV2785 @ SV2828 @ SV2857 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7921]) ).
thf(8084,plain,
! [SV1942: $i,SV1212: $i,SV2829: $i,SV2788: $i,SV2739: $i,SV2647: $i,SV2422: $i,SV358: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV358 @ SV2422 @ SV2647 @ SV2739 @ SV2788 @ SV2829 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV358 @ SV1212 ) @ SV1942 )
= ( hAPP @ ( hAPP @ SV358 @ SV1942 ) @ SV1212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7924]) ).
thf(8085,plain,
! [SV2858: $i,SV2830: $i,SV2789: $i,SV2740: $i,SV2648: $i,SV2423: $i,SV1943: $i,SV1213: $i,SV359: $i] :
( ( ( ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ ( hAPP @ ( hAPP @ SV359 @ SV1943 ) @ SV2423 ) )
= ( hAPP @ ( hAPP @ SV359 @ ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ SV1943 ) ) @ SV2423 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV359 @ SV2648 @ SV2740 @ SV2789 @ SV2830 @ SV2858 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7925]) ).
thf(8086,plain,
! [SV2859: $i,SV2831: $i,SV2791: $i,SV2742: $i,SV2650: $i,SV2425: $i,SV1945: $i,SV1215: $i,SV361: $i] :
( ( ( ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ ( hAPP @ ( hAPP @ SV361 @ SV1945 ) @ SV2425 ) )
= ( hAPP @ ( hAPP @ SV361 @ ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ SV1945 ) ) @ SV2425 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV361 @ SV2650 @ SV2742 @ SV2791 @ SV2831 @ SV2859 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7927]) ).
thf(8087,plain,
! [SV1946: $i,SV1216: $i,SV2832: $i,SV2792: $i,SV2743: $i,SV2651: $i,SV2426: $i,SV362: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV362 @ SV2426 @ SV2651 @ SV2743 @ SV2792 @ SV2832 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV362 @ SV1216 ) @ SV1946 )
= ( hAPP @ ( hAPP @ SV362 @ SV1946 ) @ SV1216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7928]) ).
thf(8088,plain,
! [SV2860: $i,SV2833: $i,SV2793: $i,SV2744: $i,SV2652: $i,SV2427: $i,SV1947: $i,SV1217: $i,SV363: $i] :
( ( ( ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV1947 ) ) @ SV2427 )
= ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV2427 ) ) @ SV1947 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV363 @ SV2652 @ SV2744 @ SV2793 @ SV2833 @ SV2860 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7929]) ).
thf(8089,plain,
! [SV2861: $i,SV2834: $i,SV2794: $i,SV2745: $i,SV2653: $i,SV2428: $i,SV1948: $i,SV1218: $i,SV364: $i] :
( ( ( ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ SV2428 ) )
= ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ SV2428 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV364 @ SV2653 @ SV2745 @ SV2794 @ SV2834 @ SV2861 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7930]) ).
thf(8090,plain,
! [SV2862: $i,SV2835: $i,SV2795: $i,SV2746: $i,SV2654: $i,SV2429: $i,SV1949: $i,SV1219: $i,SV365: $i] :
( ( ( ( hAPP @ ( hAPP @ SV365 @ ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ SV1949 ) ) @ SV2429 )
= ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ ( hAPP @ ( hAPP @ SV365 @ SV1949 ) @ SV2429 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV365 @ SV2654 @ SV2746 @ SV2795 @ SV2835 @ SV2862 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7931]) ).
thf(8091,plain,
! [SV2873: $i,SV2863: $i,SV2836: $i,SV2796: $i,SV2747: $i,SV2655: $i,SV2430: $i,SV1950: $i,SV1220: $i,SV366: $i] :
( ( ( ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV1950 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV2430 ) @ SV2655 ) )
= ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV2430 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV1950 ) @ SV2655 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV366 @ SV2747 @ SV2796 @ SV2836 @ SV2863 @ SV2873 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7932]) ).
thf(8092,plain,
! [SV2864: $i,SV2837: $i,SV2797: $i,SV2748: $i,SV2656: $i,SV2431: $i,SV1951: $i,SV1221: $i,SV367: $i] :
( ( ( ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ SV2431 ) )
= ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ SV2431 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2656 @ SV367 @ SV2748 @ SV2797 @ SV2837 @ SV2864 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7933]) ).
thf(8093,plain,
! [SV2865: $i,SV2838: $i,SV2798: $i,SV2749: $i,SV2657: $i,SV2432: $i,SV1952: $i,SV1222: $i,SV368: $i] :
( ( ( ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ ( hAPP @ ( hAPP @ SV368 @ SV1952 ) @ SV2432 ) )
= ( hAPP @ ( hAPP @ SV368 @ ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ SV1952 ) ) @ SV2432 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2657 @ SV368 @ SV2749 @ SV2798 @ SV2838 @ SV2865 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7934]) ).
thf(8094,plain,
! [SV2866: $i,SV2839: $i,SV2799: $i,SV2750: $i,SV2658: $i,SV2433: $i,SV1953: $i,SV1223: $i,SV369: $i] :
( ( ( ( hAPP @ ( hAPP @ SV369 @ ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ SV1953 ) ) @ SV2433 )
= ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ ( hAPP @ ( hAPP @ SV369 @ SV1953 ) @ SV2433 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2658 @ SV369 @ SV2750 @ SV2799 @ SV2839 @ SV2866 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7935]) ).
thf(8095,plain,
! [SV2867: $i,SV2840: $i,SV2800: $i,SV2751: $i,SV2659: $i,SV2434: $i,SV1954: $i,SV1224: $i,SV370: $i] :
( ( ( ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV1954 ) ) @ SV2434 )
= ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV2434 ) ) @ SV1954 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2659 @ SV370 @ SV2751 @ SV2800 @ SV2840 @ SV2867 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7936]) ).
thf(8096,plain,
! [SV2874: $i,SV2868: $i,SV2841: $i,SV2801: $i,SV2752: $i,SV2660: $i,SV2435: $i,SV1955: $i,SV1225: $i,SV371: $i] :
( ( ( ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ SV2660 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ SV2660 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2752 @ SV371 @ SV2801 @ SV2841 @ SV2868 @ SV2874 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7937]) ).
thf(8097,plain,
! [SV2875: $i,SV2869: $i,SV2842: $i,SV2802: $i,SV2753: $i,SV2661: $i,SV2436: $i,SV1956: $i,SV1226: $i,SV372: $i] :
( ( ( ( hAPP @ ( hAPP @ SV372 @ ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ SV1956 ) ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) )
= ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ ( hAPP @ ( hAPP @ SV372 @ SV1956 ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2753 @ SV372 @ SV2802 @ SV2842 @ SV2869 @ SV2875 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7938]) ).
thf(8098,plain,
! [SV2876: $i,SV2870: $i,SV2843: $i,SV2803: $i,SV2754: $i,SV2662: $i,SV2437: $i,SV1957: $i,SV1227: $i,SV373: $i] :
( ( ( ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV1957 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV2437 ) @ SV2662 ) )
= ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV2437 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV1957 ) @ SV2662 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV2754 @ SV373 @ SV2803 @ SV2843 @ SV2870 @ SV2876 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7939]) ).
thf(8099,plain,
! [SV2871: $i,SV2844: $i,SV2808: $i,SV2759: $i,SV2667: $i,SV2442: $i,SV1962: $i,SV1232: $i,SV378: $i] :
( ( ( ( hAPP @ ( hAPP @ SV378 @ ( hAPP @ ( hAPP @ SV1232 @ SV1962 ) @ SV2442 ) ) @ SV2667 )
= ( hAPP @ ( hAPP @ SV1232 @ ( hAPP @ ( hAPP @ SV378 @ SV1962 ) @ SV2667 ) ) @ ( hAPP @ ( hAPP @ SV378 @ SV2442 ) @ SV2667 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1232 @ SV378 @ SV2759 @ SV2808 @ SV2844 @ SV2871 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7944]) ).
thf(8100,plain,
! [SV1963: $i,SV1233: $i,SV2845: $i,SV2809: $i,SV2760: $i,SV2668: $i,SV379: $i,SV2443: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2443 @ SV379 @ SV2668 @ SV2760 @ SV2809 @ SV2845 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV379 @ SV1233 ) @ SV1963 )
= ( hAPP @ ( hAPP @ SV379 @ SV1963 ) @ SV1233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7945]) ).
thf(8101,plain,
! [SV2447: $i,SV1237: $i,SV2846: $i,SV2672: $i,SV2813: $i,SV2764: $i,SV1967: $i,SV383: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV383 @ SV1967 @ SV2764 @ SV2813 @ SV2672 @ SV2846 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV383 @ SV1237 ) @ ( hAPP @ ( hAPP @ SV1967 @ SV2447 ) @ SV1237 ) )
= ( hAPP @ ( hAPP @ SV1967 @ ( hAPP @ ( hAPP @ SV383 @ SV2447 ) @ SV2672 ) ) @ SV1237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7949]) ).
thf(8102,plain,
! [SV2448: $i,SV1968: $i,SV2847: $i,SV2673: $i,SV2814: $i,SV2765: $i,SV1238: $i,SV384: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV384 @ SV1238 @ SV2765 @ SV2814 @ SV2673 @ SV2847 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV384 @ ( hAPP @ ( hAPP @ SV1238 @ SV1968 ) @ SV2448 ) ) @ SV2448 )
= ( hAPP @ ( hAPP @ SV1238 @ ( hAPP @ ( hAPP @ SV384 @ SV1968 ) @ SV2673 ) ) @ SV2448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7950]) ).
thf(8103,plain,
! [SV2872: $i,SV2848: $i,SV2815: $i,SV2766: $i,SV2674: $i,SV2449: $i,SV1969: $i,SV1239: $i,SV385: $i] :
( ( ( ( hAPP @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ SV1239 @ SV1969 ) @ SV2449 ) ) @ ( hAPP @ ( hAPP @ SV1239 @ SV2674 ) @ SV2449 ) )
= ( hAPP @ ( hAPP @ SV1239 @ ( hAPP @ ( hAPP @ SV385 @ SV1969 ) @ SV2674 ) ) @ SV2449 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV385 @ SV1239 @ SV2766 @ SV2815 @ SV2848 @ SV2872 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[7951]) ).
thf(8104,plain,
! [SV2465: $i,SV1281: $i,SV2849: $i,SV2816: $i,SV2767: $i,SV2003: $i,SV433: $i,SV2676: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2676 @ SV433 @ SV2003 @ SV2767 @ SV2816 @ SV2849 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV433 @ SV1281 ) @ ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ SV2465 ) )
= ( hAPP @ ( hAPP @ SV2003 @ SV1281 ) @ ( c_Suc @ SV2465 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7956]) ).
thf(8105,plain,
! [SV2466: $i,SV2004: $i,SV2850: $i,SV2817: $i,SV2768: $i,SV1282: $i,SV434: $i,SV2677: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2677 @ SV434 @ SV1282 @ SV2768 @ SV2817 @ SV2850 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV434 @ ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ SV2466 ) ) @ SV2004 )
= ( hAPP @ ( hAPP @ SV1282 @ SV2004 ) @ ( c_Suc @ SV2466 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7957]) ).
thf(8106,plain,
! [SV2005: $i,SV1283: $i,SV2851: $i,SV2818: $i,SV2769: $i,SV435: $i,SV2467: $i,SV2678: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2678 @ SV2467 @ SV435 @ SV2769 @ SV2818 @ SV2851 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ ( c_Suc @ SV2005 ) )
= ( hAPP @ ( hAPP @ SV2467 @ SV1283 ) @ ( hAPP @ ( hAPP @ SV435 @ SV1283 ) @ SV2005 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7958]) ).
thf(8107,plain,
! [SV2006: $i,SV1284: $i,SV2852: $i,SV2819: $i,SV2770: $i,SV436: $i,SV2468: $i,SV2679: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2679 @ SV2468 @ SV436 @ SV2770 @ SV2819 @ SV2852 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ ( c_Suc @ SV2006 ) )
= ( hAPP @ ( hAPP @ SV2468 @ SV1284 ) @ ( hAPP @ ( hAPP @ SV436 @ SV1284 ) @ SV2006 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[7959]) ).
thf(8108,plain,
! [SV2012: $i,SV442: $i,SV2470: $i,SV1290: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1290 @ ( c_Suc @ SV2470 ) @ SV442 ) @ ( c_Power_Opower__class_Opower @ SV2012 @ ( c_Suc @ SV2470 ) @ SV442 ) @ SV442 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV442 ) @ SV2012 @ SV442 )
= $false )
| ( ( c_lessequals @ SV1290 @ SV2012 @ SV442 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV442 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7960]) ).
thf(8109,plain,
! [SV2472: $i,SV2680: $i,SV1295: $i,SV2015: $i,SV447: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
| ~ ( c_lessequals @ SV2015 @ SV2680 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SV2472 @ SV447 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SV2472 @ SV2680 @ SV447 ) @ SV447 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7961]) ).
thf(8110,plain,
! [SV2473: $i,SV2681: $i,SV1296: $i,SV2016: $i,SV448: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
| ~ ( c_HOL_Oord__class_Oless @ SV2016 @ SV2681 @ SV448 )
| ~ ( c_lessequals @ SV1296 @ SV2473 @ SV448 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SV2473 @ SV2681 @ SV448 ) @ SV448 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7962]) ).
thf(8111,plain,
! [SV2475: $i,SV1313: $i,SV2029: $i,SV466: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV2029 @ SV466 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1313 @ SV2475 @ SV466 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1313 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ SV2029 ) @ SV2475 ) @ SV466 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7968]) ).
thf(8112,plain,
! [SV2033: $i,SV474: $i,SV1321: $i,SV2476: $i] :
( ( ( c_lessequals @ SV2476 @ SV1321 @ SV474 )
= $false )
| ( ( c_lessequals @ SV2033 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1321 @ SV2033 @ SV474 ) @ ( c_HOL_Otimes__class_Otimes @ SV2476 @ SV2033 @ SV474 ) @ SV474 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7969]) ).
thf(8113,plain,
! [SV1322: $i,SV475: $i,SV2034: $i,SV2477: $i] :
( ( ( c_lessequals @ SV2477 @ SV2034 @ SV475 )
= $false )
| ( ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2034 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1322 @ SV2477 @ SV475 ) @ SV475 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV475 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7970]) ).
thf(8114,plain,
! [SV2035: $i,SV476: $i,SV2478: $i,SV1323: $i] :
( ( ( c_lessequals @ SV1323 @ SV2478 @ SV476 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV2035 @ SV476 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1323 @ SV2035 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SV2478 @ SV2035 @ SV476 ) @ SV476 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7971]) ).
thf(8115,plain,
! [SV1324: $i,SV477: $i,SV2479: $i,SV2036: $i] :
( ( ( c_lessequals @ SV2036 @ SV2479 @ SV477 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV477 ) @ SV1324 @ SV477 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2036 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1324 @ SV2479 @ SV477 ) @ SV477 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7972]) ).
thf(8116,plain,
! [SV1325: $i,SV478: $i,SV2480: $i,SV2037: $i] :
( ( ( c_lessequals @ SV2037 @ SV2480 @ SV478 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV478 ) @ SV1325 @ SV478 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2037 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1325 @ SV2480 @ SV478 ) @ SV478 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono1 @ SV478 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7973]) ).
thf(8117,plain,
! [SV1339: $i,SV492: $i,SV2050: $i,SV2487: $i] :
( ( ( c_lessequals @ SV2487 @ SV2050 @ SV492 )
= $false )
| ( ( c_lessequals @ SV1339 @ SV2487 @ SV492 )
= $false )
| ( ( c_lessequals @ SV1339 @ SV2050 @ SV492 )
= $true )
| ( ( class_Orderings_Oorder @ SV492 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7974]) ).
thf(8118,plain,
! [SV1340: $i,SV493: $i,SV2051: $i,SV2488: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2488 @ SV2051 @ SV493 )
= $false )
| ( ( c_lessequals @ SV1340 @ SV2488 @ SV493 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1340 @ SV2051 @ SV493 )
= $true )
| ( ( class_Orderings_Oorder @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7975]) ).
thf(8119,plain,
! [SV1341: $i,SV494: $i,SV2052: $i,SV2489: $i] :
( ( ( c_lessequals @ SV2489 @ SV2052 @ SV494 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1341 @ SV2489 @ SV494 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1341 @ SV2052 @ SV494 )
= $true )
| ( ( class_Orderings_Oorder @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7976]) ).
thf(8120,plain,
! [SV2054: $i,SV496: $i,SV2490: $i,SV1343: $i] :
( ( ( c_lessequals @ SV1343 @ SV2490 @ SV496 )
= $false )
| ( ( c_lessequals @ SV2490 @ SV2054 @ SV496 )
= $false )
| ( ( c_lessequals @ SV1343 @ SV2054 @ SV496 )
= $true )
| ( ( class_Orderings_Opreorder @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7978]) ).
thf(8121,plain,
! [SV1355: $i,SV2062: $i,SV511: $i,SV2491: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2491 @ ( c_HOL_Ozero__class_Ozero @ SV511 ) @ SV511 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV2062 @ SV511 ) @ ( c_HOL_Otimes__class_Otimes @ SV2491 @ SV1355 @ SV511 ) @ SV511 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1355 @ SV2062 @ SV511 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV511 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7979]) ).
thf(8122,plain,
! [SV2063: $i,SV2492: $i,SV512: $i,SV1356: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1356 @ ( c_HOL_Ozero__class_Ozero @ SV512 ) @ SV512 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2492 @ SV2063 @ SV512 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2063 @ SV512 ) @ ( c_HOL_Otimes__class_Otimes @ SV1356 @ SV2492 @ SV512 ) @ SV512 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV512 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7980]) ).
thf(8123,plain,
! [SV2064: $i,SV1357: $i,SV2493: $i,SV513: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV513 ) @ SV2493 @ SV513 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV1357 @ SV513 ) @ ( c_HOL_Otimes__class_Otimes @ SV2493 @ SV2064 @ SV513 ) @ SV513 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1357 @ SV2064 @ SV513 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7981]) ).
thf(8124,plain,
! [SV2494: $i,SV2065: $i,SV1358: $i,SV514: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SV1358 @ SV514 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2065 @ SV2494 @ SV514 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2065 @ SV514 ) @ ( c_HOL_Otimes__class_Otimes @ SV1358 @ SV2494 @ SV514 ) @ SV514 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7982]) ).
thf(8125,plain,
! [SV1359: $i,SV515: $i,SV2066: $i,SV2495: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2495 @ SV2066 @ SV515 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1359 @ ( c_HOL_Ozero__class_Ozero @ SV515 ) @ SV515 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2066 @ SV515 ) @ ( c_HOL_Otimes__class_Otimes @ SV1359 @ SV2495 @ SV515 ) @ SV515 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV515 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7983]) ).
thf(8126,plain,
! [SV1360: $i,SV516: $i,SV2496: $i,SV2067: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2067 @ SV2496 @ SV516 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV516 ) @ SV1360 @ SV516 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2067 @ SV516 ) @ ( c_HOL_Otimes__class_Otimes @ SV1360 @ SV2496 @ SV516 ) @ SV516 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV516 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7984]) ).
thf(8127,plain,
! [SV2497: $i,SV2068: $i,SV1361: $i,SV517: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1361 @ SV517 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2068 @ SV2497 @ SV517 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2068 @ SV517 ) @ ( c_HOL_Otimes__class_Otimes @ SV1361 @ SV2497 @ SV517 ) @ SV517 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV517 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7985]) ).
thf(8128,plain,
! [SV2069: $i,SV2498: $i,SV518: $i,SV1362: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1362 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2498 @ SV2069 @ SV518 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2069 @ SV518 ) @ ( c_HOL_Otimes__class_Otimes @ SV1362 @ SV2498 @ SV518 ) @ SV518 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV518 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7986]) ).
thf(8129,plain,
! [SV2070: $i,SV519: $i,SV1363: $i,SV2499: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2499 @ SV1363 @ SV519 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2070 @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV519 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1363 @ SV2070 @ SV519 ) @ ( c_HOL_Otimes__class_Otimes @ SV2499 @ SV2070 @ SV519 ) @ SV519 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV519 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7987]) ).
thf(8130,plain,
! [SV2071: $i,SV520: $i,SV2500: $i,SV1364: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1364 @ SV2500 @ SV520 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV2071 @ SV520 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1364 @ SV2071 @ SV520 ) @ ( c_HOL_Otimes__class_Otimes @ SV2500 @ SV2071 @ SV520 ) @ SV520 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV520 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7988]) ).
thf(8131,plain,
! [SV2501: $i,SV1365: $i,SV2072: $i,SV521: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV521 ) @ SV2072 @ SV521 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1365 @ SV2501 @ SV521 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1365 @ SV2072 @ SV521 ) @ ( c_HOL_Otimes__class_Otimes @ SV2501 @ SV2072 @ SV521 ) @ SV521 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV521 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7989]) ).
thf(8132,plain,
! [SV1366: $i,SV2502: $i,SV522: $i,SV2073: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2073 @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV522 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2502 @ SV1366 @ SV522 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1366 @ SV2073 @ SV522 ) @ ( c_HOL_Otimes__class_Otimes @ SV2502 @ SV2073 @ SV522 ) @ SV522 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV522 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7990]) ).
thf(8133,plain,
! [SV1367: $i,SV523: $i,SV2503: $i,SV2074: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2074 @ SV2503 @ SV523 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV1367 @ SV523 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2074 @ SV523 ) @ ( c_HOL_Otimes__class_Otimes @ SV1367 @ SV2503 @ SV523 ) @ SV523 )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7991]) ).
thf(8134,plain,
! [SV1372: $i,SV2682: $i,SV2506: $i,SV2078: $i,SV529: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2506 @ SV529 )
| ~ ( c_lessequals @ SV2078 @ SV2682 @ SV529 )
| ~ ( c_lessequals @ SV1372 @ SV2506 @ SV529 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SV2506 @ SV2682 @ SV529 ) @ SV529 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7992]) ).
thf(8135,plain,
! [SV2507: $i,SV2683: $i,SV1373: $i,SV2079: $i,SV530: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
| ~ ( c_lessequals @ SV2079 @ SV2683 @ SV530 )
| ~ ( c_lessequals @ SV1373 @ SV2507 @ SV530 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SV2507 @ SV2683 @ SV530 ) @ SV530 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7993]) ).
thf(8136,plain,
! [SV2513: $i,SV1391: $i,SV550: $i,SV2685: $i,SV2092: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2092 @ SV2685 @ SV550 )
= $false )
| ( ( ~ ( c_lessequals @ SV1391 @ SV2513 @ SV550 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV1391 ) @ SV2092 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV2513 ) @ SV2685 ) @ SV550 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV550 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7994]) ).
thf(8137,plain,
! [SV2514: $i,SV1392: $i,SV551: $i,SV2686: $i,SV2093: $i] :
( ( ( c_lessequals @ SV2093 @ SV2686 @ SV551 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1392 @ SV2514 @ SV551 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV1392 ) @ SV2093 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV2514 ) @ SV2686 ) @ SV551 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV551 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7995]) ).
thf(8138,plain,
! [SV2095: $i,SV586: $i,SV2515: $i,SV1425: $i] :
( ( ( c_lessequals @ SV1425 @ SV2515 @ SV586 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2515 @ SV2095 @ SV586 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1425 @ SV2095 @ SV586 )
= $true )
| ( ( class_Orderings_Opreorder @ SV586 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7996]) ).
thf(8139,plain,
! [SV2096: $i,SV587: $i,SV2516: $i,SV1426: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1426 @ SV2516 @ SV587 )
= $false )
| ( ( c_lessequals @ SV2516 @ SV2096 @ SV587 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1426 @ SV2096 @ SV587 )
= $true )
| ( ( class_Orderings_Opreorder @ SV587 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7997]) ).
thf(8140,plain,
! [SV2097: $i,SV1427: $i,SV588: $i,SV2517: $i,SV2687: $i] :
( ( ( c_lessequals @ SV2687 @ SV2517 @ SV588 )
= $false )
| ( ( ~ ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2687 ) @ SV588 ) )
= $true )
| ( ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2517 ) @ SV588 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV588 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7998]) ).
thf(8141,plain,
! [SV2518: $i,SV2688: $i,SV1433: $i,SV2101: $i,SV594: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV2101 @ SV2688 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SV2518 @ SV594 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SV2518 @ SV2688 @ SV594 ) @ SV594 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8000]) ).
thf(8142,plain,
! [SV1540: $i,SV723: $i] :
( ( ( class_Power_Opower @ SV723 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV723 ) @ SV1540 @ SV723 )
= ( c_HOL_Ozero__class_Ozero @ SV723 ) )
| ( SV1540
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV723 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV723 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV723 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8013]) ).
thf(8143,plain,
! [SV1544: $i,SV2775: $i,SV2700: $i,SV2183: $i,SV2560: $i,SV728: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV728 @ SV2560 @ SV2183 @ tc_Type_Otype ) @ SV2700 @ SV2775 )
= $false )
| ( ( c_Type_Otyping @ SV728 @ ( c_Lambda_Osubst @ SV2700 @ SV1544 @ SV2560 ) @ SV2775 )
= $true )
| ( ( c_Type_Otyping @ SV728 @ SV1544 @ SV2183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8015]) ).
thf(8144,plain,
! [SV2564: $i,SV2702: $i,SV737: $i,SV1553: $i,SV2188: $i] :
( ( ( c_lessequals @ SV2188 @ SV1553 @ SV737 )
= $true )
| ( ( ~ ( c_lessequals @ SV2702 @ SV2564 @ SV737 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1553 @ SV2188 @ SV737 )
= ( c_HOL_Ominus__class_Ominus @ SV2564 @ SV2702 @ SV737 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV737 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8016]) ).
thf(8145,plain,
! [SV2776: $i,SV2705: $i,SV2569: $i,SV2199: $i,SV1566: $i,SV750: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV1566 @ SV2199 @ SV750 ) ) @ SV2569 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ SV2705 @ SV2199 @ SV750 ) ) @ SV2776 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV750 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ SV2705 @ SV750 ) @ SV2199 @ SV750 ) ) @ SV2569 )
= SV2776 )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV750 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8018]) ).
thf(8146,plain,
! [SV2205: $i,SV1576: $i,SV760: $i,SV2706: $i,SV2574: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2574 @ SV2706 @ SV760 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1576 @ SV2205 @ SV760 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV2205 @ SV760 )
= ( c_HOL_Ominus__class_Ominus @ SV2574 @ SV2706 @ SV760 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV760 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8019]) ).
thf(8147,plain,
! [SV1579: $i,SV2575: $i,SV763: $i,SV2208: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2208 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV2575 @ SV763 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 ) )
= $true )
| ( ( SV1579 = SV2575 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1579 @ SV2208 @ SV763 )
= ( c_Power_Opower__class_Opower @ SV2575 @ SV2208 @ SV763 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV763 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8020]) ).
thf(8148,plain,
! [SV2707: $i,SV2578: $i,SV2215: $i,SV1589: $i,SV774: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2578 @ SV774 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2707 @ SV774 ) ) )
= $true )
| ( ( ( SV2578 = SV2707 )
| ( SV2215
= ( c_HOL_Ozero__class_Ozero @ SV774 ) ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV774 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV774 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8022]) ).
thf(8149,plain,
! [SV2709: $i,SV2580: $i,SV778: $i,SV2217: $i,SV1592: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1592 @ SV2217 @ SV778 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2580 @ SV2709 @ SV778 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1592 @ SV2217 @ SV778 )
= ( c_HOL_Ominus__class_Ominus @ SV2580 @ SV2709 @ SV778 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV778 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8023]) ).
thf(8150,plain,
! [SV2711: $i,SV2584: $i,SV2224: $i,SV1600: $i,SV787: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2224 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2711 @ SV787 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2711 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2224 @ SV787 ) ) )
= $true )
| ( ( ( SV2224 = SV2711 )
| ( SV1600 = SV2584 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV787 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV787 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8024]) ).
thf(8151,plain,
! [SV1602: $i,SV2225: $i,SV789: $i,SV2585: $i,SV2712: $i] :
( ( ( c_lessequals @ SV2712 @ SV2585 @ SV789 )
= $true )
| ( ( ~ ( c_lessequals @ SV2225 @ SV1602 @ SV789 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1602 @ SV2225 @ SV789 )
= ( c_HOL_Ominus__class_Ominus @ SV2585 @ SV2712 @ SV789 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV789 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8025]) ).
thf(8152,plain,
! [SV1605: $i,SV792: $i] :
( ( ( class_Power_Opower @ SV792 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV1605 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV792 )
!= ( c_HOL_Ozero__class_Ozero @ SV792 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV792 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV792 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV792 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8026]) ).
thf(8153,plain,
! [SV2227: $i,SV1606: $i,SV793: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV1606 @ SV793 ) )
= $true )
| ( ( SV1606
= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV2227 @ SV793 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV793 ) @ SV1606 ) @ SV2227 )
= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV793 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8027]) ).
thf(8154,plain,
! [SV2715: $i,SV2592: $i,SV2239: $i,SV1619: $i,SV806: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2239 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2715 @ SV806 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2715 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2239 @ SV806 ) ) )
= $true )
| ( ( ( SV2239 = SV2715 )
| ( SV1619 = SV2592 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV806 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV806 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8031]) ).
thf(8155,plain,
! [SV2777: $i,SV2716: $i,SV2594: $i,SV2241: $i,SV1621: $i,SV808: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV1621 @ SV2241 @ SV808 ) ) @ SV2594 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ SV2716 @ SV2241 @ SV808 ) ) @ SV2777 ) )
= $false )
| ( ( SV2594
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV808 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2716 @ SV1621 @ SV808 ) @ SV2241 @ SV808 ) ) @ SV2777 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV808 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8032]) ).
thf(8156,plain,
! [SV2252: $i,SV1636: $i,SV2599: $i,SV823: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV2599 @ SV823 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV1636 @ SV823 ) )
= $true )
| ( ( SV1636 = SV2599 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1636 @ ( c_Suc @ SV2252 ) @ SV823 )
= ( c_Power_Opower__class_Opower @ SV2599 @ ( c_Suc @ SV2252 ) @ SV823 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV823 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8034]) ).
thf(8157,plain,
! [SV2601: $i,SV2259: $i,SV1644: $i,SV832: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2259 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV832 ) @ SV1644 ) @ SV2601 ) )
= $false )
| ( ( SV2259 = SV2601 )
= $true )
| ( ( class_Int_Onumber__ring @ SV832 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV832 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8035]) ).
thf(8158,plain,
! [SV838: $i,SV2821: $i,SV1650: $i,SV2778: $i,SV2718: $i,SV2603: $i,SV2264: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV2778 @ SV2603 @ SV1650 )
| ~ ( c_InductTermi_OIT @ SV2603 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2778 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SV2821 )
| ~ ( c_InductTermi_OIT @ SV2264 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8036]) ).
thf(8159,plain,
! [SV2265: $i,SV1651: $i,SV839: $i] :
( ( ( ~ ( class_Power_Opower @ SV839 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1651 @ SV2265 @ SV839 )
!= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
| ( SV1651
= ( c_HOL_Ozero__class_Ozero @ SV839 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV839 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV839 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV839 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8037]) ).
thf(8160,plain,
! [SV2276: $i,SV1666: $i,SV855: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV1666 @ SV855 ) )
= $true )
| ( ( SV2276
= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV2276 @ SV855 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV855 ) @ SV1666 ) @ SV2276 )
= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV855 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8038]) ).
thf(8161,plain,
! [SV1673: $i,SV2822: $i,SV863: $i,SV2779: $i,SV2721: $i,SV2609: $i,SV2282: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV2779 @ SV2609 @ SV863 )
| ~ ( c_InductTermi_OIT @ SV2609 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2779 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SV2822 )
| ~ ( c_InductTermi_OIT @ SV2282 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8039]) ).
thf(8162,plain,
! [SV873: $i,SV2615: $i,SV1680: $i,SV2289: $i,SV9: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV2289 @ SV9 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1680 @ SV2615 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV873 @ SV2289 @ SV9 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV2289 @ SV2615 @ SV9 ) @ SV9 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8040]) ).
thf(8163,plain,
! [SV1691: $i,SV22: $i,SV2296: $i,SV886: $i] :
( ( ( c_lessequals @ SV886 @ SV2296 @ SV22 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV1691 @ SV22 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV886 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1691 ) @ SV2296 ) @ SV22 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV22 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8045]) ).
thf(8164,plain,
! [SV2619: $i,SV1716: $i,SV52: $i,SV2305: $i,SV915: $i] :
( ( ( c_lessequals @ SV915 @ SV2305 @ SV52 )
= $false )
| ( ( c_lessequals @ SV1716 @ SV2619 @ SV52 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV915 ) @ SV1716 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV2305 ) @ SV2619 ) @ SV52 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8047]) ).
thf(8165,plain,
! [SV2315: $i,SV1738: $i,SV951: $i,SV2853: $i,SV2823: $i,SV2780: $i,SV90: $i,SV2722: $i,SV2620: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2620 @ SV2722 @ SV90 @ SV2780 @ SV2823 @ SV2853 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV90 @ ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ SV1738 ) ) @ SV2315 )
= ( hAPP @ ( hAPP @ SV90 @ SV951 ) @ ( c_HOL_Otimes__class_Otimes @ SV1738 @ SV2315 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8053]) ).
thf(8166,plain,
! [SV1741: $i,SV93: $i,SV2318: $i,SV954: $i] :
( ( ( c_lessequals @ SV954 @ SV2318 @ SV93 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV1741 @ SV93 ) )
= $true )
| ( ( c_lessequals @ SV954 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV1741 ) @ SV2318 ) @ SV93 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV93 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8054]) ).
thf(8167,plain,
! [SV2319: $i,SV94: $i,SV1742: $i,SV955: $i] :
( ( ( c_lessequals @ SV955 @ SV1742 @ SV94 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV2319 @ SV94 ) )
= $true )
| ( ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV1742 ) @ SV2319 ) @ SV94 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV94 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8055]) ).
thf(8168,plain,
! [SV2625: $i,SV2331: $i,SV1765: $i,SV2854: $i,SV2824: $i,SV2781: $i,SV989: $i,SV128: $i,SV2727: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2727 @ SV128 @ SV989 @ SV2781 @ SV2824 @ SV2854 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV128 @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2331 ) ) @ ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ SV2625 ) )
= ( hAPP @ ( hAPP @ SV989 @ SV1765 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV2331 ) @ SV2625 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8064]) ).
thf(8169,plain,
! [SV1815: $i,SV192: $i,SV2360: $i,SV1052: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1052 @ SV2360 @ SV192 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV1815 @ SV192 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1052 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV1815 ) @ SV2360 ) @ SV192 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV192 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8070]) ).
thf(8170,plain,
! [SV1849: $i,SV2378: $i,SV1092: $i,SV235: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV235 ) @ SV1092 @ SV235 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SV2378 @ SV235 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1849 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1092 @ SV1849 @ SV235 ) @ ( c_Power_Opower__class_Opower @ SV2378 @ SV1849 @ SV235 ) @ SV235 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8078]) ).
thf(8171,plain,
! [SV2640: $i,SV1910: $i,SV320: $i,SV2407: $i,SV1174: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1174 @ SV2407 @ SV320 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1910 @ SV2640 @ SV320 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV1174 ) @ SV1910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ SV2407 ) @ SV2640 ) @ SV320 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8079]) ).
thf(8172,plain,
! [SV2641: $i,SV2416: $i,SV1936: $i,SV2855: $i,SV2825: $i,SV2782: $i,SV352: $i,SV1206: $i,SV2733: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2733 @ SV1206 @ SV352 @ SV2782 @ SV2825 @ SV2855 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV352 @ ( hAPP @ ( hAPP @ SV1206 @ SV1936 ) @ SV2416 ) ) @ SV2641 )
= ( hAPP @ ( hAPP @ SV1206 @ ( hAPP @ ( hAPP @ SV352 @ SV1936 ) @ SV2641 ) ) @ ( hAPP @ ( hAPP @ SV352 @ SV2416 ) @ SV2641 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8080]) ).
thf(8173,plain,
! [SV2642: $i,SV2417: $i,SV1207: $i,SV2856: $i,SV2826: $i,SV2783: $i,SV2734: $i,SV353: $i,SV1937: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1937 @ SV353 @ SV2734 @ SV2783 @ SV2826 @ SV2856 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ ( hAPP @ ( hAPP @ SV1937 @ SV2417 ) @ SV2642 ) )
= ( hAPP @ ( hAPP @ SV1937 @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2417 ) ) @ ( hAPP @ ( hAPP @ SV353 @ SV1207 ) @ SV2642 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8081]) ).
thf(8174,plain,
! [SV2419: $i,SV1939: $i,SV1209: $i,SV2857: $i,SV2828: $i,SV2785: $i,SV2736: $i,SV355: $i,SV2644: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2644 @ SV355 @ SV2736 @ SV2785 @ SV2828 @ SV2857 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ ( hAPP @ ( hAPP @ SV355 @ SV1939 ) @ SV2419 ) )
= ( hAPP @ ( hAPP @ SV355 @ ( hAPP @ ( hAPP @ SV355 @ SV1209 ) @ SV1939 ) ) @ SV2419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8083]) ).
thf(8175,plain,
! [SV2423: $i,SV1943: $i,SV1213: $i,SV2858: $i,SV2830: $i,SV2789: $i,SV2740: $i,SV2648: $i,SV359: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV359 @ SV2648 @ SV2740 @ SV2789 @ SV2830 @ SV2858 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ ( hAPP @ ( hAPP @ SV359 @ SV1943 ) @ SV2423 ) )
= ( hAPP @ ( hAPP @ SV359 @ ( hAPP @ ( hAPP @ SV359 @ SV1213 ) @ SV1943 ) ) @ SV2423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8085]) ).
thf(8176,plain,
! [SV2425: $i,SV1945: $i,SV1215: $i,SV2859: $i,SV2831: $i,SV2791: $i,SV2742: $i,SV2650: $i,SV361: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV361 @ SV2650 @ SV2742 @ SV2791 @ SV2831 @ SV2859 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ ( hAPP @ ( hAPP @ SV361 @ SV1945 ) @ SV2425 ) )
= ( hAPP @ ( hAPP @ SV361 @ ( hAPP @ ( hAPP @ SV361 @ SV1215 ) @ SV1945 ) ) @ SV2425 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8086]) ).
thf(8177,plain,
! [SV2427: $i,SV1947: $i,SV1217: $i,SV2860: $i,SV2833: $i,SV2793: $i,SV2744: $i,SV2652: $i,SV363: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV363 @ SV2652 @ SV2744 @ SV2793 @ SV2833 @ SV2860 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV1947 ) ) @ SV2427 )
= ( hAPP @ ( hAPP @ SV363 @ ( hAPP @ ( hAPP @ SV363 @ SV1217 ) @ SV2427 ) ) @ SV1947 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8088]) ).
thf(8178,plain,
! [SV2428: $i,SV1948: $i,SV1218: $i,SV2861: $i,SV2834: $i,SV2794: $i,SV2745: $i,SV2653: $i,SV364: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV364 @ SV2653 @ SV2745 @ SV2794 @ SV2834 @ SV2861 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ SV2428 ) )
= ( hAPP @ ( hAPP @ SV364 @ SV1948 ) @ ( hAPP @ ( hAPP @ SV364 @ SV1218 ) @ SV2428 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8089]) ).
thf(8179,plain,
! [SV2429: $i,SV1949: $i,SV1219: $i,SV2862: $i,SV2835: $i,SV2795: $i,SV2746: $i,SV2654: $i,SV365: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV365 @ SV2654 @ SV2746 @ SV2795 @ SV2835 @ SV2862 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV365 @ ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ SV1949 ) ) @ SV2429 )
= ( hAPP @ ( hAPP @ SV365 @ SV1219 ) @ ( hAPP @ ( hAPP @ SV365 @ SV1949 ) @ SV2429 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8090]) ).
thf(8180,plain,
! [SV2873: $i,SV2863: $i,SV2836: $i,SV2796: $i,SV2747: $i,SV2655: $i,SV2430: $i,SV1950: $i,SV1220: $i,SV366: $i] :
( ( ( ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV1950 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV2430 ) @ SV2655 ) )
= ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV2430 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV1950 ) @ SV2655 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV366 @ SV2747 @ SV2796 @ SV2836 @ SV2863 @ SV2873 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8091]) ).
thf(8181,plain,
! [SV2431: $i,SV1951: $i,SV1221: $i,SV2864: $i,SV2837: $i,SV2797: $i,SV2748: $i,SV367: $i,SV2656: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2656 @ SV367 @ SV2748 @ SV2797 @ SV2837 @ SV2864 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ SV2431 ) )
= ( hAPP @ ( hAPP @ SV367 @ SV1951 ) @ ( hAPP @ ( hAPP @ SV367 @ SV1221 ) @ SV2431 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8092]) ).
thf(8182,plain,
! [SV2432: $i,SV1952: $i,SV1222: $i,SV2865: $i,SV2838: $i,SV2798: $i,SV2749: $i,SV368: $i,SV2657: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2657 @ SV368 @ SV2749 @ SV2798 @ SV2838 @ SV2865 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ ( hAPP @ ( hAPP @ SV368 @ SV1952 ) @ SV2432 ) )
= ( hAPP @ ( hAPP @ SV368 @ ( hAPP @ ( hAPP @ SV368 @ SV1222 ) @ SV1952 ) ) @ SV2432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8093]) ).
thf(8183,plain,
! [SV2433: $i,SV1953: $i,SV1223: $i,SV2866: $i,SV2839: $i,SV2799: $i,SV2750: $i,SV369: $i,SV2658: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2658 @ SV369 @ SV2750 @ SV2799 @ SV2839 @ SV2866 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV369 @ ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ SV1953 ) ) @ SV2433 )
= ( hAPP @ ( hAPP @ SV369 @ SV1223 ) @ ( hAPP @ ( hAPP @ SV369 @ SV1953 ) @ SV2433 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8094]) ).
thf(8184,plain,
! [SV2434: $i,SV1954: $i,SV1224: $i,SV2867: $i,SV2840: $i,SV2800: $i,SV2751: $i,SV370: $i,SV2659: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2659 @ SV370 @ SV2751 @ SV2800 @ SV2840 @ SV2867 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV1954 ) ) @ SV2434 )
= ( hAPP @ ( hAPP @ SV370 @ ( hAPP @ ( hAPP @ SV370 @ SV1224 ) @ SV2434 ) ) @ SV1954 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8095]) ).
thf(8185,plain,
! [SV2874: $i,SV2868: $i,SV2841: $i,SV2801: $i,SV2752: $i,SV2660: $i,SV2435: $i,SV1955: $i,SV1225: $i,SV371: $i] :
( ( ( ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ SV2660 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ SV2660 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2752 @ SV371 @ SV2801 @ SV2841 @ SV2868 @ SV2874 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8096]) ).
thf(8186,plain,
! [SV2875: $i,SV2869: $i,SV2842: $i,SV2802: $i,SV2753: $i,SV2661: $i,SV2436: $i,SV1956: $i,SV1226: $i,SV372: $i] :
( ( ( ( hAPP @ ( hAPP @ SV372 @ ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ SV1956 ) ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) )
= ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ ( hAPP @ ( hAPP @ SV372 @ SV1956 ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2753 @ SV372 @ SV2802 @ SV2842 @ SV2869 @ SV2875 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8097]) ).
thf(8187,plain,
! [SV2876: $i,SV2870: $i,SV2843: $i,SV2803: $i,SV2754: $i,SV2662: $i,SV2437: $i,SV1957: $i,SV1227: $i,SV373: $i] :
( ( ( ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV1957 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV2437 ) @ SV2662 ) )
= ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV2437 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV1957 ) @ SV2662 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV2754 @ SV373 @ SV2803 @ SV2843 @ SV2870 @ SV2876 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[8098]) ).
thf(8188,plain,
! [SV2667: $i,SV2442: $i,SV1962: $i,SV2871: $i,SV2844: $i,SV2808: $i,SV2759: $i,SV378: $i,SV1232: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1232 @ SV378 @ SV2759 @ SV2808 @ SV2844 @ SV2871 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV378 @ ( hAPP @ ( hAPP @ SV1232 @ SV1962 ) @ SV2442 ) ) @ SV2667 )
= ( hAPP @ ( hAPP @ SV1232 @ ( hAPP @ ( hAPP @ SV378 @ SV1962 ) @ SV2667 ) ) @ ( hAPP @ ( hAPP @ SV378 @ SV2442 ) @ SV2667 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8099]) ).
thf(8189,plain,
! [SV2674: $i,SV2449: $i,SV1969: $i,SV2872: $i,SV2848: $i,SV2815: $i,SV2766: $i,SV1239: $i,SV385: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV385 @ SV1239 @ SV2766 @ SV2815 @ SV2848 @ SV2872 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV385 @ ( hAPP @ ( hAPP @ SV1239 @ SV1969 ) @ SV2449 ) ) @ ( hAPP @ ( hAPP @ SV1239 @ SV2674 ) @ SV2449 ) )
= ( hAPP @ ( hAPP @ SV1239 @ ( hAPP @ ( hAPP @ SV385 @ SV1969 ) @ SV2674 ) ) @ SV2449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8103]) ).
thf(8190,plain,
! [SV2472: $i,SV2680: $i,SV2015: $i,SV1295: $i,SV447: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2015 @ SV2680 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SV2472 @ SV447 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SV2472 @ SV2680 @ SV447 ) @ SV447 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8109]) ).
thf(8191,plain,
! [SV2473: $i,SV2681: $i,SV2016: $i,SV1296: $i,SV448: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2016 @ SV2681 @ SV448 )
| ~ ( c_lessequals @ SV1296 @ SV2473 @ SV448 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SV2473 @ SV2681 @ SV448 ) @ SV448 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8110]) ).
thf(8192,plain,
! [SV1372: $i,SV2682: $i,SV2078: $i,SV2506: $i,SV529: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2506 @ SV529 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2078 @ SV2682 @ SV529 )
| ~ ( c_lessequals @ SV1372 @ SV2506 @ SV529 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SV2506 @ SV2682 @ SV529 ) @ SV529 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8134]) ).
thf(8193,plain,
! [SV2507: $i,SV2683: $i,SV2079: $i,SV1373: $i,SV530: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2079 @ SV2683 @ SV530 )
| ~ ( c_lessequals @ SV1373 @ SV2507 @ SV530 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SV2507 @ SV2683 @ SV530 ) @ SV530 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV530 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8135]) ).
thf(8194,plain,
! [SV2685: $i,SV2092: $i,SV550: $i,SV2513: $i,SV1391: $i] :
( ( ( c_lessequals @ SV1391 @ SV2513 @ SV550 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2092 @ SV2685 @ SV550 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV1391 ) @ SV2092 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV550 ) @ SV2513 ) @ SV2685 ) @ SV550 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV550 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8136]) ).
thf(8195,plain,
! [SV2686: $i,SV2093: $i,SV551: $i,SV2514: $i,SV1392: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1392 @ SV2514 @ SV551 )
= $false )
| ( ( c_lessequals @ SV2093 @ SV2686 @ SV551 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV1392 ) @ SV2093 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV551 ) @ SV2514 ) @ SV2686 ) @ SV551 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV551 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8137]) ).
thf(8196,plain,
! [SV2517: $i,SV2687: $i,SV2097: $i,SV588: $i,SV1427: $i] :
( ( ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2687 ) @ SV588 )
= $false )
| ( ( c_lessequals @ SV2687 @ SV2517 @ SV588 )
= $false )
| ( ( c_lessequals @ SV1427 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV588 ) @ SV2097 ) @ SV2517 ) @ SV588 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV588 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8140]) ).
thf(8197,plain,
! [SV2518: $i,SV2688: $i,SV2101: $i,SV1433: $i,SV594: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2101 @ SV2688 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SV2518 @ SV594 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SV2518 @ SV2688 @ SV594 ) @ SV594 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8141]) ).
thf(8198,plain,
! [SV1540: $i,SV723: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV723 ) @ SV1540 @ SV723 )
= ( c_HOL_Ozero__class_Ozero @ SV723 ) )
= $true )
| ( ( SV1540
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV723 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV723 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV723 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV723 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8142]) ).
thf(8199,plain,
! [SV1553: $i,SV2188: $i,SV737: $i,SV2564: $i,SV2702: $i] :
( ( ( c_lessequals @ SV2702 @ SV2564 @ SV737 )
= $false )
| ( ( c_lessequals @ SV2188 @ SV1553 @ SV737 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1553 @ SV2188 @ SV737 )
= ( c_HOL_Ominus__class_Ominus @ SV2564 @ SV2702 @ SV737 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV737 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8144]) ).
thf(8200,plain,
! [SV2706: $i,SV2574: $i,SV760: $i,SV2205: $i,SV1576: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1576 @ SV2205 @ SV760 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2574 @ SV2706 @ SV760 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1576 @ SV2205 @ SV760 )
= ( c_HOL_Ominus__class_Ominus @ SV2574 @ SV2706 @ SV760 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV760 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8146]) ).
thf(8201,plain,
! [SV1579: $i,SV2575: $i,SV763: $i,SV2208: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2208 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV2575 @ SV763 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 ) )
= $true )
| ( ( SV1579 = SV2575 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1579 @ SV2208 @ SV763 )
= ( c_Power_Opower__class_Opower @ SV2575 @ SV2208 @ SV763 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV763 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8147]) ).
thf(8202,plain,
! [SV2707: $i,SV2578: $i,SV2215: $i,SV1589: $i,SV774: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2578 @ SV774 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2707 @ SV774 ) ) )
= $false )
| ( ( ( SV2578 = SV2707 )
| ( SV2215
= ( c_HOL_Ozero__class_Ozero @ SV774 ) ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV774 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV774 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8148]) ).
thf(8203,plain,
! [SV2217: $i,SV1592: $i,SV778: $i,SV2709: $i,SV2580: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2580 @ SV2709 @ SV778 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1592 @ SV2217 @ SV778 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1592 @ SV2217 @ SV778 )
= ( c_HOL_Ominus__class_Ominus @ SV2580 @ SV2709 @ SV778 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV778 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8149]) ).
thf(8204,plain,
! [SV2711: $i,SV2584: $i,SV2224: $i,SV1600: $i,SV787: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2224 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2711 @ SV787 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2711 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2224 @ SV787 ) ) )
= $false )
| ( ( ( SV2224 = SV2711 )
| ( SV1600 = SV2584 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV787 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV787 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8150]) ).
thf(8205,plain,
! [SV2585: $i,SV2712: $i,SV789: $i,SV1602: $i,SV2225: $i] :
( ( ( c_lessequals @ SV2225 @ SV1602 @ SV789 )
= $false )
| ( ( c_lessequals @ SV2712 @ SV2585 @ SV789 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1602 @ SV2225 @ SV789 )
= ( c_HOL_Ominus__class_Ominus @ SV2585 @ SV2712 @ SV789 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV789 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8151]) ).
thf(8206,plain,
! [SV792: $i,SV1605: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1605 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV792 )
= ( c_HOL_Ozero__class_Ozero @ SV792 ) )
= $false )
| ( ( class_Power_Opower @ SV792 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV792 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV792 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV792 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8152]) ).
thf(8207,plain,
! [SV2227: $i,SV1606: $i,SV793: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV1606 @ SV793 )
= $false )
| ( ( SV1606
= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV793 ) @ SV2227 @ SV793 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV793 ) @ SV1606 ) @ SV2227 )
= ( c_HOL_Ozero__class_Ozero @ SV793 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV793 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8153]) ).
thf(8208,plain,
! [SV2715: $i,SV2592: $i,SV2239: $i,SV1619: $i,SV806: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2239 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2715 @ SV806 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2715 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2239 @ SV806 ) ) )
= $false )
| ( ( ( SV2239 = SV2715 )
| ( SV1619 = SV2592 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV806 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV806 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8154]) ).
thf(8209,plain,
! [SV2252: $i,SV1636: $i,SV2599: $i,SV823: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV2599 @ SV823 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV1636 @ SV823 ) )
= $true )
| ( ( SV1636 = SV2599 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1636 @ ( c_Suc @ SV2252 ) @ SV823 )
= ( c_Power_Opower__class_Opower @ SV2599 @ ( c_Suc @ SV2252 ) @ SV823 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV823 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8156]) ).
thf(8210,plain,
! [SV838: $i,SV2821: $i,SV2264: $i,SV2718: $i,SV1650: $i,SV2603: $i,SV2778: $i] :
( ( ( ~ ( c_Type_Otyping @ SV2778 @ SV2603 @ SV1650 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV2603 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2778 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SV2821 )
| ~ ( c_InductTermi_OIT @ SV2264 ) )
= $true )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8158]) ).
thf(8211,plain,
! [SV2265: $i,SV1651: $i,SV839: $i] :
( ( ( class_Power_Opower @ SV839 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1651 @ SV2265 @ SV839 )
!= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
| ( SV1651
= ( c_HOL_Ozero__class_Ozero @ SV839 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV839 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV839 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV839 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8159]) ).
thf(8212,plain,
! [SV2276: $i,SV1666: $i,SV855: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV1666 @ SV855 )
= $false )
| ( ( SV2276
= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV855 ) @ SV2276 @ SV855 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV855 ) @ SV1666 ) @ SV2276 )
= ( c_HOL_Ozero__class_Ozero @ SV855 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV855 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8160]) ).
thf(8213,plain,
! [SV1673: $i,SV2822: $i,SV2282: $i,SV2721: $i,SV863: $i,SV2609: $i,SV2779: $i] :
( ( ( ~ ( c_Type_Otyping @ SV2779 @ SV2609 @ SV863 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV2609 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2779 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SV2822 )
| ~ ( c_InductTermi_OIT @ SV2282 ) )
= $true )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8161]) ).
thf(8214,plain,
! [SV873: $i,SV2615: $i,SV1680: $i,SV2289: $i,SV9: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV2289 @ SV9 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1680 @ SV2615 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV873 @ SV2289 @ SV9 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV2289 @ SV2615 @ SV9 ) @ SV9 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8162]) ).
thf(8215,plain,
! [SV2296: $i,SV886: $i,SV1691: $i,SV22: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV1691 @ SV22 )
= $false )
| ( ( c_lessequals @ SV886 @ SV2296 @ SV22 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV886 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1691 ) @ SV2296 ) @ SV22 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV22 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8163]) ).
thf(8216,plain,
! [SV2318: $i,SV954: $i,SV1741: $i,SV93: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV1741 @ SV93 )
= $false )
| ( ( c_lessequals @ SV954 @ SV2318 @ SV93 )
= $false )
| ( ( c_lessequals @ SV954 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV1741 ) @ SV2318 ) @ SV93 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV93 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8166]) ).
thf(8217,plain,
! [SV1742: $i,SV955: $i,SV2319: $i,SV94: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV2319 @ SV94 )
= $false )
| ( ( c_lessequals @ SV955 @ SV1742 @ SV94 )
= $false )
| ( ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV1742 ) @ SV2319 ) @ SV94 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV94 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8167]) ).
thf(8218,plain,
! [SV2360: $i,SV1052: $i,SV1815: $i,SV192: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV1815 @ SV192 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1052 @ SV2360 @ SV192 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1052 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV192 ) @ SV1815 ) @ SV2360 ) @ SV192 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV192 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8169]) ).
thf(8219,plain,
! [SV1849: $i,SV235: $i,SV2378: $i,SV1092: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1092 @ SV2378 @ SV235 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV235 ) @ SV1092 @ SV235 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1849 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1092 @ SV1849 @ SV235 ) @ ( c_Power_Opower__class_Opower @ SV2378 @ SV1849 @ SV235 ) @ SV235 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8170]) ).
thf(8220,plain,
! [SV2655: $i,SV2430: $i,SV1950: $i,SV1220: $i,SV2873: $i,SV2863: $i,SV2836: $i,SV2796: $i,SV2747: $i,SV366: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV366 @ SV2747 @ SV2796 @ SV2836 @ SV2863 @ SV2873 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV1950 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV2430 ) @ SV2655 ) )
= ( hAPP @ ( hAPP @ SV366 @ ( hAPP @ ( hAPP @ SV366 @ SV1220 ) @ SV2430 ) ) @ ( hAPP @ ( hAPP @ SV366 @ SV1950 ) @ SV2655 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8180]) ).
thf(8221,plain,
! [SV2660: $i,SV2435: $i,SV1955: $i,SV1225: $i,SV2874: $i,SV2868: $i,SV2841: $i,SV2801: $i,SV371: $i,SV2752: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2752 @ SV371 @ SV2801 @ SV2841 @ SV2868 @ SV2874 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ SV2660 ) )
= ( hAPP @ ( hAPP @ SV371 @ SV2435 ) @ ( hAPP @ ( hAPP @ SV371 @ ( hAPP @ ( hAPP @ SV371 @ SV1225 ) @ SV1955 ) ) @ SV2660 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8185]) ).
thf(8222,plain,
! [SV2661: $i,SV2436: $i,SV1956: $i,SV1226: $i,SV2875: $i,SV2869: $i,SV2842: $i,SV2802: $i,SV372: $i,SV2753: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2753 @ SV372 @ SV2802 @ SV2842 @ SV2869 @ SV2875 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV372 @ ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ SV1956 ) ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) )
= ( hAPP @ ( hAPP @ SV372 @ SV1226 ) @ ( hAPP @ ( hAPP @ SV372 @ SV1956 ) @ ( hAPP @ ( hAPP @ SV372 @ SV2436 ) @ SV2661 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8186]) ).
thf(8223,plain,
! [SV2662: $i,SV2437: $i,SV1957: $i,SV1227: $i,SV2876: $i,SV2870: $i,SV2843: $i,SV2803: $i,SV373: $i,SV2754: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV2754 @ SV373 @ SV2803 @ SV2843 @ SV2870 @ SV2876 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV1957 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV2437 ) @ SV2662 ) )
= ( hAPP @ ( hAPP @ SV373 @ ( hAPP @ ( hAPP @ SV373 @ SV1227 ) @ SV2437 ) ) @ ( hAPP @ ( hAPP @ SV373 @ SV1957 ) @ SV2662 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[8187]) ).
thf(8224,plain,
! [SV2472: $i,SV2680: $i,SV2015: $i,SV1295: $i,SV447: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
= $false )
| ( ( ~ ( c_lessequals @ SV2015 @ SV2680 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SV2472 @ SV447 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SV2472 @ SV2680 @ SV447 ) @ SV447 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8190]) ).
thf(8225,plain,
! [SV2473: $i,SV2681: $i,SV2016: $i,SV1296: $i,SV448: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2016 @ SV2681 @ SV448 )
| ~ ( c_lessequals @ SV1296 @ SV2473 @ SV448 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SV2473 @ SV2681 @ SV448 ) @ SV448 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8191]) ).
thf(8226,plain,
! [SV1372: $i,SV2682: $i,SV2078: $i,SV2506: $i,SV529: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2506 @ SV529 )
= $false )
| ( ( ~ ( c_lessequals @ SV2078 @ SV2682 @ SV529 )
| ~ ( c_lessequals @ SV1372 @ SV2506 @ SV529 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SV2506 @ SV2682 @ SV529 ) @ SV529 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8192]) ).
thf(8227,plain,
! [SV2507: $i,SV2683: $i,SV2079: $i,SV1373: $i,SV530: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
= $false )
| ( ( ~ ( c_lessequals @ SV2079 @ SV2683 @ SV530 )
| ~ ( c_lessequals @ SV1373 @ SV2507 @ SV530 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SV2507 @ SV2683 @ SV530 ) @ SV530 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8193]) ).
thf(8228,plain,
! [SV2518: $i,SV2688: $i,SV2101: $i,SV1433: $i,SV594: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2101 @ SV2688 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SV2518 @ SV594 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SV2518 @ SV2688 @ SV594 ) @ SV594 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8197]) ).
thf(8229,plain,
! [SV2208: $i,SV1579: $i,SV2575: $i,SV763: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV2575 @ SV763 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2208 @ tc_nat )
= $false )
| ( ( SV1579 = SV2575 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1579 @ SV2208 @ SV763 )
= ( c_Power_Opower__class_Opower @ SV2575 @ SV2208 @ SV763 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV763 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8201]) ).
thf(8230,plain,
! [SV1589: $i,SV774: $i,SV2215: $i,SV2707: $i,SV2578: $i] :
( ( ( SV2578 = SV2707 )
= $true )
| ( ( SV2215
= ( c_HOL_Ozero__class_Ozero @ SV774 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2578 @ SV774 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV774 ) @ SV1589 ) @ ( c_HOL_Otimes__class_Otimes @ SV2215 @ SV2707 @ SV774 ) ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV774 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV774 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8202]) ).
thf(8231,plain,
! [SV787: $i,SV2584: $i,SV1600: $i,SV2711: $i,SV2224: $i] :
( ( ( SV2224 = SV2711 )
= $true )
| ( ( SV1600 = SV2584 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2224 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2711 @ SV787 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV787 ) @ ( c_HOL_Otimes__class_Otimes @ SV1600 @ SV2711 @ SV787 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2584 @ SV2224 @ SV787 ) ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV787 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV787 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8204]) ).
thf(8232,plain,
! [SV806: $i,SV2592: $i,SV1619: $i,SV2715: $i,SV2239: $i] :
( ( ( SV2239 = SV2715 )
= $true )
| ( ( SV1619 = SV2592 )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2239 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2715 @ SV806 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV806 ) @ ( c_HOL_Otimes__class_Otimes @ SV1619 @ SV2715 @ SV806 ) ) @ ( c_HOL_Otimes__class_Otimes @ SV2592 @ SV2239 @ SV806 ) ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV806 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV806 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8208]) ).
thf(8233,plain,
! [SV2252: $i,SV2599: $i,SV1636: $i,SV823: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV1636 @ SV823 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV823 ) @ SV2599 @ SV823 )
= $false )
| ( ( SV1636 = SV2599 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1636 @ ( c_Suc @ SV2252 ) @ SV823 )
= ( c_Power_Opower__class_Opower @ SV2599 @ ( c_Suc @ SV2252 ) @ SV823 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV823 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8209]) ).
thf(8234,plain,
! [SV838: $i,SV2821: $i,SV2264: $i,SV2718: $i,SV1650: $i,SV2603: $i,SV2778: $i] :
( ( ( c_Type_Otyping @ SV2778 @ SV2603 @ SV1650 )
= $false )
| ( ( ~ ( c_InductTermi_OIT @ SV2603 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2778 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SV2821 )
| ~ ( c_InductTermi_OIT @ SV2264 ) )
= $true )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8210]) ).
thf(8235,plain,
! [SV839: $i,SV2265: $i,SV1651: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1651 @ SV2265 @ SV839 )
!= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
= $true )
| ( ( SV1651
= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
= $true )
| ( ( class_Power_Opower @ SV839 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV839 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV839 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV839 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8211]) ).
thf(8236,plain,
! [SV1673: $i,SV2822: $i,SV2282: $i,SV2721: $i,SV863: $i,SV2609: $i,SV2779: $i] :
( ( ( c_Type_Otyping @ SV2779 @ SV2609 @ SV863 )
= $false )
| ( ( ~ ( c_InductTermi_OIT @ SV2609 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2779 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SV2822 )
| ~ ( c_InductTermi_OIT @ SV2282 ) )
= $true )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8213]) ).
thf(8237,plain,
! [SV2289: $i,SV873: $i,SV9: $i,SV2615: $i,SV1680: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1680 @ SV2615 @ SV9 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV873 @ SV2289 @ SV9 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV2289 @ SV9 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV2289 @ SV2615 @ SV9 ) @ SV9 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8214]) ).
thf(8238,plain,
! [SV2472: $i,SV1295: $i,SV447: $i,SV2680: $i,SV2015: $i] :
( ( ( ~ ( c_lessequals @ SV2015 @ SV2680 @ SV447 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SV2472 @ SV447 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SV2472 @ SV2680 @ SV447 ) @ SV447 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8224]) ).
thf(8239,plain,
! [SV2473: $i,SV1296: $i,SV448: $i,SV2681: $i,SV2016: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2016 @ SV2681 @ SV448 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1296 @ SV2473 @ SV448 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SV2473 @ SV2681 @ SV448 ) @ SV448 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8225]) ).
thf(8240,plain,
! [SV2506: $i,SV1372: $i,SV529: $i,SV2682: $i,SV2078: $i] :
( ( ( ~ ( c_lessequals @ SV2078 @ SV2682 @ SV529 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1372 @ SV2506 @ SV529 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2506 @ SV529 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SV2506 @ SV2682 @ SV529 ) @ SV529 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8226]) ).
thf(8241,plain,
! [SV2507: $i,SV1373: $i,SV530: $i,SV2683: $i,SV2079: $i] :
( ( ( ~ ( c_lessequals @ SV2079 @ SV2683 @ SV530 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1373 @ SV2507 @ SV530 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SV2507 @ SV2683 @ SV530 ) @ SV530 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV530 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8227]) ).
thf(8242,plain,
! [SV2518: $i,SV1433: $i,SV594: $i,SV2688: $i,SV2101: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2101 @ SV2688 @ SV594 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SV2518 @ SV594 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SV2518 @ SV2688 @ SV594 ) @ SV594 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8228]) ).
thf(8243,plain,
! [SV2208: $i,SV1579: $i,SV2575: $i,SV763: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV2575 @ SV763 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2208 @ tc_nat )
= $false )
| ( ( SV1579 = SV2575 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1579 @ SV2208 @ SV763 )
= ( c_Power_Opower__class_Opower @ SV2575 @ SV2208 @ SV763 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV763 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8229]) ).
thf(8244,plain,
! [SV838: $i,SV2821: $i,SV2264: $i,SV1650: $i,SV2718: $i,SV2778: $i,SV2603: $i] :
( ( ( ~ ( c_InductTermi_OIT @ SV2603 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2778 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SV2821 )
| ~ ( c_InductTermi_OIT @ SV2264 ) )
= $true )
| ( ( c_Type_Otyping @ SV2778 @ SV2603 @ SV1650 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8234]) ).
thf(8245,plain,
! [SV839: $i,SV2265: $i,SV1651: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1651 @ SV2265 @ SV839 )
= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
= $false )
| ( ( SV1651
= ( c_HOL_Ozero__class_Ozero @ SV839 ) )
= $true )
| ( ( class_Power_Opower @ SV839 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV839 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV839 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV839 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8235]) ).
thf(8246,plain,
! [SV1673: $i,SV2822: $i,SV2282: $i,SV863: $i,SV2721: $i,SV2779: $i,SV2609: $i] :
( ( ( ~ ( c_InductTermi_OIT @ SV2609 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2779 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SV2822 )
| ~ ( c_InductTermi_OIT @ SV2282 ) )
= $true )
| ( ( c_Type_Otyping @ SV2779 @ SV2609 @ SV863 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8236]) ).
thf(8247,plain,
! [SV2289: $i,SV873: $i,SV9: $i,SV2615: $i,SV1680: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1680 @ SV2615 @ SV9 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV873 @ SV2289 @ SV9 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV2289 @ SV9 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV2289 @ SV2615 @ SV9 ) @ SV9 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8237]) ).
thf(8248,plain,
! [SV2472: $i,SV1295: $i,SV447: $i,SV2680: $i,SV2015: $i] :
( ( ( c_lessequals @ SV2015 @ SV2680 @ SV447 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1295 @ SV2472 @ SV447 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SV2472 @ SV2680 @ SV447 ) @ SV447 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8238]) ).
thf(8249,plain,
! [SV2473: $i,SV1296: $i,SV448: $i,SV2681: $i,SV2016: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2016 @ SV2681 @ SV448 )
= $false )
| ( ( ~ ( c_lessequals @ SV1296 @ SV2473 @ SV448 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SV2473 @ SV2681 @ SV448 ) @ SV448 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8239]) ).
thf(8250,plain,
! [SV2506: $i,SV1372: $i,SV529: $i,SV2682: $i,SV2078: $i] :
( ( ( c_lessequals @ SV2078 @ SV2682 @ SV529 )
= $false )
| ( ( ~ ( c_lessequals @ SV1372 @ SV2506 @ SV529 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2506 @ SV529 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SV2506 @ SV2682 @ SV529 ) @ SV529 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8240]) ).
thf(8251,plain,
! [SV2507: $i,SV1373: $i,SV530: $i,SV2683: $i,SV2079: $i] :
( ( ( c_lessequals @ SV2079 @ SV2683 @ SV530 )
= $false )
| ( ( ~ ( c_lessequals @ SV1373 @ SV2507 @ SV530 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SV2507 @ SV2683 @ SV530 ) @ SV530 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8241]) ).
thf(8252,plain,
! [SV2518: $i,SV1433: $i,SV594: $i,SV2688: $i,SV2101: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2101 @ SV2688 @ SV594 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1433 @ SV2518 @ SV594 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SV2518 @ SV2688 @ SV594 ) @ SV594 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8242]) ).
thf(8253,plain,
! [SV2208: $i,SV2575: $i,SV1579: $i,SV763: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV1579 @ SV763 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV763 ) @ SV2575 @ SV763 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2208 @ tc_nat )
= $false )
| ( ( SV1579 = SV2575 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1579 @ SV2208 @ SV763 )
= ( c_Power_Opower__class_Opower @ SV2575 @ SV2208 @ SV763 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV763 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8243]) ).
thf(8254,plain,
! [SV838: $i,SV2821: $i,SV2264: $i,SV1650: $i,SV2718: $i,SV2778: $i,SV2603: $i] :
( ( ( c_InductTermi_OIT @ SV2603 )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2778 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SV2821 )
| ~ ( c_InductTermi_OIT @ SV2264 ) )
= $true )
| ( ( c_Type_Otyping @ SV2778 @ SV2603 @ SV1650 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8244]) ).
thf(8255,plain,
! [SV1673: $i,SV2822: $i,SV2282: $i,SV863: $i,SV2721: $i,SV2779: $i,SV2609: $i] :
( ( ( c_InductTermi_OIT @ SV2609 )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2779 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SV2822 )
| ~ ( c_InductTermi_OIT @ SV2282 ) )
= $true )
| ( ( c_Type_Otyping @ SV2779 @ SV2609 @ SV863 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8246]) ).
thf(8256,plain,
! [SV2615: $i,SV1680: $i,SV9: $i,SV2289: $i,SV873: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV873 @ SV2289 @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1680 @ SV2615 @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV2289 @ SV9 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV1680 @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV873 @ SV1680 @ SV9 ) @ ( c_HOL_Otimes__class_Otimes @ SV2289 @ SV2615 @ SV9 ) @ SV9 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8247]) ).
thf(8257,plain,
! [SV2680: $i,SV2015: $i,SV447: $i,SV2472: $i,SV1295: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1295 @ SV2472 @ SV447 )
= $false )
| ( ( c_lessequals @ SV2015 @ SV2680 @ SV447 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1295 @ SV447 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV2015 @ SV447 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1295 @ SV2015 @ SV447 ) @ ( c_HOL_Otimes__class_Otimes @ SV2472 @ SV2680 @ SV447 ) @ SV447 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8248]) ).
thf(8258,plain,
! [SV2681: $i,SV2016: $i,SV448: $i,SV2473: $i,SV1296: $i] :
( ( ( c_lessequals @ SV1296 @ SV2473 @ SV448 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2016 @ SV2681 @ SV448 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV1296 @ SV448 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV448 ) @ SV2016 @ SV448 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1296 @ SV2016 @ SV448 ) @ ( c_HOL_Otimes__class_Otimes @ SV2473 @ SV2681 @ SV448 ) @ SV448 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV448 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8249]) ).
thf(8259,plain,
! [SV2682: $i,SV2078: $i,SV529: $i,SV2506: $i,SV1372: $i] :
( ( ( c_lessequals @ SV1372 @ SV2506 @ SV529 )
= $false )
| ( ( c_lessequals @ SV2078 @ SV2682 @ SV529 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2506 @ SV529 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV529 ) @ SV2078 @ SV529 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1372 @ SV2078 @ SV529 ) @ ( c_HOL_Otimes__class_Otimes @ SV2506 @ SV2682 @ SV529 ) @ SV529 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8250]) ).
thf(8260,plain,
! [SV2683: $i,SV2079: $i,SV530: $i,SV2507: $i,SV1373: $i] :
( ( ( c_lessequals @ SV1373 @ SV2507 @ SV530 )
= $false )
| ( ( c_lessequals @ SV2079 @ SV2683 @ SV530 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV1373 @ SV530 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV530 ) @ SV2079 @ SV530 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1373 @ SV2079 @ SV530 ) @ ( c_HOL_Otimes__class_Otimes @ SV2507 @ SV2683 @ SV530 ) @ SV530 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8251]) ).
thf(8261,plain,
! [SV2688: $i,SV2101: $i,SV594: $i,SV2518: $i,SV1433: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1433 @ SV2518 @ SV594 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2101 @ SV2688 @ SV594 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV1433 @ SV594 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV594 ) @ SV2101 @ SV594 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1433 @ SV2101 @ SV594 ) @ ( c_HOL_Otimes__class_Otimes @ SV2518 @ SV2688 @ SV594 ) @ SV594 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV594 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8252]) ).
thf(8262,plain,
! [SV838: $i,SV2603: $i,SV2821: $i,SV2264: $i,SV1650: $i,SV2718: $i,SV2778: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2778 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SV2821 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV2264 ) )
= $true )
| ( ( c_InductTermi_OIT @ SV2603 )
= $false )
| ( ( c_Type_Otyping @ SV2778 @ SV2603 @ SV1650 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8254]) ).
thf(8263,plain,
! [SV1673: $i,SV2609: $i,SV2822: $i,SV2282: $i,SV863: $i,SV2721: $i,SV2779: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV2779 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SV2822 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV2282 ) )
= $true )
| ( ( c_InductTermi_OIT @ SV2609 )
= $false )
| ( ( c_Type_Otyping @ SV2779 @ SV2609 @ SV863 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[8255]) ).
thf(8264,plain,
! [SV838: $i,SV2603: $i,SV2821: $i,SV2264: $i,SV1650: $i,SV2718: $i,SV2778: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV2778 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SV2821 )
= $false )
| ( ( ~ ( c_InductTermi_OIT @ SV2264 ) )
= $true )
| ( ( c_InductTermi_OIT @ SV2603 )
= $false )
| ( ( c_Type_Otyping @ SV2778 @ SV2603 @ SV1650 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8262]) ).
thf(8265,plain,
! [SV1673: $i,SV2609: $i,SV2822: $i,SV2282: $i,SV863: $i,SV2721: $i,SV2779: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV2779 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SV2822 )
= $false )
| ( ( ~ ( c_InductTermi_OIT @ SV2282 ) )
= $true )
| ( ( c_InductTermi_OIT @ SV2609 )
= $false )
| ( ( c_Type_Otyping @ SV2779 @ SV2609 @ SV863 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8263]) ).
thf(8266,plain,
! [SV838: $i,SV2603: $i,SV2821: $i,SV1650: $i,SV2718: $i,SV2778: $i,SV2264: $i] :
( ( ( c_InductTermi_OIT @ SV2264 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV2778 @ SV2718 @ SV1650 @ tc_Type_Otype ) @ SV2264 @ SV2821 )
= $false )
| ( ( c_InductTermi_OIT @ SV2603 )
= $false )
| ( ( c_Type_Otyping @ SV2778 @ SV2603 @ SV1650 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2264 @ SV2603 @ SV2718 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV838 ) @ SV1650 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8264]) ).
thf(8267,plain,
! [SV1673: $i,SV2609: $i,SV2822: $i,SV863: $i,SV2721: $i,SV2779: $i,SV2282: $i] :
( ( ( c_InductTermi_OIT @ SV2282 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV2779 @ SV2721 @ SV863 @ tc_Type_Otype ) @ SV2282 @ SV2822 )
= $false )
| ( ( c_InductTermi_OIT @ SV2609 )
= $false )
| ( ( c_Type_Otyping @ SV2779 @ SV2609 @ SV863 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV2282 @ SV2609 @ SV2721 ) )
= $true )
| ( ( v_T____
= ( hAPP @ ( hAPP @ c_Type_Otype_OFun @ SV863 ) @ SV1673 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[8265]) ).
thf(8268,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1875,8267,8266,8261,8260,8259,8258,8257,8256,8253,8245,8233,8232,8231,8230,8223,8222,8221,8220,8219,8218,8217,8216,8215,8212,8207,8206,8205,8203,8200,8199,8198,8196,8195,8194,8189,8188,8184,8183,8182,8181,8179,8178,8177,8176,8175,8174,8173,8172,8171,8168,8165,8164,8157,8155,8145,8143,8139,8138,8133,8132,8131,8130,8129,8128,8127,8126,8125,8124,8123,8122,8121,8120,8119,8118,8117,8116,8115,8114,8113,8112,8111,8108,8107,8106,8105,8104,8102,8101,8100,8087,8084,8082,8077,8076,8075,8074,8073,8072,8071,8069,8068,8067,8066,8065,8063,8062,8061,8060,8059,8058,8057,8056,8052,8051,8050,8049,8048,8046,8044,8043,8042,8041,8033,8030,8029,8028,8021,8017,8014,8012,8011,8010,8009,8008,8007,8006,8005,8004,8003,8002,8001,7999,7977,7967,7966,7965,7964,7963,7955,7954,7953,7952,7948,7947,7946,7943,7942,7941,7940,7926,7923,7922,7917,7916,7915,7914,7913,7912,7911,7910,7909,7907,7906,7905,7904,7903,7902,7901,7900,7899,7898,7897,7896,7895,7893,7885,7884,7881,7880,7879,7878,7877,7871,7854,7845,7844,7843,7842,7840,7836,7833,7832,7828,7826,7821,7815,7813,7811,7803,7801,7800,7799,7798,7791,7790,7789,7788,7787,7786,7785,7784,7772,7771,7770,7769,7766,7747,7746,7745,7744,7743,7742,7730,7729,7728,7727,7719,7718,7717,7716,7715,7714,7666,7665,7664,7663,7662,7655,7646,7645,7644,7643,7642,7641,7640,7639,7638,7637,7634,7633,7632,7631,7630,7629,7618,7617,7616,7605,7604,7603,7602,7601,7600,7599,7598,7581,7576,7575,7574,7562,7560,7558,7556,7555,7554,7550,7547,7546,7543,7539,7535,7532,7526,7525,7524,7522,7515,7511,7509,7506,7503,7502,7501,7474,7448,7447,7446,7445,7444,7443,7442,7425,7401,7400,7399,7398,7397,7392,7350,7347,7342,7341,7338,7337,7336,7335,7332,7329,7328,7325,7324,7323,7315,7313,7302,7301,7298,7285,7284,7283,7282,7274,7273,7272,7247,7236,7235,7233,7232,7228,7225,7224,7220,7219,7218,7215,7214,7209,7198,7197,7188,7183,7181,7178,7176,7173,7159,7152,7146,7143,7142,7141,7139,7135,7130,7128,7126,7125,7122,7119,7116,7113,7112,7111,7110,7109,7108,7107,7106,7105,7090,7089,7088,7087,7086,7085,7084,7079,7072,7071,7070,7069,7066,7061,7060,7059,7055,7029,7016,7015,7011,7010,7009,6999,6998,6977,6975,6974,6973,6972,6937,6908,6907,6892,6878,6877,6865,6854,6849,6848,6846,6844,6841,6840,6839,6836,6835,6834,6833,6832,6831,6830,6829,6827,6822,6821,6820,6819,6818,6804,6802,6796,6794,6789,6788,6785,6784,6776,6775,6772,6765,6764,6761,6760,6756,6750,6744,6742,6732,6727,6726,6723,6722,6720,6716,6715,6713,6710,6709,6703,6702,6700,6692,6690,6676,6670,6666,6664,6657,6656,6655,6653,6651,6650,6646,6644,6643,6639,6634,6627,6622,6621,6619,6618,6617,6615,6612,6611,6610,6609,6608,6607,6606,6579,6578,6577,6571,6566,6561,6560,6559,6558,6548,6542,6537,6510,6509,6501,6500,6499,6492,6491,6482,6481,6467,6466,6461,6459,6458,6457,6456,6451,6450,6449,6437,6432,6430,6429,6428,6427,6423,6422,6385,6383,6382,6381,6380,6379,6346,6344,6343,6342,6340,6339,6338,6334,6333,6332,6331,6330,6326,6317,6316,6307,6297,6278,6277,6276,6272,6271,6267,6261,6254,6253,6252,6251,6250,6249,6247,6223,6212,6209,6201,6200,6199,6198,6193,6192,6191,6190,6189,6181,6180,6165,6163,6160,6159,6158,6157,6154,6153,6152,6149,6148,6137,6129,6128,6116,6115,6110,6106,6103,6100,6087,6086,6085,6083,6070,6064,6050,6047,6043,6041,6032,6031,6030,6025,6016,6015,6009,5998,5997,5996,5995,5982,5981,5968,5967,5948,5947,5946,5945,5939,5938,5934,5916,5909,5904,5903,5902,5901,5900,5892,5887,5886,5885,5884,5883,5882,5881,5879,5878,5877,5876,5875,5874,5872,5871,5870,5869,5868,5867,5866,5862,5861,5860,5859,5858,5855,5847,5846,5845,5844,5837,5780,5779,5764,5762,5753,5752,5751,5735,5734,5727,5679,5678,5655,5654,5651,5646,5641,5638,5632,5631,5625,5605,5604,5585,5584,5579,5578,5576,5557,5544,5524,5523,5471,5461,5460,5459,5458,5450,5449,5429,5428,5427,5418,5417,5396,5332,5289,5248,5240,5239,5221,5214,5213,5211,5209,5205,5201,5200,5193,5162,5155,5149,5134,5120,5090,5076,5056,5035,5028,5027,4971,4956,4951,4910,4894,4848,4817,4816,4802,4795,4794,4776,4767,4747,4746,4661,4660,4647,4625,4622,4621,4593,4575,4562,4516,4508,4498,4466,4435,4426,4424,4423,4337,4331,4330,4329,4294,4293,4252,4250,4215,4158,4058,4057,4056,4055,4053,4047,4046,4044,4028,4017,4016,3988,3963,3956,3886,3874,3847,3846,3845,3844,3843,3835,3834,3833,3821,3818,3792,3767,3766,3632,3592,3591,3590,3589,3588,3586,3585,3583,3577,3576,3572,3571,3570,3569,3566,3565,3536,3477,3427,3422,3393,3391,3313,3312,3299,3297,3293,3114,3113,3024,2894,2762,2761,2760,2759,2758,2757,2756,2755,2754,2753,2752,2751,2750,2749,2748,2747,2746,2745,2744,2743,2742,2741,2740,2739,2738,2737,2736,2735,2734,2733,2732,2731,2730,2729,2728,2723,2719,2717,2716,2708,2707,2706,2678,2660,2656,2654,2538,2520,2180,2170,2063,2012,2007]) ).
thf(8269,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[8268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL795-1 : 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
% 0.09/0.17 % Computer : n005.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 12:34:14 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 248.70/50.10 .......
% 248.70/50.10
% 248.70/50.10 No.of.Axioms: 920
% 248.70/50.10
% 248.70/50.10 Length.of.Defs: 0
% 248.70/50.10
% 248.70/50.10 Contains.Choice.Funs: false
% 248.70/50.10 ...................................................................................................................................................................................................................................................................................................
% 248.70/50.10
% 248.70/50.10 ********************************
% 248.70/50.10 * All subproblems solved! *
% 248.70/50.10 ********************************
% 248.70/50.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:920,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:296,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:8268,loop_count:0,foatp_calls:1,translation:fof_full)
% 248.70/50.10
% 248.70/50.10 %**** Beginning of derivation protocol ****
% 248.70/50.10 % SZS output start CNFRefutation
% See solution above
% 248.70/50.16
% 248.70/50.16 %**** End of derivation protocol ****
% 248.70/50.16 %**** no. of clauses in derivation: 8269 ****
% 248.70/50.16 %**** clause counter: 8268 ****
% 248.70/50.16
% 248.70/50.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:920,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:296,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:8268,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------